6. Calculate the molecular mass of acetylsalicylic acid (HOOC-C6H4-OOCCH3).

Answers

Answer 1

The molecular mass of acetylsalicylic acid (HOOC-C6H4-OOCCH3) is 180.157 g/mol.What is molecular mass Molecular mass is the sum of the masses of all the atoms in a molecule. The unit of molecular mass is grams per mole the are (g/mol).Acetylsalicylic acid molecular

mass calculation In acetylsalicylic acid, HOOC-C6H4-OOCCH3, add the mass of each atom:Oxygen (O) = 2 x 16.00 g/mol = 32.00 g/ (C) = 9 x 12.01 g/mol = 108.09 g/mol Hydrogen (H) = 8 x 1.01 g/mol = 8.08 g/molAdd the masses of all the atoms to calculate the molecular mass:32.00 g/mol + 108.09 g/mol + 8.08 g/mol = 148.17 g/molThe molecular mass of acetylsalicylic acid is 180.157 g/mol (approximately)

Molecular mass is the mass of a molecule measured in atomic mass units (amu). The molecular mass is the sum of the atomic masses of all the atoms present in the molecule.The molecular mass formula can be written as: Molecular mass = (mass of first element × number of atoms) + (mass of second element × number of atoms) + ...The molecular mass of acetylsalicylic acid (HOOC-C6H4-OOCCH3) can be calculated by adding the mass of each atom. Here's how to calculate the molecular mass of acetylsalicylic acid:Oxygen (O) = 2 x 16.00 g/mol = 32.00 g/molCarbon (C) = 9 x 12.01 g/mol = 108.09 g/molHydrogen (H) = 8 x 1.01 g/mol = 8.08 g/molAdd the masses of all the atoms to calculate the molecular mass:32.00 g/mol + 108.09 g/mol + 8.08 g/mol = 148.17 g/molThe molecular mass of acetylsalicylic acid is 180.157 g/mol (approximately) the formula to calculate molecular mass.

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Related Questions

Which of Graphs 1 correctly represents the relationship between the pressure and volume of a gas?

Answers

Answer:

D

Explanation:

pressure is inversely proportional to gas volume

Compound X has molecular formula C5H10. In the presence of a metal catalyst, compound X reacts with one equivalent of molecular hydrogen to yield 2-methylbutane.
a. Suggest three possible structures for compound X.
b. Hydroboration-oxidation of compound X yields a product with no chirality centers. Identify the structure of compound X.

Answers

The structure of compound X is likely 2-Methyl-1-butene (CH3CH=C(CH3)CH2CH3) to yield a product without chirality centers during hydroboration-oxidation.

a. Suggesting three possible structures for compound X (C5H10) can involve considering different isomers of pentane and pentene. Here are three possibilities:

Pentane: CH3CH2CH2CH2CH3

2-Methylbutane: CH3CH(CH3)CH2CH3

2-Methyl-1-butene: CH3CH=C(CH3)CH2CH3

These structures satisfy the molecular formula C5H10 and represent different isomeric possibilities for compound X.

b. Hydroboration-oxidation of compound X yields a product with no chirality centers. This suggests that compound X must be an alkene with a symmetric or non-chiral structure. Among the three possible structures suggested above, the alkene 2-Methyl-1-butene (CH3CH=C(CH3)CH2CH3) would result in a product with no chirality centers when subjected to hydroboration-oxidation.

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An amphoteric species is neither an acid nor a base. True or False

Answers

Answer: False

Explanation: just took on edge

What is the absolute magnitude of the rate of change for [NH₃] if the rate of change for [H₂] is 8.70 m/s in the reaction 2 NH₃(g) → N₂(g) + 3 H₂(g)?
a. 4.35 m/s
b. 8.70 m/s
c. 17.40 m/s
d. 26.10 m/s

Answers

Given, the balanced chemical equation is:

2 NH₃(g) → N₂(g) + 3 H₂(g)

The absolute magnitude of the rate of change for [NH₃] is 4.35 m/s.

Therefore, option A is the correct answer.

