The equation of line u, given that it is parallel to line t is:
y = –17x – 113
How to determine the equation of line uWe know that the equation of straight line is given as
y = mx + c
Where
y is the coordinate on y-axis x is the coordinate on x-axis m is the slope or gradient c is the intercept on y-axisFirst, we shall determine the slope of line u. This can be obtained as follow:
y = –17x – 2
Comparing y = mx + c with y = –17x – 2,
The slope (m₁) = –17
Recall,
The slope of parallel lines are equal.
Thus,
The slope of line u, is given as:
m₂ = m₁ = –17
Finally, we shall obtain the equation of line u as follow:
Coordinate = (7, 6) x coordinate 1 (x₁) = 7y coordinate 1 (y₁) = 6Slope of line u (m₂) = –17Equation of line u=?y – y₁ = m₂(x – x₁)
y – 6 = –17(x – 7)
Clear bracket
y – 6 = –17x – 119
Rearrange
y = –17x – 119 + 6
y = –17x – 113
Thus, the equation of line u is y = –17x – 113
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Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so gradient of line u is -17.
Equation of line u is y = -17x + c
Substitute (7,6) into the equation to find c.
6 = -17(7) + c
c = 125
Hence, equation of line u is y = -17x + 125.
A piece of metal has a mass of 32.4g and has a volume of 24.9cm³. What is its
density?
Answer:
1.30 g/cm3
Explanation:
d = m/V = 32.4g / 24.9cm3 = 1.30 g/cm3
What is the meaning of molecules
The question requires us to provide the meaning of "molecules".
A molecule can be defined as a group of atoms (being from the same or different elements) that are bonded together, which forms the smallest unit of a chemical compound. A molecule can also be defined as the smallest unit of a substance that presents the same physical and chemical properties of the substance.
Give the shell electron configuration for the following. (For example, the shell electron configuration of lithium is written 2,1.)(a) fluorine(b) nitrogen
(a) Fluorine= (2,7)
(b) Nitrogen=(2,5)
13. The percentage composition of a compound is
a . the percentage by volume of each element in the compound.
b . the percentage by mass of each element in the compound.
c . molar mass of the compound ÷ the mass of each element in 1 mol of the compound.
d . the mass of each element in 1 mol of the compound the molar
e . mass of the compound.
Explanation:
The percentage composition of any given compound is nothing but the ratio of the amount of each element present in the compound to the total amount of individual elements present in the compound multiplied by 100. Here, we measure the quantity in terms of grams of the elements present in the solution.
The Kp for the reaction A (g) ⇌ 2 B (g) is 0.0440. What is Kp for the reaction 4 B (g) ⇌ 2 A (g)?
The Kp for the reaction is 516.52.
When a chemical process reaches equilibrium, the equilibrium constant (often represented by the letter K) sheds light on the interaction between the reactants and products.
The equation is :
A (g) ⇌ 2 B (g)
The reaction in question is the reverse of 2 times the original
4 B (g) ⇌ 2 A (g)
K for the reverse reaction is 1/K forward
K for doubling the coefficients is K squared
Therefore K in the present condition is 1 / K2 of the original...
1 / (0.044)² = 516.52
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What is the mass in grams of 7.54 x10^30 formula units of magnesium chloride?
The molar mass of magnesium chloride is 95.211 grams/mole.
Mass in grams of 7.54 x10³⁰ formula units of magnesium chloride is 7.178 gram
Mass is the measure of amount of matter in a substance or an object and magnesium chloride is the chemical compound this salt are typically ionic halide being highly soluble in water
Here given data is
Molar mass of magnesium chloride = 95.211 grams/mole
Number of mole of magnesium given = 7.54 x10³⁰
Therefore mass of magnesium chloride
Molar mass × number of mole
Mass = 95.211 grams/mole × 7.54 x10³⁰
Mass = 7.178 gram
Mass in gram is 7.178 gram
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1) A cup of kidney beans weighs about 177 g, and contains 15 g of protein, 1.0 g of fat, and 39
g of carbohydrate. Determine the amount of protein, fat, carbohydrate, and the total
energy content (in nutritional calories) for a 100 g sample of beans.
The total energy contain for a 100g sample of beans is 0.24 kcal.
What is energy contain?
the capacity for doing work. It may exist in kinetic, thermal, electrical or chemical, nuclear, or various forms. There are moreover, heat and work eg, energy in the process of transfer from one body to other.
