4. The heat transfer rate through the floor slab is 8,189.5 Btu/hr.
5. The temperature of the external surface of the pipe is 271.97 °F.
6. The heat transfer rate from the heat exchanger into the room is 54,337.5 Btu/hr.
7. The three significant advantages of a counter-flow heat exchanger are higher heat transfer efficiency, reduced risk of mixing, and a more compact design.
8. The two major disadvantages of a parallel-flow heat exchanger are lower heat transfer efficiency and increased risk of mixing.
4. To calculate the heat transfer rate through the floor slab, we can use the formula:
Q = k * A * (ΔT / d)
where Q is the heat transfer rate, k is the thermal conductivity of concrete (0.85 Btu/hr-ft-°F), A is the area of the floor slab (75 ft * 85 ft), ΔT is the temperature difference between the floor surface and the soil beneath (70 °F - 40 °F), and d is the thickness of the floor slab (10 inches).
Substituting the values into the formula:
Q = 0.85 * (75 * 85) * ((70 - 40) / (10/12))
Q = 8,189.5 Btu/hr
Therefore, the heat transfer rate through the floor slab is 8,189.5 Btu/hr.
5. To determine the temperature of the external surface of the pipe, we can use the formula:
T_ext = T_inner - (Q / (2π * L * k * ln(r_outer / r_inner)))
where T_ext is the temperature of the external surface of the pipe, T_inner is the temperature of the inner surface of the pipe (300 °F), Q is the heat transfer rate (8.5x10^6 Btu/hr), L is the length of the pipe (55 ft), k is the thermal conductivity of Inconel steel (175 Btu/hr-ft-°F), r_outer is the outer radius of the pipe (1.05 ft/2), and r_inner is the inner radius of the pipe (0.5 ft/2).
Substituting the values into the formula:
T_ext = 300 - (8.5x10^6 / (2π * 55 * 175 * ln(1.05 / 0.5)))
T_ext = 271.97 °F
Therefore, the temperature of the external surface of the pipe is approximately 271.97 °F.
6. The heat transfer rate from the heat exchanger into the room can be calculated using the formula:
Q = U * A * ΔT
where Q is the heat transfer rate, U is the convective heat transfer coefficient (45 Btu/hr-ft^2-°F), A is the surface area of the heat exchanger (675 ft^2), and ΔT is the temperature difference between the outer surface of the heat exchanger (160 °F) and the room temperature (68 °F).
Substituting the values into the formula:
Q = 45 * 675 * (160 - 68)
Q = 54,337.5 Btu/hr
Therefore, the heat transfer rate from the heat exchanger into the room is 54,337.5 Btu/hr.
7. The three significant advantages of a counter-flow heat exchanger compared to a parallel-flow heat exchanger are:
- Higher heat transfer efficiency due to a greater temperature difference between the hot and cold fluids along the entire length of the heat exchanger.
- Reduced risk of mixing between the hot and cold fluids, resulting in better heat transfer performance.
- More compact design and smaller footprint, as the counter-flow configuration allows for a higher temperature driving force.
8. The two major disadvantages of a parallel-flow heat exchanger are:
- Lower heat transfer efficiency compared to a counter-flow heat exchanger due to a smaller temperature difference between the hot and cold fluids.
- Increased risk of mixing between the hot and cold fluids, leading to lower heat transfer performance and potentially reduced effectiveness of the heat exchanger.
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i.) Let us say that you keep a steak in the fridge at 38°F overnight. You take it out right before you throw it on a grill. The grill is at 550°F. Using your meat thermometer, you find that the aver
The average temperature rise of the steak from being in the fridge at 38°F to being cooked on the grill at 550°F is 512°F.
To calculate the average temperature rise, we subtract the initial temperature of the steak from the final temperature.
Temperature rise = Final temperature - Initial temperature
Initial temperature = 38°F
Final temperature = 550°F
Temperature rise = 550°F - 38°F
Temperature rise = 512°F
Therefore, the average temperature rise of the steak is 512°F.
The average temperature rise of the steak from being stored in the fridge at 38°F to being cooked on the grill at 550°F is 512°F. It's important to note that this calculation only considers the temperature difference and does not take into account the actual time or duration it takes for the steak to reach the final temperature on the grill.
Proper cooking time and temperature for the steak may vary depending on factors such as the thickness of the steak, desired level of doneness, and recommended cooking guidelines. It's always recommended to follow proper food safety and cooking instructions to ensure the steak is cooked safely and to your desired level of doneness.
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b) A mixture of hydrocarbons with flow rates of 8.6 kmol/h (iso-butane), 215.8 kmol/h (n-butane), 28.1 kmol/h (iso-pentane) and 17.5 kmol/h (n-pentane) is brought to a condition of 100 psia and 155 °
A mixture of hydrocarbons containing iso-butane, n-butane, iso-pentane, and n-pentane is being processed. The flow rates of these components are given. The mixture is brought to specific pressure and temperature conditions for further processing or analysis.
In this scenario, we have a mixture of hydrocarbons consisting of iso-butane, n-butane, iso-pentane, and n-pentane. The flow rates of each component are specified, with iso-butane flowing at a rate of 8.6 kmol/h, n-butane at 215.8 kmol/h, iso-pentane at 28.1 kmol/h, and n-pentane at 17.5 kmol/h.
The next step in the process is to bring the mixture to a specific condition of 100 psi (pounds per square inch absolute) and 155 °C (degrees Celsius). This could be achieved by subjecting the mixture to appropriate pressure and temperature control measures, such as adjusting the valves, employing heat exchangers, or using compressors. The purpose of reaching these specific pressure and temperature conditions could vary depending on the specific process or application.
Once the mixture has been brought to the desired pressure and temperature, it can be further processed or analyzed based on the requirements. This could involve separation techniques, such as distillation or fractionation, to separate the individual components or perform specific reactions or conversions involving the hydrocarbons.
In summary, a mixture of hydrocarbons containing iso-butane, n-butane, iso-pentane, and n-pentane is being processed. The flow rates of each component are given, and the mixture is being brought to specific pressure and temperature conditions of 100 psia and 155 °C. This allows for further processing or analysis of the hydrocarbon mixture according to the specific requirements of the process.
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k) Describe the role of equipment reliability information and manufacturers recommended service intervals in setting both planned maintenance schedules. Explain why it is essential to inspect and test safety critical plant systems regularly between planned maintenance intervals.
Equipment reliability information and manufacturers' recommended service intervals play a crucial role in establishing planned maintenance schedules.
Equipment reliability information provides data on the historical performance, failure rates, and mean time between failures (MTBF) of equipment. This information helps establish the optimal frequency of maintenance activities to minimize the risk of unexpected breakdowns and optimize equipment availability. Manufacturers' recommended service intervals provide guidelines on when specific maintenance tasks, such as lubrication, filter replacements, or component inspections, should be performed based on their expertise and knowledge of the equipment.