Given, the balanced chemical equation is:

2 NH₃(g) → N₂(g) + 3 H₂(g)

The rate of change for H2 is 8.70 m/s.

To find the absolute magnitude of the rate of change for [NH₃], we have to use the stoichiometric coefficient in the balanced chemical equation. From the balanced chemical equation, 2 mol NH₃ reacts with 3 mol H₂

We can write,

Rate of change of NH₃ (in m/s) = -1/2 * rate of change of H₂ (in m/s)

So,Rate of change of NH₃ = -1/2 * 8.70 m/s= -4.35 m/s

The absolute magnitude of the rate of change for [NH₃] is 4.35 m/s.

Therefore, option A is the correct answer.

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how much water, in grams, can be made from 3.58 × 1024 hydrogen molecules? answer in units of g.

Answers

To determine the amount of water that can be made from a given number of hydrogen molecules, the molar ratio between hydrogen and water needs to be considered. Based on the balanced chemical equation for the formation of water, 2 moles of hydrogen molecules (H2) react to form 2 moles of water (H2O). Using the Avogadro's number and molar mass of water, the calculation can be performed to find the mass of water in grams.

The balanced chemical equation for the formation of water is:

2H2(g) + O2(g) → 2H2O(l)

From the equation, it can be observed that 2 moles of hydrogen molecules (H2) react to produce 2 moles of water (H2O).

Using Avogadro's number (6.022 × 10^23 molecules per mole), we can determine the number of moles of hydrogen molecules present in 3.58 × 10^24 hydrogen molecules:

Number of moles of hydrogen = (3.58 × 10^24) / (6.022 × 10^23) = 5.95 moles

Since the molar ratio between hydrogen and water is 2:2, we can conclude that 5.95 moles of hydrogen will produce 5.95 moles of water.

To find the mass of water, we need to multiply the number of moles of water by the molar mass of water. The molar mass of water (H2O) is approximately 18.015 g/mol.

Mass of water = 5.95 moles × 18.015 g/mol = 107.17 g

Therefore, approximately 107.17 grams of water can be made from 3.58 × 10^24 hydrogen molecules.

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calculate the percent by mass of a solution made from 17 g nacl (the solute) and 59 g water.

Answers

The percent by mass of the solution made from 17 g sodium chloride, NaCl (the solute) and 59 g water is 22.4%

How do i determine the percent by mass of the solution?

First, we shall obtain the mass of the solution. Details below:

Mass of NaCl = 17 gramsMass of water = 59 gramsMass of solution = ?

Mass of solution = Mass of NaCl + mass of water

Mass of solution = 17 + 59

Mass of solution = 76 grams

Finally, we shall determine the percent by mass of the solution. Details below:

Mass of NaCl = 17 gramsMass of solution = 76 gramsPercent by mass =?

Percent by mass = (mass of NaCl / mass of solution) × 100

= (17 / 76) × 100

= 22.4%

Thus, the percent by mass of the solution is 22.4%

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Consider atoms of the following elements. Assume that the atoms are in the ground state.
(A) S (B) Ca (C) Ga (D) Sb (E) Br
1. The atom that contains exactly two unpaired elec¬trons
2. The atom that contains only one electron in the highest occupied energy sublevel

Answers

(A) Sulfur (S) is the atom that contains exactly two unpaired electrons, and (E) Bromine (Br) is the atom that contains only one electron in the highest occupied energy sublevel.

(A) Sulfur (S) has an electron configuration of 1s² 2s² 2p⁶ 3s² 3p⁴. The highest energy level, or valence shell, for sulfur is the third energy level (n = 3). The 3p sublevel has four electrons (3p⁴), and among them, two are unpaired. These two unpaired electrons in the 3p sublevel make sulfur the atom that contains exactly two unpaired electrons.

(E) Bromine (Br) has an electron configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵. The highest occupied energy level for bromine is the fourth energy level (n = 4). The highest energy sublevel within the fourth energy level is the 4p sublevel. In the 4p sublevel, there are five electrons (4p⁵), and only one electron is needed to complete the sublevel. Thus, bromine contains only one electron in the highest occupied energy sublevel.