Sol-
15 g protein x 4 cal/g = 60 cal
1.0 g fat x 9 cal/g =
9 cal
42 g carb x 4 cal/g =
168 cal
Total calories =
60 + 9 + 168 = 237 calories
237 cal x 1 kcal/1000 cal = 0.237 kcal
The significant figure would 0.24 kcal .
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Which one of the following gases would be expected to have the highest speed if all the gases were at the same temperature?
A) O2
B) N2
C) F2
D) H2
Please explain why!
Hydrogen(H₂) will have the highest speed if all the gases were at the same temperature; correct option is D
What is hydrogen?Hydrogen is described as the chemical element with the symbol H and atomic number 1. Hydrogen is also known as the lightest element which at standard conditions is a gas of diatomic molecules having the formula H₂.
Hydrogen has lowest molecular mass as compared to other gases in the group of options . So, therefore we can conclude that it will have highest speed.
Hydrogen is known to be a colorless, odorless, tasteless, flammable gaseous substance that is the simplest member of the family of chemical elements.
Hydrogen is found to be present in water and in almost all molecules in living things and remains bonded with carbon and oxygen atoms. Hydrogen is widely said to be the most abundant element in the universe.
Hydrogen is spotless and is non-toxic and safe to produce from various different sources, transport, and store in large amounts.
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Help
- Correct answer to multiple choice = marked, rated to max and thanked
Any liquid has a 1 atmosphere vapor pressure at its boiling point. At 90 degrees Celsius, water has a vapor pressure of 0.692 atm.
How to calculate water pressure?The weight exerted on a unit area of the surface where the tank is kept determines the pressure at the bottom of a tank that is holding water.
That is equivalent to:
pressure = weight/area,
weight = mass (m) × acceleration due to gravity, and
weight = mass (m) (g).
Thus, pressure is defined as m × g/area.
At 90 degrees Celsius, water has a vapor pressure of 0.692 atm.
simple pressure = e^(20.386 - (5132 / (temperature + 273)) , where vapor pressure exists represented in mmHg and temperature in kelvins.
P total = p1 + p2
The relationship between mole fraction and vapour pressure at constant temperature.
Any liquid has a 1 atmosphere vapor pressure at its boiling point. Water has a single atmosphere of vapor pressure at 100 degrees Celsius. As a result, the boiling point of water is 100 degrees Celsius.
Therefore, the correct answer is option b) 69 k pa.
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What is the most common version of an isotope?
a. atomic number
b. average atomic number
c. mass number
The quantity of protons in an atom's nucleus is known as the atomic number. The number of protons determines an element's identity (i.e., an element with 6 protons is a carbon atom, no matter how many neutrons may be present).
Answer :A. Atomic number
What is an isotope's atomic number?The number of protons in an atom determines its atomic number, and isotopes have the same atomic number but different numbers of neutrons.
All isotopes of a given element have the same atomic number because they all have the same amount of protons (for example, the atomic number of helium is always 2).
An isotope is one of two or more chemical elements that exist in different forms. Varied isotopes of an element share the same atomic number and protons in their nuclei, giving them the same atomic weight. However, each elemental isotope has a different amount of neutrons, which changes its atomic weight.
The two chlorine isotopes that are found in nature are represented by the symbols 3517Cl and 3717Cl.
The elements hydrogen, deuterium, and tritium each have one isotope.
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You order a glass of lemonade, 150 mL, in a restaurant only to discover that it is warm and too sweet. The sugar concentration of the lemonade is 2.27 M but you would like it to be reduced to a concentration of 1.88 M.How many moles of sugar are in the lemonade solution?
0.3405moles.
Explanations:
In order to get the moles of sugar, we need to get the final volume using the dilution factor as shown below:
[tex]C_1V_1=C_2V_2[/tex]where:
• C1 and C2 are the, initial and final ,concentration
,• V1 and V2 are the, initial and final, volume
Given the following parameters:
C1 = 2.27M
V1 = 150mL = 0.15L
C2 = 1.88M
V2 = ?
Substitute the given parameters into the formula:
[tex]\begin{gathered} 2.27\times0.15=1.88\times V_2 \\ 0.3405=1.88V_2 \\ V_2=\frac{0.3405}{1.88} \\ V_2=0.181L \end{gathered}[/tex]Next is to get the moles of sugar in the lemonade solution using the formula below:
[tex]\begin{gathered} \text{Molarity}=\frac{\text{number of mole}}{volume} \\ n=vM \\ n=0.181L\times1.88\frac{mol}{L} \\ n=0.3405moles \end{gathered}[/tex]Hence the number of moles of sugar that are in the lemonade solution is 0.3405moles.