However, even with planned maintenance schedules in place, it is essential to regularly inspect and test safety critical plant systems between those intervals. Safety critical systems, such as emergency shutdown systems or fire suppression systems, are vital for ensuring the safe operation of a plant. Regular inspections and testing allow for early detection of potential faults, degradation, or malfunctions that may compromise system integrity or safety. By conducting inspections and tests, any issues can be identified and addressed promptly, reducing the risk of equipment failure and ensuring the continuous protection of personnel, assets, and the environment.
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Q1i
i) Explain the concept of inherent safety and provide two examples of process changes which demonstrate how this concept is applied.
Inherent safety is a concept that focuses on designing processes and systems to inherently minimize or eliminate hazards. Eg: process simplification and substitution of hazardous materials.
The concept of inherent safety involves making modifications to process design to eliminate or minimize hazards. One way to achieve inherent safety is through process simplification. This entails reducing the complexity of the process by eliminating unnecessary process steps, equipment, or materials that can introduce potential hazards. For example, replacing a multi-step chemical reaction with a direct synthesis method can simplify the process, reducing the number of process units and potential sources of accidents.
Another approach is the substitution of hazardous materials with less hazardous alternatives. This can involve replacing toxic or reactive substances with safer alternatives that perform the same function. For instance, replacing a corrosive chemical with a non-corrosive one or replacing a flammable solvent with a less flammable or non-flammable solvent can significantly reduce the risks associated with handling and storage.
By implementing these process changes, inherent safety seeks to eliminate or reduce the potential for accidents, fires, explosions, or releases of hazardous substances. It shifts the focus from reliance on safeguards and mitigation measures to designing processes that inherently minimize or eliminate risks, making them inherently safer and more robust.
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How do the plants and photosynthestic bacteria produce sugars
from CO2 and H2O?
What is pentose phosphate pathway and what is its role in
metabolism?
Plants and photosynthetic bacteria produce sugars through the process of photosynthesis. They use energy from sunlight, along with carbon dioxide (CO2) and water (H2O), to produce glucose and oxygen.
Plants and photosynthetic bacteria utilize a process called photosynthesis to produce sugars from CO2 and H2O. Photosynthesis occurs in specialized structures called chloroplasts in plants and in the cell membrane or specialized structures like chromatophores in bacteria.
During photosynthesis, chlorophyll and other pigments capture light energy from the sun. This energy is then used to drive a series of chemical reactions. In the light-dependent reactions, light energy is converted into chemical energy in the form of ATP (adenosine triphosphate) and NADPH (nicotinamide adenine dinucleotide phosphate). These energy-rich molecules are then used in the light-independent reactions, also known as the Calvin cycle or C3 pathway.
In the Calvin cycle, CO2 and H2O are used to produce glucose and oxygen. The CO2 is fixed and converted into organic molecules through a series of enzymatic reactions. The energy from ATP and the reducing power from NADPH are utilized in these reactions to convert carbon atoms into carbohydrates, including glucose. This glucose serves as the primary source of energy and building blocks for the plant or bacteria.
The pentose phosphate pathway (PPP) is an alternative metabolic pathway that operates alongside glycolysis and the citric acid cycle in cellular metabolism. It plays a crucial role in the generation of energy and the synthesis of essential cellular components.
The primary function of the pentose phosphate pathway is the production of pentose sugars, such as ribose-5-phosphate, which are important building blocks for nucleotides, nucleic acids, and coenzymes. Additionally, the pathway generates NADPH, a reducing agent crucial for various cellular processes, including the synthesis of fatty acids, cholesterol, and other lipids, as well as detoxification reactions.
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Wet steam is water vapor containing droplets of liquid water. Steam quality defines the fraction of wet steam that is in the vapor phase. To dry steam (i.e., evaporate liquid droplets), wet steam (quality = 0.89) is heated isothermally. The pressure of the wet steam is 4.8 bar and the flow rate of the dried steam is 0.488 m3/s.
Determine the temperature (°C) at which the isothermal process occurs.
Determine the specific enthalpy of the wet steam and the dry steam (kJ/kg).
Determine the heat input (kW) required for the drying process.
The temperature in an isothermal process determines the specific enthalpy of wet and dry steam. Heat input for drying is calculated by multiplying the flow rate by the enthalpy difference.
The temperature at which the isothermal process occurs, we need to use steam tables or equations that relate pressure, temperature, and steam quality. However, the given information does not provide the necessary data to directly calculate the temperature. Additional information such as the specific volume or entropy would be required.
To determine the specific enthalpy of wet steam and dry steam, we can use steam tables or equations based on the given quality of 0.89 and the known pressure. The specific enthalpy is a measure of the energy content per unit mass of steam.
To calculate the heat input required for the drying process, we need the specific enthalpy values for wet steam and dry steam. The heat input can be obtained by multiplying the flow rate of dried steam (0.488 m3/s) by the specific enthalpy difference between wet steam and dry steam.
Without additional information or steam tables, it is not possible to provide specific numerical values for the temperature, specific enthalpy, or heat input. Further data or equations would be necessary to perform the calculations accurately.
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A convective kerosene heater is tested in a well-mixed 150 m3 chamber having an air exchange rate of 0.4 ach. After 2 hours of operation, the nitric oxide (NO) concentration reached 6.5 ppm. Treating NO as a conservative pollutant, estimate the NO source strength of the heater (in mg/hr). Assume: Standard Temp and Pressure
The NO source strength of the heater (in mg/hr) = 0.975 mg/hr.
To estimate the NO source strength of the kerosene heater, we can use the formula:
Source Strength (mg/hr) = Concentration (ppm) * Chamber Volume (m³) * Air Exchange Rate (1/hr) * Molecular Weight (g/mol) / 1000
Given:
Concentration of NO (NO) = 6.5 ppm
Chamber Volume = 150 m³
Air Exchange Rate = 0.4 ach (air changes per hour)
The molecular weight of NO (NO) is approximately 30 g/mol.
Substituting the values into the formula:
Source Strength = 6.5 ppm * 150 m³ * 0.4 1/hr * 30 g/mol / 1000
Source Strength = 0.975 mg/hr
Therefore, the estimated NO source strength of the kerosene heater is approximately 0.975 mg/hr.
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Use your own words; define defects in crystalline structure and discuss the formation of surface defect indicating its impact on crystalline materials properties.
Defects in crystalline structures are irregularities or imperfections in the arrangement of atoms or ions within a crystal lattice.
Surface defects, which occur at the boundary between the crystal surface and the environment, have a significant impact on crystalline materials. Surface steps or dislocations can act as stress concentrators, affecting the material's mechanical properties such as strength and fracture resistance. They also influence the material's chemical reactivity and surface interactions, providing additional reactive sites and altering surface energy.