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What is the herbivore in the following food chain: algae → fish → herons?

Answers

Answer:

algae

Explanation:

fish and herons arent herbivores

Herbivores are typically tagged as animals that feeds directly on the plants in a food chain.

In the given food chain, Fish is the herbivore

As stated, Fish in the food chain is the herbivore as it feeds directly on the plants. The algae in this case is the producer. While the herons are the carnivore that feeds directly on the flesh of the fish but indirectly on the algae.

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Think about a wooden chair and a balloon. What do these two objects always have in common?


Both are made of atoms.


Both have the same physical properties.


Both are made of the same kind of atom.

Both are made of the same number of atoms.

Answers

Answer:

both are made of atoms. .

Answer:

Both are made of atoms.

Explanation:

50 POINTS PLEASE ANSWER CORRECTLY
What happens to the momentum of two cars when they collide?

A. The total momentum after the collision increases.

B. The total momentum after the collision decreases.

C. The total momentum after the collision is equal to the total momentum before the collision.

D. The total momentum before and after the collision is not conserved.

Answers

Answer: I honestly think it might be C

Explanation: Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. ... In the collision between the two cars, total system momentum is conserved.

Answer: C. The total momentum after the collision is equal to the total momentum before the collision.

Hope this helps

Explanation: Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. ... In the collision between the two cars, total system momentum is conserved.

Which statement correctly describes extreme weather?
O A. Extreme weather events follow normal climate patterns.
o O B. Extreme weather events are random occurrences.
O C. Extreme weather events started with global warming.
O D. Extreme weather events are unpredictable until they strike.

Answers

Answer: A

Explanation:

Extreme weather events follow normal climate patterns.

2. Below is a chemical reaction in which two solutions are combined:
CdSO. (aq)+KS(aq) → CdS(s)+ K₂SO4(aq)
a) What does the (s) mean?
b) For the reactants, cadmium sulfate and potassium sulfide, write a chemical equation showing that each of these dissolve in water.
c) On the products side, potassium sulfate is aqueous and cadmium sulfide is solid. What is the difference? How can you observe this difference in the lab?
d) What is the name for this type of reaction?

Answers

The reaction between CdSO₄ and K₂S is a precipitation reaction where cadmium sulfide precipitates as a solid, while potassium sulfate remains in the aqueous form.

a) The "(s)" in the chemical equation CdS(s) represents that cadmium sulfide is a solid precipitate. It indicates that the product formed in the reaction is solid.

b) The chemical equation for the dissolution of cadmium sulfate (CdSO₄) in water is:

CdSO₄(s) → Cd²⁺(aq) + SO₄²⁻(aq)

The chemical equation for the dissolution of potassium sulfide (K₂S) in water is:

K₂S(s) → 2K⁺(aq) + S²⁻(aq)

c) The difference between potassium sulfate being aqueous (K₂SO₄(aq)) and cadmium sulfide being a solid (CdS(s)) lies in their solubility in water. Potassium sulfate is soluble in water, meaning it dissolves and dissociates into its respective ions (K⁺ and SO₄²⁻) in the solution. On the other hand, cadmium sulfide is insoluble in water and forms a solid precipitate, indicating that it does not dissolve but instead forms solid particles.

In the lab, the difference can be observed by visual inspection. When the reaction between CdSO₄ and K₂S takes place, a yellow precipitate of cadmium sulfide will form, indicating the presence of the solid. The potassium sulfate, being in an aqueous form, will remain dissolved and not form any visible solid.

d) The name for this type of reaction is a precipitation reaction or double displacement reaction. In this reaction, the ions from two compounds exchange to form an insoluble solid (precipitate) and a soluble compound.

In the given reaction between CdSO₄ and K₂S, cadmium sulfide (CdS) is the insoluble solid (precipitate), and potassium sulfate (K₂SO₄) is the soluble compound formed in solution.

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For the Experiment, 10 mL of a DIVA Sciences’ White Vinegar sample will be dispensed and diluted to 100 mL in a 100-mL Volumetric Flask. Determine the range of initial concentrations.
Diluted DIVA Sciences’ White Vinegar (5%) Solution = ____________________ M
Diluted DIVA Sciences’ White Vinegar (8%) Solution = ____________________ M

Answers

To determine the range of initial concentrations, we need to consider the dilution process and the given information.