What is the density of a sample if its mass is 44.3g and its volume is 22.1cm?
Answer:
about 2 g/cm
Explanation:
D = M/V
D = 44.3/22.1
D ≈ 2
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What is the molarity of a solution containing 14.6 g of KCl in 281 mL of KCl solution?
Answer:
0.698 M.
Explanation:
Let's remember the concept of molarity: The molarity (M) of a solution is the number of moles of solute dissolved in one liter of solution. To calculate the molarity of a solution, divide the moles of solute by the volume of the solution expressed in liters, like this:
[tex]Molarity\text{ \lparen M\rparen=}\frac{moles\text{ of solute}}{liter\text{s of solution}}=\frac{mol}{L}.[/tex]To find the moles of solute (KCl, in this case) we have to convert 14.6 g of KCl to moles using its molar mass which is 74.5 g/mol, like this:
[tex]14.6\text{ g KCl}\cdot\frac{1\text{ mol KCl}}{74.5\text{ g KCl}}=0.196\text{ moles KCl.}[/tex]Now, let's convert 281 mL to L. Remember that 1 L equals 1000 mL:
[tex]281\text{ mL}\cdot\frac{1\text{ L}}{1000\text{ mL}}=0.281\text{ L.}[/tex]The final step is to replace the data that we obtained in the molarity formula:
[tex]Molarity=\frac{0.196\text{ moles}}{0.281\text{ L}}=0.698\text{ M.}[/tex]The answer would be that the molarity of the solution is 0.698 M.
What is the mass in grams of magnesium chloride that can be produced from 4.61 moles of chlorine gas reacting with excess magnesium? Mg(s) + Cl₂(g) → MgCI₂(s)
The mass of MgCI₂ produced from 4.61 moles of chlorine is 437.95g
What is mole ?
In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.
The mole designates 6.02214076 1023 units, which is a very large number. The mole for the International System of Units is this quantity, according to the General Conference on Weights and Measures (SI)
Mg(s) + Cl₂(g) → MgCI₂(s)
1mol Cl2 gives 1 mol MgCl2
4.61mol Cl2 gives 4.61 mol MgCl2
Mass of 1 mol of MgCl2 = 24+35.5*2 = 95g
Mass of 4.61 mol of MgCl2 = 437.95g
The mass of MgCl2 produced from 4.61 moles of chlorine is 437.95g
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what volume of 0.125M Oxalic acid, is required to react with 35.2mL of 0.546 M NaOH
The volume of oxalic acid required for the reaction is 76.8 mL.
What are neutralization reactions?Neutralization reactions are reaction in which acids reacts with bases to form salt and water only.
The neutralization reaction between oxalic acid and NaOH is given in the equation below:
(COOH)₂ (aq) + 2 NaOH (aq) ---> (COONa)₂ (aq) + H₂O (l)
The mole ratio of oxalic acid to NaOH is 1 : 2
moles = volume * molaritymoles of NaOH = Moles of oxalic acid /2
Moles of NaOH = 35.2 mL * 0.546 = 19.2 mmoles
Moles of oxalic acid = 19.2 / 2 = 9.6 mmoles
Volume of oxalic acid required = 9.6 / 0.125
Volume of oxalic acid = 76.8 mL
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a large university says that it has several satellite campuses. what does this mean?
Answer:
A satellite campus or branch campus or regional campus is a campus of a university or college that is physically at a distance from the original university or college area. This branch campus may be located in a different city, state, or country, and is often smaller than the main campus of an institution.
During an experiment, a student adds 1.23 g CaO
to 200.0 mL
of 0.500 M HCl
. The student observes a temperature increase of 5.10 °C
.
Assuming that the solution's final volume is 200.0 mL
, the density is 1.00 g/mL
, and the heat capacity is 4.184 J/g⋅°C
, calculate the heat of the reaction, Δrxn
.
CaO(s)+2H+(aq)⟶Ca2+(aq)+H2O(l)
CaO
(
s
)
+
2
H
+
(
aq
)
⟶
Ca
2
+
(
aq
)
+
H
2
O
(
l
)
The heat released by the experiment, assuming that the solution's final volume is 200.0 mL, the density is 1.00 g/mL, and the heat capacity is 4.184 J/g⋅°C is -194 KJ/mol.