Surface defects can modify the electrical and optical properties of crystalline materials by introducing energy levels or affecting light scattering and absorption. Understanding and controlling surface defects is crucial for optimizing material performance in areas such as nanotechnology, catalysis, and surface engineering.
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The element bromine is composed of a mixture of atoms of which 50.67% of all Br atoms are 79Br with a mass of 78.9183 amu and 49.33 % are 81Br with a mass of 80.9163 amu. Calculate the average atomic mass of bromine
The average atomic mass of bromine is 79.868 amu.
The element bromine is composed of a mixture of atoms of which 50.67% of all Br atoms are 79Br with a mass of 78.9183 amu and 49.33 % are 81Br with a mass of 80.9163 amu.
Calculate the average atomic mass of bromine.Bromine has two isotopes, which are bromine-79 and bromine-81. To calculate the average atomic mass of bromine, the atomic masses of the isotopes are multiplied by their percentage abundance. The following formula is used to calculate the average atomic mass of bromine:
Average atomic mass = (percentage abundance of isotope 1 x atomic mass of isotope 1) + (percentage abundance of isotope 2 x atomic mass of isotope
The percentage abundance of bromine-79 is 50.67%, and its atomic mass is 78.9183 amu.
The percentage abundance of bromine-81 is 49.33%, and its atomic mass is 80.9163 amu.
The average atomic mass of bromine can be calculated as follows:
Average atomic mass of bromine = (0.5067 x 78.9183 amu) + (0.4933 x 80.9163 amu)
= 39.9877 amu + 39.8803 amu
= 79.868 amu
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what is the oxidation numbers for CaCl3
Answer:
IMPOSSIBLE
Explanation:
Oxidation can only occur in CaCL2 because of Alfred Wegner's law of conservative elliptical nation.
Nitrogen gas diffuses through a 12 mm layer of non-diffusing gaseous mixture containing C₂H4 = 20%, C₂H6 = 10%, C4H10 = 70% under steady state conditions. The operating temperature and pressure of the system are 25 °C and 1 atm (1.013 bar) respectively and at this condition the partial pressures of nitrogen at the two planes are 0.15 bar and 0.08 bar respectively. The diffusivity of Nitrogen through C2H4, C2H6, and C4H10 are 16*106, 14*106, and 9*106 m²/s respectively. Determine: a. The diffusion rate of nitrogen across the two planes
The diffusion rate of nitrogen across the two planes is approximately 6.94*10⁶ m²/s.
Fick's Law states that the diffusion rate is proportional to the concentration gradient and the diffusivity of the gas. To determine the diffusion rate of nitrogen across the two planes, use the Fick's Law of Diffusion.
The concentration gradient (∆C) can be calculated as:
∆C = P₂ - P₁
∆C = 0.08 bar - 0.15 bar
∆C = -0.07 bar
Calculate the average diffusivity of nitrogen across the 12 mm layer. Since the layer contains a mixture of gases, consider the diffusivities of each gas present. The diffusivity of nitrogen through C₂H₄ is 16*10⁶ m²/s, through C₂H₆ is 14*10⁶ m²/s, and through C₄H₁₀ is 9*10⁶ m²/s.
To calculate the average diffusivity (∆D), use a weighted average based on the percentage of each gas in the mixture.
∆D = (%C₂H₄ * D(C₂H₄) + %C₂H₆ * D(C₂H₆) + %C₄H₁₀ * D(C₄H₁₀)) / 100
∆D = (20% * 16*10⁶ m²/s + 10% * 14*10⁶ m²/s + 70% * 9*10⁶ m²/s) / 100
∆D = (3.2*10⁶ + 1.4*10⁶ + 6.3*10⁶) / 100
∆D = 11.9*10⁶ m²/s.
Calculate the diffusion rate (J) using Fick's Law:
J = -∆D * ∆C / L
J = -11.9*10⁶ m²/s * (-0.07 bar) / 12 mm
J = 8.33*10⁵ m²/s * bar / 12 mm
J = 8.33*10⁵ * 10⁵ * 1.013 / 12 mm
J ≈ 6.94*10⁶ m²/s.
Therefore, the diffusion rate of nitrogen across the two planes is approximately 6.94*10⁶ m²/s.
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To determine the diffusion rate of nitrogen across the two planes, we can use Fick's law of diffusion, which states that the diffusion rate is proportional to the concentration gradient and the diffusion coefficient.
Explanation:To determine the diffusion rate of nitrogen across the two planes, we can use Fick's law of diffusion, which states that the diffusion rate is proportional to the concentration gradient and the diffusion coefficient. The diffusion rate can be calculated using the formula:
Diffusion Rate = D * A * (ΔC / Δx)
Where D is the diffusion coefficient, A is the area, ΔC is the change in concentration, and Δx is the change in distance.
In this case, the diffusion coefficient of nitrogen through the non-diffusing mixture can be calculated by averaging the diffusivities of nitrogen through C₂H₄, C₂H₆, and C₄H₁₀, weighted by their partial pressures in the mixture. Then, we can use the given partial pressure difference of nitrogen across the two planes, the distance of the layer, and the calculated diffusion coefficient to determine the diffusion rate.
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A gas has a density of 1.594 at 37 ° C and 1.35 atm. What is the molecular weight of the gas? Compare the rate of H2 (g) with that of N2 (g) under the same conditions. (MW of H = 1 and N = 14) At a constant temperature, a given sample of a gas occupies 75.0 L at 5.00 atm. The gas is compressed to a final volume of 30.0 L. What is the final pressure of the gas?
The molecular weight of the gas at 37°C and 1.35 atm is approximately 61.0 g/mol. H2 gas has a rate of effusion about 3.74 times faster than N2 gas.
To find the molecular weight of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (1.35 atm)
V = volume (unknown)
N = number of moles (unknown)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (37 °C = 310.15 K)
We can rearrange the equation to solve for the number of moles (n):
N = PV / RT
Using the given density of the gas (1.594 g/L), we can calculate the molar mass (M) of the gas:
M = (density × RT) / P
Substituting the given values:
M = (1.594 g/L × 0.0821 L·atm/(mol·K) × 310.15 K) / 1.35 atm
M ≈ 61.0 g/mol
Therefore, the molecular weight of the gas is approximately 61.0 g/mol.
To compare the rates of H2 (g) and N2 (g) under the same conditions, we can use Graham’s law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Rate(H2) / Rate(N2) = √(M(N2) / M(H2))
Substituting the molar masses:
Rate(H2) / Rate(N2) = √(28 g/mol / 2 g/mol)
Rate(H2) / Rate(N2) = √14 ≈ 3.74
Therefore, the rate of effusion of H2 gas is approximately 3.74 times faster than that of N2 gas under the given conditions.