The initial volume of the vinegar sample is 10 mL, and it is diluted to a final volume of 100 mL. Therefore, the dilution factor is calculated by dividing the final volume by the initial volume:

Dilution factor = Final volume / Initial volume = 100 mL / 10 mL = 10

The diluted solutions are prepared by adding 10 mL of the vinegar sample to a 100 mL volumetric flask and filling it up to the mark with water. So, the final volume of each diluted solution is 100 mL.

Given that the diluted solutions are prepared from the original vinegar sample, we can infer that the percentage concentration refers to the mass/volume percentage. In this case, the percentages (5% and 8%) represent the mass of acetic acid (the main component of vinegar) present in 100 mL of the original sample.

To calculate the molarity of the diluted solutions, we need to know the molar mass of acetic acid, which is approximately 60.05 g/mol.

For the 5% solution:

Mass of acetic acid in 100 mL = (5 g / 100 mL) × 100 mL = 5 g

Using the molar mass, we can convert the mass of acetic acid to moles:

Moles of acetic acid = Mass of acetic acid / Molar mass = 5 g / 60.05 g/mol

Now, we can calculate the molarity:

Molarity (5% solution) = Moles of acetic acid / Final volume (in liters) = (5 g / 60.05 g/mol) / 0.1 L

For the 8% solution, we follow the same steps:

Mass of acetic acid in 100 mL = (8 g / 100 mL) × 100 mL = 8 g

Moles of acetic acid = Mass of acetic acid / Molar mass = 8 g / 60.05 g/mol

Molarity (5% solution) ≈ 0.833 M (rounded to three decimal places)

Molarity (8% solution) ≈ 1.333 M (rounded to three decimal places)

Therefore, the range of initial concentrations is approximately 0.833 M to 1.333 M for the diluted DIVA Sciences' White Vinegar solutions.

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In a heat engine, 500 J of heat enters the system, and the piston does 300 J of work. What is the final internal (thermal) energy of the system if the initial energy is 1500 J?

200 J
800 J
1300 J
1700 J

Answers

Answer:

200J

Explanation:

This is because 500J - 300J = 200J

I hope this helps!!!

Answer:

1700 Joules. I Took the test.

Explanation:

If the Earth did not have internal energy, explain what would happen to the carbon cycle and why?

Answers

Answer: Carbon cycle wouldn't be able to create rock formation. Respiration, consumption, combustion (such as fossil burning) are all part of the carbon cycle. They would all be possible without internal energy. Except rock formation.

Explanation:

What variable represents thermal energy in the equation Q = mcΔT?
A.
The variable c
B.
The variable Q
C.
The variable T
D.
The variable m

Answers

Answer:

The variable Q

Explanation:

i just took the test and got it right.... i hope this helps :)

The variable Q represents thermal energy in the equation Q = mcΔT. Hence, option B is correct.

What is specific heat capacity?

The specific heat capacity is defined as the quantity of heat (J) absorbed per unit mass (kg) of the material when its temperature increases by 1 K (or 1 °C), and its units are J/(kg K) or J/(kg °C).

Q =  mcΔT

Q = heat energy

m = mass

c = specific heat capacity

ΔT = change in temperature

Hence, option B is correct.

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How many mL of water to be added to 10 mL of 0.5M solution to make 0.2 M solution?

Answers

Answer:

0.7 is the right

Explanation:

Using standard heats of formation, calculate the standard enthalpy change for the following reaction. Fe(s) + 2HCl(aq)FeCl2(s) + H2(g) ANSWER: ___ kJ

Answers

The standard enthalpy change for the given reaction is approximately -156.87 kJ.