What is density?Density is defined as mass of a material substance per unit of the volume. The equation for density is d = M/V, where d stands for density, M for mass, and V for volume.
Grams per cubic centimeter are a common unit of density measurement. For instance, the density of Earth is 5.51 grams per cubic centimeter, whereas the density of water is 1 gram per cubic centimeter.
The equation of the reaction is;
CaOH(aq) + 2HCl(aq) --------> CaCl2(aq) + 2H2O(l)
From the information provided in the question;
No. of moles of CaO = 1.23 g/ 56 g/mol = 0.022 moles
No. of moles of HCl = 0.500 M × 200/1000 = 0.1 moles
We now have to obtain the limiting reactant
From the reaction equation;
one mole of CaO reacts with 2 moles of HCl
0.022 moles moles of CaO reacts with 0.022 moles × 2 moles/1 mole
= 0.044 moles
Hence there is more than enough HCl so CaO is the limiting reactant.
Temperature rise of the reaction = 5.10 °C
Total volume of solution = 200.0 ml
Density of solution = 1.00 g/ml
Mass of solution = 200 g
Heat capacity of solution = 4.184 J/g·°C
We know that, heat absorbed by solution = heat released by the reaction
Heat absorbed by solution = mcθ
m = mass of solution
c = heat capacity of solution
θ = temperature rise
Substituting values;
ΔH = 200g × 4.184J/g·°C × 5.10°C
ΔH = 4.27 KJ
Therefore, heat released by the reaction;
ΔHrxn = (- 4.27 KJ)/0.022 moles
ΔHrxn = -194 KJ/mol
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copper, x-rays of frequency 2.74 × 10^19 Hz
are emitted. What is the wavelength of these
x-rays?
Answer in units of pm.
The wavelength of the x-rays is 1.094 * 10⁻⁵ pm.
What is the relationship between the frequency and wavelength of a wave?The frequency of a wave is the number of complete oscillations completed by the wave per second. Its unit is Hertz.
The wavelength of a wave is the distance between successive points in phase in the wave. It is measured in units of meter.
The relationship between the wavelength and frequency of a wave is given below.
Wavelength = velocity of the wave / frequency
The frequency of X-rays = 3.0 * 10⁸ m/s
frequency of the wave = 2.74 × 10¹⁹ Hz
Wavelength = (3.0 * 10⁸ m/s) / (2.74 × 10¹⁹ Hz)
wavelength = 1.094 * 10⁻¹¹ m
wavelength = 1.094 * 10⁻⁵ pm.
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A researcher studying the nutritional value of a new candy places a 5.30 g sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.49 ∘C. If the heat capacity of the calorimeter is 40.80 kJ⋅K−1, how many nutritional Calories are there per gram of the candy
The nutritional calories per gram of candy will be 5010 Cal/g
Given,
mass(m) = 4.1g
ΔT = 2.1K
Heat capacity (C) = 41.50KJ/K
= 41.50÷ 4.2 Kcal/K (since, 1cal = 4.2j)
(C) = 9.8 ×1000 Cal/K
We know that,
Q = msΔT where (C = ms) and also,
Q = CΔT = (9.8 × 1000×2.1)Cal
(Q/m = nutritional calorie per gram)
Q/m = 9.8×1000×2.1 ÷ 4.1 Cal/g
= 5010 Cal/g or 5.01KCal/g
Therefore the nutritional calories per gram of the candy will be 5010Cal/g or 5.1 KCal/g
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The nutritional calories per gram of candy will be 5010 Cal/g.
mass (m) is 4.1 g
ΔT is 2.1 K
Heat capacity (C) is 41.50 KJ/K
= 41.50÷ 4.2 K cal/K (since, 1 cal is 4.2 j)
(C) = 9.8 ×1000 Cal/K
We know that,
Q is msΔT where (C = ms) and also,
Q = CΔT = (9.8 × 1000×2.1)Cal
(Q/m = nutritional calorie per gram)
Q/m = 9.8×1000×2.1 ÷ 4.1 Cal/g
= 5010 Cal/g or 5.01KCal/g
Therefore, if the heat capacity of the calorimeter is 40.80 kJ⋅K−1 the nutritional calories per gram of the candy will be 5010 Cal/g or 5.1 KCal/g.