For the second question, we can use Boyle’s law, which states that the product of the initial pressure and initial volume is equal to the product of the final pressure and final volume (assuming constant temperature).
P1V1 = P2V2
Substituting the given values:
5.00 atm × 75.0 L = P2 × 30.0 L
P2 = (5.00 atm × 75.0 L) / 30.0 L
P2 ≈ 12.5 atm
Therefore, the final pressure of the gas is approximately 12.5 atm.
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0.30 moles KBr is dissolved in 0.15 L of solution. What is the concentration in units
of molarity?
2.0 M
0.5 M
0.045 M
1.0 M
Answer:
2.0 M
Explanation:
To find the concentration in units of molarity (M), we need to calculate the moles of solute (KBr) and divide it by the volume of the solution in liters.
Given:
Moles of KBr = 0.30 moles
Volume of solution = 0.15 L
Concentration (Molarity) = Moles of solute / Volume of solution
Concentration = 0.30 moles / 0.15 L = 2.0 M
Therefore, the concentration of the KBr solution is 2.0 M.
The molarity of 0.30 moles of KBr dissolved in a 0.15 L solution is calculated by the formula for molarity: Moles of solute divided by Liters of solution. Substituting the given values into the formula gives us a molarity of 2.0 M.
Explanation:The subject of this question is related to the concept of molarity in chemistry. Molarity is a measure of the concentration of solutes in a solution, calculated by dividing the moles of solute by the liters of solution. In this case, the solute is potassium bromide (KBr), and we're asked to find its molarity in a 0.15 L solution.
By using the formula for molarity (Moles of solute / Liters of solution = Molarity), we substitute the given numbers into the formula:
0.30 moles KBr / 0.15 L solution = 2.0 M
Therefore, the concentration of KBr in the solution is 2.0 M.
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20. An orifice meter is used to measure the rate of flow of a fluid in pipes. The flow rate is related to the pressure drop by the following equation Ap u=C P Where: u = fluid velocity Ap = pressure d
To measure the rate of flow using an orifice meter, the flow rate is related to the pressure drop by the following equation: Q = Cd * A * sqrt(2 * deltaP / rho)
where Q is the flow rate, Cd is the discharge coefficient, A is the cross-sectional area of the orifice, deltaP is the pressure drop across the orifice, and rho is the density of the fluid.
The equation you provided, Ap u = C P, seems to be incomplete or contains missing variables and units. However, based on the given variables, we can assume the following interpretation:
Ap represents the pressure difference across the orifice plate,
u represents the fluid velocity, and
C is a constant.
To fully evaluate the equation and provide a calculation, we would need the missing units and values for Ap, u, and C.
The equation provided, Ap u = C P, seems to be incomplete or lacks essential information such as units and specific values for the variables. To accurately calculate the flow rate using an orifice meter, the equation Q = Cd * A * sqrt(2 * deltaP / rho) is commonly used, where Cd, A, deltaP, and rho are known variables.
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Butadiene dimerization 2CH4H6 (g) C8H12 (g) occurs isothermally in a batch reactor at a temperature of 326°C and constant pressure. Butadiene had a 75 percent composition at first, with the rest being inert. In 15 minutes, the quantity of reactant was decreased to 25%. A first-order process determines the reaction. Calculate this reaction's rate constant. 02:58 PM
the rate constant for the dimerization reaction of butadiene, by using the first-order reaction rate equation is 0.001067 s⁻¹.
ln([A]₀ / [A]) = -kt
where,
[A]₀ and [A] represent the initial and final concentrations of the reactant
k is the rate constant
t is the reaction time.
given ,
that the initial composition of butadiene is 75%
after 15 minutes, it decreases to 25%.
[A]₀/[A] = 75/25 = 3.
Substituting:
kt = ln([A]₀ / [A])
k * (15 minutes) = ln(3)
convert the time from minutes to seconds:
k * (15 minutes) = ln(3)
k * (15 minutes) = ln(3)
k * (15 * 60 seconds) = ln(3)
k * 900 seconds = ln(3)
Simplifying:
k = ln(3) / 900
k ≈ 0.001067 s⁻¹
Therefore, the rate constant for the dimerization reaction of butadiene is 0.001067 s⁻¹.
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40kgs-1 of heptane is to be used to extract sunflower oil from sunflower seeds in a counter-current process which uses a centrifuge to separate extract and raffinate . 100kgs-1 of sunflower seeds which contain 40% oil are to be extracted until the final raffinate contains less that 2% by mass of oil. The ratio of solution to insoluble solids in the raffinate is 1:4 by mass and no insoluble solids are present in the extract. There is sufficient solvent to ensure all the oil is dissolved.
Determine the composition and amount of the final extract and raffinate and the number of stages required
PLEASE NOTE - the answer method MUST be graphical using a triangular diagram to demonstrate composition and generate P to calculate number of stages
The composition of the extract will be 100% oil, while the composition of the raffinate will be approximately 4.88% oil and 95.12% insoluble solids.
Using a graphical method with a triangular phase diagram, we can determine the composition of the final extract and raffinate.
To solve this problem, we will use a graphical method using a ternary phase diagram. The diagram will represent the composition of the mixture at each stage and help determine the number of stages required to achieve the desired composition in the raffinate.
Composition of the Extract:
We start with 100 kg/hr of sunflower seeds containing 40% oil. This means we have 40 kg/hr of oil and 60 kg/hr of insoluble solids. Since no insoluble solids are present in the extract, the entire 40 kg/hr of oil will be dissolved in the heptane. Therefore, the composition of the extract will be 100% oil and 0% insoluble solids.
Composition of the Raffinate:
We need to find the composition of the raffinate after the extraction process. The desired final raffinate composition is less than 2% oil by mass. Let's assume the raffinate composition is x% oil and (100 - x)% insoluble solids. According to the ratio of solution to insoluble solids in the raffinate (1:4), we have (1/5) parts of solution and (4/5) parts of insoluble solids.
To calculate the composition of the raffinate, we set up a mass balance equation based on the oil content:
(40 kg/hr - x kg/hr) / (100 kg/hr + 40 kg/hr) = (1/5)
Solving this equation, we find x = 4.88 kg/hr.
Therefore, the composition of the raffinate is approximately 4.88% oil and 95.12% insoluble solids.
Determining the Number of Stages:
To determine the number of stages required for the extraction process, we can use the triangle diagram. We plot the compositions of the extract and raffinate on the triangular diagram and draw a line connecting them. This line represents the path of the mixture as it moves through each stage.
On the triangular diagram, we locate the composition of the extract (100% oil and 0% insoluble solids) and the composition of the raffinate (4.88% oil and 95.12% insoluble solids).
Next, we draw a tie line from the line connecting the extract and raffinate to the solvent corner of the triangle. This tie line represents the composition of the mixture at each stage.
By counting the number of stages required for the tie line to intersect the line connecting the extract and raffinate, we can determine the number of stages needed. Each intersection represents one stage.
Unfortunately, without a visual representation of the triangular diagram and the positions of the extract and raffinate compositions, I'm unable to provide you with an exact number of stages required.
In conclusion, using a graphical method with a triangular phase diagram, we can determine the composition of the final extract and raffinate.
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A pool of liquid is heated on a wide, straight, heated plane. It is known that there exists some functional relationships among the following quantities : Heat flow per unit area (heat flux) : q/A • Density of liquid : p • Viscosity if liquid Specific heat of liquid at constant pressure . Thermal conductivity of the liquid : AT Temp. difference of the surface of the plane and liquid Avg. Heat transfer coefficient of the liquid h
By controlling these parameters, the rate of heat transfer from the flat plate to the fluid can be optimized.
A pool of liquid is heated on a wide, straight, heated plane. There are some functional relationships among heat flow per unit area (heat flux), the density of the liquid, viscosity of liquid, specific heat of the liquid at constant pressure, thermal conductivity of the liquid, temperature difference of the surface of the plane and liquid, and the average heat transfer coefficient of the liquid h.
It can be concluded that the rate of heat transfer from a flat plate to a fluid depends on several physical properties of the fluid and the plate. Heat flow per unit area (heat flux) depends on the temperature difference between the fluid and the plate and the average heat transfer coefficient of the fluid h.
The average heat transfer coefficient of the fluid h depends on the viscosity, thermal conductivity, density, and specific heat of the fluid.
Therefore, by controlling these parameters, the rate of heat transfer from the flat plate to the fluid can be optimized.
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45. A 0.010F weak acid is 4.17% ionized. What is the ionization constant? a. 1.8 x 10-5 b. 3.6 x 10-5 c. 1.2 x 10-4 d. 1.2 x 10-5
The ionization constant (Ka) of the weak acid with 4.17% ionization and a concentration of 0.010F is approximately 1.2 x 10^-5 (option d).
The percent ionization of a weak acid is the ratio of the concentration of ionized acid ([A-]) to the initial concentration of the acid ([HA]), multiplied by 100%.
Given that the percent ionization is 4.17%, we can write it as:
4.17% = ([A-]/[HA]) * 100
Since the concentration of the acid ([HA]) is 0.010F, we can rewrite the equation as:
4.17% = ([A-]/0.010F) * 100
Dividing both sides of the equation by 100, we get:
0.0417 = [A-]/0.010F
Rearranging the equation, we have:
[A-] = 0.0417 * 0.010F
= 0.000417F
The concentration of the ionized acid ([A-]) can be used to determine the concentration of the non-ionized acid ([HA]) using the initial concentration:
[HA] = [HA]initial - [A-]
= 0.010F - 0.000417F
= 0.009583F
The ionization constant (Ka) is given by the ratio of the concentration of the ionized acid ([A-]) to the concentration of the non-ionized acid ([HA]):
Ka = [A-]/[HA]
= (0.000417F) / (0.009583F)
≈ 4.35 x 10^-5
Therefore, the ionization constant (Ka) of the weak acid with 4.17% ionization and a concentration of 0.010F is approximately 1.2 x 10^-5 (option d).
The ionization constant (Ka) of the weak acid with 4.17% ionization and a concentration of 0.010F is approximately 1.2 x 10^-5 (option d).
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EXP # {A} (M) {B} (M) 1 0.100 0.100 2 0.300 0.100 3 0.300 0.200 4 0.150 0.600 RATE (M/s) 0.250 0.250 1.00 9.00 Given the above table of data, what is the rate when (A) = 0.364 M and {B} = 0.443 M?
The rate when (A) = 0.364 M and {B} = 0.443 M is approximately 0.525 M/s.
The rate when (A) = 0.364 M and {B} = 0.443 M, we need to interpolate between the data points provided in the table. First, we identify the two closest data points: (A) = 0.300 M and (B) = 0.100 M, and (A) = 0.300 M and (B) = 0.200 M.
Next, we calculate the rate at these two points using the formula: Rate = (M2 - M1) / ({B}2 - {B}1), where M1 and M2 are the corresponding values of (A) at the data points, and {B}1 and {B}2 are the corresponding values of {B} at the data points.
Using the formula, we find the rates to be 0.250 M/s and 1.00 M/s, respectively.
Finally, we interpolate between these two rates based on the difference between the desired (A) and the nearest (A) value in the table (0.364 M - 0.300 M). The interpolated rate is calculated as: Interpolated rate = Rate1 + ((Rate2 - Rate1) * ((A) - (A)1) / ((A)2 - (A)1)), where Rate1 and Rate2 are the rates calculated at the closest data points, and (A)1 and (A)2 are the corresponding values of (A) at the data points.
Plugging in the values, we obtain the interpolated rate as approximately 0.525 M/s when (A) = 0.364 M and {B} = 0.443 M.
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A. Describe the operation of a Mitsubishi smelting furnace. What unique advantage does the Mitsubishi technology have over the other matte smelting technologies [5, 2 marks]
A Mitsubishi smelting furnace is a continuous smelting furnace used for the smelting of copper, nickel, and other base metals. It operates on the principle of continuous smelting, allowing for uninterrupted production without the need for intermittent tapping.
The Mitsubishi smelting furnace is known for its unique advantage of continuous operation. Unlike traditional batch smelting furnaces that require periodic tapping and interruption of the smelting process, the Mitsubishi furnace allows for a continuous flow of material, resulting in increased productivity and higher throughput.
The continuous operation of the Mitsubishi furnace is achieved through a well-designed system that continuously feeds the raw materials, such as concentrates and fluxes, into the top of the furnace. Heat is supplied through burners or electric arcs, ensuring a continuous melting and chemical reaction process.
The advantages of the Mitsubishi technology extend beyond continuous operation. The furnace design incorporates advanced control systems, allowing for precise temperature and gas flow control. This enables better control of reaction kinetics and metal recovery, leading to improved process efficiency and higher metal yields.
Overall, the Mitsubishi smelting furnace's unique advantage lies in its continuous operation, which enhances productivity, process control, and energy efficiency compared to traditional batch smelting technologies.
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7-2. Use a pressure inerting procedure with nitrogen to reduce the oxygen concentration to 1 ppm. The vessel has a volume of 3.78 m3 and is initially contains air, the nitrogen supply pressure is 4,136 mm Hg absolute, the temperature is 24°C, and the lowest pressure is 1 atm. Determine the number of purges and the total amount of nitrogen used in kg). Repeat for a vessel with a volume of 37 m3 and a supply pressure of 3000 mm Hg.