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What do you notice about the force and the product of mass and acceleration, ma?
The force and the product of mass and acceleration, ma , is used to describe the relationship between the mass of object and the amount of force acting to accelerate it.
The newtons second law states that : The force ( F ) acting on a moving body is the product of mass ( m ) and the acceleration ( a).
the expression is given as :
F = ma
where,
F = net force acting on an object
m = mass of the object
a = acceleration
of the object
we can use this formula in three different ways:
1) To calculate the force :
F = ma
2) To calculate the mass :
m = F / a
3) To calculate the acceleration :
a = F / m
Thus, The force and the product of mass and acceleration, ma , is used to describe the relationship between the mass of object and the amount of force acting to accelerate it.
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You are in charge of a plant that makes methyl bromide, CH3Br. This compound is used as a fumigant for nematodes. The thermochemical equation for the reaction is: CH3OH(aq) + Br−(aq) equilibrium reaction arrow CH3Br(aq) + OH −(aq) ΔH = +78 kJ/mol. You must maximize the yield of the product. Which of the following actions should you take? (Select all that apply.)
remove Br− ion
remove CH3OH
allow excess CH3Br to build up in the reaction
run the reaction with excess CH3OH
run the reaction with excess Br− ion
cool the reaction
heat the reaction
remove CH3Br as it is formed
You are in charge of a plant that makes methyl bromide,CH₃Br this compound is used as a fumigant for nematodes the thermochemical equation for the reaction is: CH₃OH(aq) + Br⁻(aq) equilibrium reaction arrow CH₃Br(aq) + OH⁻(aq) ΔH = +78 kJ/mol you must maximize the yield of the product when run the reaction with excess CH₃OH
Thermochemical is the reaction in which energy and heat associated with chemical reaction or physical transformation
The yield is maximum because the reactant will allow more and more to build up the reaction and here given reaction is
CH₃OH(aq) + Br⁻(aq)
In which when run the reaction with excess CH₃OH then automatically the yield of the reaction is become maximize and in the reaction the reactant run in excess amount automatically the yield as well as the product are become more
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slice of Swiss cheese contains 42 mg of sodium.
(a) What is this mass in grams?
g
(b) What is this mass in ounces? (16 oz = 453.6 g)
oz
(c) What is this mass in pounds? (1 lb = 453.6 g)
grams would be 47 mg of sodium based on conversion ratios.
a. 0.047
b. 0.00166 ounces
c. 0.000104 kg.
grams of mass
A gram is one gram.
47 mg is equivalent to 0.47 / 1,000 or 0.047 grams.
Since 16 ounces are equal to 453.6 grams of mass, 0.047 grams would be equal to 0.00166 ounces when divided by 453.6.
Weight in Pounds
Given that 1 pound weighs 453.6 grams, 0.047 grams would equal 0.000104 pounds.
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C2H4O2 IS THE EMPIRICAL FORMULA FOR GLUCOSE?
The correct empirical formula of the glucose molecule is [tex]CH_{2} O[/tex].
What is the empirical formula?The empirical formula is the simplest formula of the compound. Let us note that the structural formula shows the arrangement of the atoms of the compound while the molecular formula shows the number of each of the atoms that is in the substance.
Now we know that the empirical formula determines the ratio of each of the atoms that are in a compound as such the formula that is shown can not be the empirical formula of glucose as we can see in the question that is above here.
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The absolute magnitude (brightness) of Antares is -5.28, and the absolute magnitude of procyon is 2.68. Which star is more luminous? Which star is closer?
The absolute magnitude (brightness) of Antares is -5.28, and the absolute magnitude of procyon is 2.68 then antares star is more luminous and antares is closer
Magnitude is simply defined as the distance or quantity and absolute or relative direction or size in which an object move in the sense of motion called magnitude and here given data is
Absolute magnitude of Antares = -5.28
Absolute magnitude of procyon = 2.68
And here given according to the given magnitude the Antares has negative magnitude so it is star closer and also the more luminous star because the Absolute magnitude of procyon is in positive number so it is far away and not a luminous as well as closer star so the because of less magnitude the antares star is more luminous and antares is closer
Larger magnitudes correspond to fainter stars so here 2.68>-5.28 and that means Antares appear in closer star as well as more luminous
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would He gain stability by adding one H
Helium gains no stability by adding one H because it is already stable due to a complete valance shell or orbit.