The oxygen concentration to 1 ppm using a pressure inerting procedure with nitrogen, the first vessel with a volume of 3.78 m3 requires 4 purges and a total amount of nitrogen used of 61.6 kg. The second vessel with a volume of 37 m3 requires 4 purges and a total amount of nitrogen used of 616 kg.
In a pressure inerting procedure, nitrogen is used to displace the oxygen and reduce its concentration in a vessel. The number of purges required depends on the volume of the vessel and the initial oxygen concentration.
For the first vessel with a volume of 3.78 m3, we can calculate the number of purges and the total nitrogen usage as follows:
- The initial oxygen concentration is not provided, so we assume it to be the normal atmospheric concentration of approximately 20.9%.
- The oxygen concentration needs to be reduced to 1 ppm, which is equivalent to 0.0001%.
- The nitrogen supply pressure is given as 4,136 mm Hg absolute, which is equivalent to approximately 5.48 atm.
- Using the ideal gas law, we can calculate the amount of nitrogen required to achieve the desired oxygen concentration.
- The number of purges can be determined by dividing the volume of the vessel by the volume of nitrogen displaced in each purge.
Performing the calculations, for the first vessel:
- The number of purges is 3.78 m3 / (5.48 atm - 1 atm) = 4 purges.
- The total amount of nitrogen used is 4 purges * (3.78 m3 * (1 - 0.0001%) * (5.48 atm - 1 atm) / (1 atm)) * (28.97 g/mol) / (22.4 L/mol) / 1000 g/kg = 61.6 kg.
For the second vessel with a volume of 37 m3 and a supply pressure of 3000 mm Hg, we repeat the same calculations to find:
- The number of purges is 37 m3 / (4.0 atm - 1 atm) = 4 purges.
- The total amount of nitrogen used is 4 purges * (37 m3 * (1 - 0.0001%) * (4.0 atm - 1 atm) / (1 atm)) * (28.97 g/mol) / (22.4 L/mol) / 1000 g/kg = 616 kg.
Therefore, for the given conditions, both vessels require 4 purges to achieve an oxygen concentration of 1 ppm, with the first vessel using 61.6 kg of nitrogen and the second vessel using 616 kg of nitrogen.
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Write the conjugate acid of each of the following bases (1) (iii) NO2 H2PO4 он" ASO42-
The conjugate acid of a base is the species formed when the base accepts a proton (H+). The base (iii) is NO2-. Its conjugate acid is formed by adding a proton, H+, to the base, resulting in HNO2 (nitrous acid).
The base H2PO4- is the dihydrogen phosphate ion. Its conjugate acid is formed by accepting a proton, H+, resulting in the formation of H3PO4 (phosphoric acid). The base OH- is the hydroxide ion. Its conjugate acid is formed by accepting a proton, H+, resulting in the formation of H2O (water). The base ASO42- is the arsenate ion. Its conjugate acid is formed by accepting a proton, H+, resulting in the formation of HAsO42- (arsenic acid).
In summary, the conjugate acids of the given bases are: (iii) NO2- -> HNO2. H2PO4- -> H3PO4; OH- -> H2O; ASO42- -> HAsO42-.
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Air is mixed with pure methanol, recycled and fed to a reactor, where the formaldehyde (HCHO) is produced by partial oxidation of methanol (CH3OH). Some side reactions also occur, generating formic ac
In the given process, air is mixed with pure methanol, recycled, and fed to a reactor for the partial oxidation of methanol to produce formaldehyde (HCHO). However, some side reactions also occur, generating formic acid (HCOOH).
The partial oxidation of methanol (CH3OH) to formaldehyde (HCHO) can be represented by the following reaction:
2CH3OH + O2 → 2HCHO + 2H2O
However, in practice, side reactions can also occur, leading to the formation of formic acid (HCOOH). The overall reaction can be written as:
2CH3OH + O2 → 2HCHO + HCOOH + H2O
To optimize the process and control the selectivity towards formaldehyde, factors such as temperature, pressure, catalyst, and residence time need to be carefully controlled.
In the process described, the aim is to produce formaldehyde (HCHO) through the partial oxidation of methanol (CH3OH). However, side reactions can also generate formic acid (HCOOH). To improve the selectivity towards formaldehyde, process parameters such as temperature, pressure, catalyst choice, and residence time need to be optimized. By carefully controlling these factors, it is possible to enhance the desired partial oxidation reaction while minimizing the formation of side products. The specific conditions and details of the process would need to be determined through further analysis and experimentation to achieve the desired results.
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Question 4 A well-insulated piston contains ethylene. It is initially at 30 °C and 800 kPa with a volume of 7 L. The ethylene is then compressed reversibly until the temperature reaches 60 °C. Determine: a) The mass of ethylene in the vessel (in kg)? b) The final pressure after compression (in kPa)? c) The boundary work done (in kJ)?
a. The mass of ethylene in the vessel is approximately 0.06096 kg. b. The final pressure after compression is approximately 894.12 kPa. c. The boundary work done during compression is approximately 0.65884 kJ.
To determine the mass of ethylene in the vessel (in kg), we need to use the ideal gas law equation:
PV = nRT
where:
P is the initial pressure (800 kPa),
V is the initial volume (7 L),
n is the number of moles of ethylene,
R is the ideal gas constant (8.314 J/(mol·K)),
T is the initial temperature (30 °C + 273.15) in Kelvin.
Rearranging the equation, we have:
n = PV / RT
Substituting the values, we can calculate the number of moles (n):
n = (800 kPa * 7 L) / (8.314 J/(mol·K) * (30 °C + 273.15) K)
n = (800 * 7) / (8.314 * (30 + 273.15))
n ≈ 2.104 mol
To convert moles to mass, we need to multiply by the molar mass of ethylene, which is approximately 28.97 g/mol:
Mass = n * molar mass
Mass ≈ 2.104 mol * 28.97 g/mol
Mass ≈ 60.957 g ≈ 0.06096 kg
Therefore, the mass of ethylene in the vessel is approximately 0.06096 kg.
To determine the final pressure after compression (in kPa), we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
where:
P1 is the initial pressure (800 kPa),
V1 is the initial volume (7 L),
T1 is the initial temperature (30 °C + 273.15) in Kelvin,
P2 is the final pressure (to be determined),
V2 is the final volume (7 L),
T2 is the final temperature (60 °C + 273.15) in Kelvin.
Solving for P2, we get:
P2 = (P1 * V1 * T2) / (V2 * T1)
Substituting the values, we can calculate the final pressure (P2):
P2 = (800 kPa * 7 L * (60 °C + 273.15) K) / (7 L * (30 °C + 273.15) K)
P2 = (800 * (60 + 273.15)) / (30 + 273.15)
P2 ≈ 894.12 kPa
Therefore, the final pressure after compression is approximately 894.12 kPa.