How do elements gain stability?
To attain stability an atom will gain, lose, or share electrons to complete the outermost shell means the last shell. Helium atom has two electrons in the first orbit which completes the doublet rule so it is stable we know that noble gases are stable elements and we know that helium is also a member of a noble family. Nuclides are the most stable because it contains even numbers of both protons and neutrons which make them less radioactive. Nuclear stability is greater in nuclides that comprise even numbers of protons and neutrons or both.
So we can conclude that the helium atom does not need hydrogen to get stability.
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PLEASE HELPPP!
Usually scientists will ___ a large isotope such as Uranium-235 with a ____. The collision results in several more nuclear fissions, also known as a ____. This results in a HUGE release in energy!
Usually scientists will collide a large isotope such as Uranium-235 with a neutron. The collision results in several more nuclear fissions, also known as a chain reaction . This results in a HUGE release in energy!
Nuclear fission occurs when large isotopes such as uranium - 235 collide with neutron and split into two or more smaller atoms. and releases a large quantity of energy. in this process nucleus of atom split into two or more smaller nuclei . this result in huge release in energy and resulting in chain reaction.
Thus, Usually scientists will collide a large isotope such as Uranium-235 with a neutron. The collision results in several more nuclear fissions, also known as a chain reaction . This results in a HUGE release in energy!
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A beaker is filled with 225.0mL of sodium hydroxide solution with an unknown concentration. A 0.00100 M solution of HCI is used in the titration. the equivalence point is reached when 27.0mL of HCI have been added.What is the initial concentration of NaOH in the beaker
The titration formula is used when we have an equivalence point of neutralization between acid and base, the formula is:
Ma * Va = Vb * Mb
Where:
Ma = concentration of acid
Va = volume of acid
Mb = concentration of base
Vb = volume of base
This formula tells us the concentration and volume of an acid must be equal to the concentration and volume of a base in order to neutralize the reaction (this applies to strong acids and strong bases only)
Ma * Va = Vb * Mb
0.00100 * 27 = 225 * Mb
0.027 = 225Mb
Mb = 0.00012M
What particles are found in the nucleus of an atom?
What is the charge of the nucleus?
Answer:
1. Protons and neutrons
2. Positive charge
Explanation:
A nucleus contains protons and neutrons. Protons have a positive charge and neutrons have a neutral charge. Neutral + positive would still be positive. So logically nucleus is positive charge.
Please explain/show how to create a concept map with the following terms. See picture for question. Thank you
Answer:
We are asked to create a concept map with the terms:
• chemical bonds
,• ionic bonds
,• covalent bonds
,• metallic bonds
,• Molecules
,• ions
As we can see we have a general topic which is chemical bonds.
Then we have 3 different types of bonds: ionic, covalent and metallic.
Finally, these types of bonds can form either molecules or an array of ions (in the case of metallic bonds.
In orther to understant it better we first list the deffinitions of these 3 types of bonding:
Covalent bonds: is a bond between two atoms that share a pair of valence electrons. This bond produces a molecule.
Ionic bonds: is a bond between a metallic element and a non metallic element. The first gives electrones to the other, resulting in a molecule.
Metallic bonds: these are bonds that result exclusevely in metal compound. Metals are crystalline solids, a huge array of atoms that share valence electrones.
Therefore we can array these concepts in the following map:
a balloon has a volume of 1.20 L at 24.0 C. The balloon is heated to 48.0 C. Calculate the new volume of the balloon.
Answer
To solve this excescise we use the ideal gas equation:
[tex]P.V=n.R.T[/tex]Where:
P is the pressure of the gas
V is the volume
T is the temperature
R is the ideal gas constant
n is the number of moles
As the balloon is a closed recipient n is the same in state 1 (T: 24°C) and state 2 (T: 48°C).
R is a constant so also remains the same.
The pressure is also a constant in this case as the only thing that we do to the balloon is heat it.
So therefore:
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}=\frac{n.R}{P}[/tex]Now we calculate the volume at 48°C (V2):
[tex]V_2=\frac{V_{1.}T_2}{T_1}=\frac{1.2L.48\degree C{}}{24\degree C}=2.4L[/tex]As we can see as the temperature rises the volume of the gas increases because the molecules have more kinetic energt and they remain farther apart.
The answer then is the new volume of the balloon is 2.4L