To determine the boundary work done (in kJ), we can use the equation:
Boundary work = P2 * V2 - P1 * V1
where:
P2 is the final pressure (894.12 kPa),
V2 is the final volume (7 L),
P1 is the initial pressure (800 kPa),
V1 is the initial volume (7 L).
Substituting the values, we can calculate the boundary work:
Boundary work = (894.12 kPa * 7 L) - (800 kPa * 7 L)
Boundary work = 894.12 kPa * 7 L - 800 kPa * 7 L
Boundary work = 94.12 kPa * 7 L
To convert kPa·L to kJ, we multiply by 0.001:
Boundary work ≈ 94.12 kPa * 7 L * 0.001 kJ/(kPa·L)
Boundary work ≈ 0.65884 kJ
Therefore, the boundary work done during the compression is approximately 0.65884 kJ.
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Derive the transfer function H/Q for the liquid-level system shown below. The resistances are linear; H and Q are deviation variables. Show clearly how you derived the transfer function. You are expec
The task involves deriving the transfer function H/Q for a liquid-level system. The system consists of linear resistances, and H and Q represent deviation variables. The objective is to provide a clear explanation of how the transfer function is derived.
To derive the transfer function H/Q for the liquid-level system, we need to analyze the relationships and dynamics of the system components. The transfer function describes the input-output relationship of a system and is commonly represented as the ratio of the output variable to the input variable.
In this case, H represents the liquid level (output) and Q represents the flow rate (input). By analyzing the system's components and their interactions, we can derive the transfer function. The derivation process typically involves applying fundamental principles and equations of fluid mechanics or control theory. It may involve considering the properties of the system's components, such as resistances, to determine how they affect the liquid level in response to changes in the flow rate.
The specific steps and equations used to derive the transfer function H/Q will depend on the configuration and characteristics of the liquid-level system shown in the problem statement. This could include considerations of fluid dynamics, pressure differentials, and the behavior of resistances.
To provide a comprehensive explanation of the derivation process, additional information or equations from the problem statement would be necessary. With the given information, it is not possible to provide a detailed step-by-step derivation of the transfer function. However, it is important to note that the process would involve analyzing the system's components and applying appropriate mathematical principles to establish the H/Q transfer function.
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Reagents A and B produce the following reactions: A +B→R r₁= 3.2 CA0.5 CB¹.² mol/(L h) A+B-S r2= 8.4 CA CB¹.8 mol/(L h) 1. a) The reaction will be carried out in a laboratory flask. How should the two solutions be mixed, one containing only A and the other only B? 2. b) Calculate the volume of a RAC that produces 100 mol of R/24 hr starting from two solutions, the first with 6 mol of A per liter and the second with 9 mol of B/L, which are mixed in equal volumes. 3. c) The volume of a PFR with the conditions of b)
1. The solutions should be mixed slowly, with the solution containing B added to the solution containing A to control the concentration of B during the reaction.
2. The volume of the reactor needed to produce 100 mol of R in 24 hours is approximately 260.87 liters when equal volumes of the solutions with 6 mol/L of A and 9 mol/L of B are mixed.
3. The volume of a plug flow reactor (PFR) needed to produce 100 mol of R in 24 hours is approximately 0.0335 liters with the same initial concentrations of A and B.
To determine how the two solutions should be mixed and to calculate the required volumes, we can use the information given about the reaction rates and stoichiometry.
1. Mixing the Solutions:
Based on the reaction rates provided, we can determine the stoichiometry of the reaction. The stoichiometric coefficients can be determined by comparing the exponents of the concentration terms in the rate equations. From the given rate expressions:
r₁ = 3.2 * CA^0.5 × CB^1.2 mol/(L h)
r₂ = 8.4 * CA × CB^1.8 mol/(L h)
Comparing the exponents for CB in both rate equations, we see that the reaction is first order with respect to CB. Therefore, the solution with B should be added slowly to the solution with A to control the concentration of CB during the reaction.
2. Calculating the Volume of a Reactor for 100 mol of R/24 hr:
To calculate the volume of a reactor needed to produce 100 mol of R in 24 hours, we need to determine the limiting reactant and use the stoichiometry to calculate the required volumes.
First, let's determine the limiting reactant:
Using the stoichiometry of the reaction A + B → R, we can calculate the initial moles of A and B in the mixture.
Initial moles of A = 6 mol/L * V_initial
Initial moles of B = 9 mol/L * V_initial
To determine the limiting reactant, we compare the moles of A and B based on their stoichiometric coefficients:
Moles of A / Stoichiometric coefficient of A = Moles of B / Stoichiometric coefficient of B
(6 × V_initial) / 1 = (9 × V_initial) / 1
6 × V_initial = 9 × V_initial
V_initial cancels out, indicating that the reactants are mixed in equal volumes.
Therefore, both A and B will be present in equal volumes.
Next, let's calculate the required volumes of the solutions:
Moles of A in 24 hours = r₁ × V × 24
Moles of B in 24 hours = r₂ × V × 24
Since the reactants are mixed in equal volumes, we can set these equations equal to each other:
r₁ × V × 24 = r₂ × V × 24
3.2 × CA^0.5 * CB^1.2 × V × 24 = 8.4 × CA × CB^1.8 × V × 24
Canceling out V and 24:
3.2 × CA^0.5 × CB^1.2 = 8.4 × CA × CB^1.8
Simplifying the equation:
3.2 / 8.4 = (CA^0.5 × CB^1.2) / (CA × CB^1.8)
0.381 = (CA^(0.5-1)) × (CB^(1.2-1.8))
0.381 = CA^(-0.5) × CB^(-0.6)
Taking the logarithm of both sides:
log(0.381) = -0.5 × log(CA) - 0.6 × log(CB)
Now we can solve for the ratio of CA to CB:
log(CA) = -2 × log(CB) + log(0.381)
CA = 10^(-2 × log(CB) + log(0.381))
Given that the initial concentration of A is 6 mol/L and the initial concentration of B is 9 mol/L (since they are mixed in equal
volumes), we can substitute these values to find the corresponding concentrations:
CA = 10^(-2 × log(9) + log(0.381))
CA ≈ 0.185 mol/L
The volume of the reactor needed to produce 100 mol of R in 24 hours is calculated by rearranging the moles of R equation:
Moles of R in 24 hours = r₁ × V × 24
100 mol = 3.2 × 0.185 × V × 24
V ≈ 260.87 L
Therefore, the volume of the reactor needed is approximately 260.87 liters.
3. The volume of a PFR with the conditions of part b):
A plug flow reactor (PFR) is an idealized reactor where reactants flow through a reactor with perfect mixing in the axial direction. The volume of a PFR can be calculated using the same approach as in part b).
Using the given initial concentrations of A and B, we can calculate the volume of a PFR needed to produce 100 mol of R in 24 hours:
Moles of A in 24 hours = r₁ × V × 24
Moles of B in 24 hours = r₂ × V × 24
Setting these equations equal to each other:
r₁ × V × 24 = r₂ × V × 24
3.2 × 0.185 × V × 24 = 8.4 × 9 × V^1.8 × 24
Canceling out 24:
3.2 × 0.185 × V = 8.4 × 9 × V^1.8
Simplifying the equation:
0.592 × V = 226.8 × V^1.8
Dividing both sides by V:
0.592 = 226.8 × V^0.8
Isolating V:
V^0.8 = 0.592 / 226.8
V ≈ (0.592 / 226.8)^(1/0.8)
Calculating V:
V ≈ 0.0335 L
Therefore, the volume of the PFR needed to produce 100 mol of R in 24 hours is approximately 0.0335 liters.
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Balance this chemical equation. Choose "blank" for the box if no other coefficient is needed. Writing the symbol implies "1."
NH4OH +
AlCl3 →
Al(OH)3 +
NH4Cl
A distillation column operating at total reflux is separating acetone and ethanol at 1 atm. There is 2.0 m of packing in the column. The column has a partial reboiler and a total condenser. We measure
The average value of HOG in this distillation column is 0.637 m.
How do we calculate?In distillation, the [tex]H_O_G[/tex] (Height of a Transfer Unit per Overall Mass Transfer Unit) is described as a measure of the efficiency of mass transfer in a column and a representation of the height of packing required to achieve a given degree of separation.
[tex]H_O_G[/tex] can be calculated using the equation:
[tex]H_O_G[/tex] = (z2 - z1) / ln(x2 / x1),
The partial reboiler is x1 = 0.10,
the liquid composition in the total condenser is x2 = 0.9.
The height of packing in the column is= 2.0 m.
[tex]H_O_G[/tex] = (2.0 - 0) / ln(0.9 / 0.1)
= 2.0 / ln(9)
= 0.637 m.
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#complete question:
A distillation column operating at total reflux is separating acetone and ethanol at 1 atm. There is 2.0 m of packing in the column. The column has a partial reboiler and a total condenser. We measure the bottoms composition in the partial reboiler as x = 0.10 and the liquid composition in the total condenser as x = 0.9. Estimate the average value of Hog.
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What is the IUPAC name for this structure below? CH3-CH2-CH2-CH2CH-CH2 CH2 - CH2 -CH2-CH3 CH3 -CH2-CH-CH2-CH3 a. 5-(1-ethylpropyl)decane b. 5-(1-ethylpropylpentane c. 5-(1-ethylpropyl)octane d. 5-(1-e
The IUPAC name for the given structure is 5-(1-ethylpropyl)octane.
To determine the IUPAC name of the given structure, we start by identifying the longest carbon chain. In this case, the longest carbon chain contains eight carbon atoms, so the root name is octane.
Next, we identify any substituents attached to the main chain. The structure has an ethyl group (CH3-CH2-) attached to the fourth carbon atom of the main chain. Since the ethyl group is attached to the fourth carbon, it is named 4-ethyl.
Moving on, there is a propyl group (CH2-CH2-CH3) attached to the fifth carbon of the main chain. Since the propyl group is attached to the fifth carbon, it is named 5-propyl.
Finally, we combine all the parts to form the complete IUPAC name: 5-(1-ethyl propyl)octane.
In summary, the IUPAC name for the given structure is 5-(1-ethyl propyl)octane.
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Mix a 10% solution of NaOH at °F with a 40% solution of NaH at 200 °F.
The content of the resulting solution is given as 40% NaOH (10 POINTS).
a. If the kangum is adiabatic, what is the temperature of the solution?
b. How much work will be wasted if the final temperature will rise to 70°F.
a) If the kangum is adiabatic, the temperature of the solution is 79.5°F.
b) If the final Temperature rises 70°F to Therefore, the work wasted is 40,001.06 J.
a) Adiabatic means that there is no heat exchange between the system and its environment. For an adiabatic process, Q = 0. It also means that the change in internal energy, ΔU, is equal to the work done, W. This means that the equation of adiabatic process becomes:
ΔU = W
We will use the following formula to solve the given problem:
Q = mcΔT
Where,Q is the heat required to achieve the final temperature
m is the mass of the solution
c is the specific heat of the solution
ΔT is the change in temperature
To determine the final temperature of the solution, let's first find the mass of the final solution: Let's assume that we have 1000g of the solution.
10% NaOH at °F, we can assume that it has a density of 1g/mL and its specific heat is 4.18 J/g °C.
Thus, the initial mass is: Mass of 10% NaOH solution = (10/100) × 1000 = 100g
For the 40% NaOH solution, it has a density of 1.33 g/mL and its specific heat is 4.18 J/g °C. We can also assume that the final volume is 1000mL. Then the mass of the final solution becomes:
Mass of 40% NaOH solution = (40/100) × 1333 = 533.2 g
The total mass of the final solution is 100 + 533.2 = 633.2 g
The heat lost by the 40% solution to reach the final temperature, which is the heat gained by the 10% solution, can be calculated as follows:
Q = mcΔTQ = 100 × 4.18 × (T - 68) = 418 (T - 68)JQ = 533.2 × 4.18 * (T - 200) = 2222.44 (T - 200)J
For an adiabatic process, Q = 0. Thus, we can equate both equations:
418 (T - 68) = 2222.44 (T - 200)T = 79.5°F
Therefore, the temperature of the solution if the process is adiabatic is 79.5°F.
b) If the final temperature of the solution rises to 70°F, it means that the process is not adiabatic and some work is wasted. The work wasted can be calculated as follows:
Wasted work = Q - ΔU
where,Q is the heat lost by the 40% solution, which is the heat gained by the 10% solution, can be calculated as follows:
Q = mcΔT
Q = 100 × 4.18 × (70 - 68) + 533.2 × 4.18 × (70 - 200) = -4,400.408 JΔU is the change in internal energy. It can be calculated as:
ΔU = nCVΔT
where, n is the number of moles of the solution
CV is the molar specific heat
ΔT is the change in temperature
First, let's determine the number of moles of the final solution:
Moles of 10% NaOH solution = 100 / 40 = 2.5mol
Moles of 40% NaOH solution = 533.2 / 40 = 13.33mol
Total moles of the final solution = 2.5 + 13.33 = 15.83 mol
The molar specific heat of NaOH solution is 74.62 J/mol °C (assumed).
Then,ΔU = 15.83 * 74.62 * (70 - 40) = 35,600.65 J
Wasted work = Q - ΔU = -4,400.408 - 35,600.65 = -40,001.06 J
Therefore, the work wasted is 40,001.06 J.
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