To calculate the standard enthalpy change (ΔH°) for the given reaction using standard heats of formation, the balanced equation for the reaction is:

Fe(s) + 2HCl(aq) → [tex]FeCl_2[/tex](s) + [tex]H_2[/tex](g)

The standard heats of formation (ΔH°f) for the compounds involved are as follows:

Fe(s): 0 kJ/mol

HCl(aq): -92.31 kJ/mol (source: NIST Chemistry WebBook)

[tex]FeCl_2[/tex](s): -341.49 kJ/mol (source: NIST Chemistry WebBook)

[tex]H_2[/tex](g): 0 kJ/mol

Now, let's calculate the standard enthalpy change (ΔH°):

ΔH° = Σ(ΔH°f products) - Σ(ΔH°f reactants)

ΔH° = [ΔH°f([tex]FeCl_2[/tex]) + ΔH°f([tex]H_2[/tex])] - [ΔH°f(Fe) + 2ΔH°f(HCl)]

ΔH° = [-341.49 kJ/mol + 0 kJ/mol] - [0 kJ/mol + 2(-92.31 kJ/mol)]

ΔH° = -341.49 kJ/mol + 2(92.31 kJ/mol)

ΔH° = -341.49 kJ/mol + 184.62 kJ/mol

ΔH° = -156.87 kJ/mol

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What is the oxidation number of bromine in the HBrO molecule? a. -1
b. +1 c. +2
d. -2

Answers

The oxidation number of bromine in the HBrO molecule is +1. Bromine usually has multiple oxidation states, and in HBrO, it has an oxidation state of +1, the correct answer is b.

This can be determined by assigning oxidation numbers to the other atoms in the molecule and applying the rules for assigning oxidation numbers. In HBrO, hydrogen (H) has an oxidation state of +1, and oxygen (O) typically has an oxidation state of -2. Since the sum of oxidation numbers in a neutral molecule is zero, the oxidation number of bromine (Br) is determined to be +1.

To further explain, oxidation numbers represent the hypothetical charge an atom would have if all the bonds were purely ionic. In HBrO, hydrogen (H) is typically assigned an oxidation state of +1, as it usually donates its one valence electron to form a single bond. Oxygen (O) is generally assigned an oxidation state of -2, as it commonly accepts two electrons to complete its valence shell. The sum of the oxidation numbers in HBrO is then +1 for hydrogen and -2 for oxygen, resulting in a net oxidation number of -1. Since the molecule is neutral, the oxidation number of bromine (Br) must be +1 to balance the charges and achieve a total oxidation number of zero. Therefore, the correct answer is b. +1.

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What happens in a redox reaction?

Answers

Electrons are transferred from one reactant to another and the oxidation states/oxidation number of certain atoms are changed

Which of the following cannot be metabolized to make molecules that can enter the citric acid cycle? a. carbohydrates b. lipids c. proteins
d. metal ions

Answers

The one that cannot be metabolised to make molecules that can enter the citric acid cycle is d. metal ions.

Carbohydrates, lipids, and proteins can all be metabolized to produce molecules that can enter the citric acid cycle (also known as the Krebs cycle or TCA cycle). These molecules can be converted into acetyl-CoA, a key intermediate in the citric acid cycle, through various metabolic pathways.

Carbohydrates can be broken down into glucose, which can then undergo glycolysis to produce pyruvate. Pyruvate can be further converted into acetyl-CoA, which enters the citric acid cycle.

Lipids (fats) can be hydrolyzed to release fatty acids and glycerol. Fatty acids are broken down through beta-oxidation, resulting in the production of acetyl-CoA. Glycerol can also be converted into glyceraldehyde-3-phosphate, an intermediate in glycolysis that can generate pyruvate and subsequently acetyl-CoA.

Proteins can be broken down into amino acids through protein digestion and cellular processes such as proteolysis. Amino acids can enter various metabolic pathways, some of which lead to the production of intermediates that can feed into the citric acid cycle.

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what is the mass of 2.31 x 10^23 formula units of SrF2?

Answers

Mole measure the number of elementary entities of a given substance that are present in a given sample. Therefore, 40.51 g is the mass of 2.31x10²³ formula units of SrF[tex]_2[/tex].

What is mole?

The SI unit of amount of substance in chemistry is mole. The mole is used to measure the quantity of amount of substance. It measure the number of elementary entities of a given substance that are present in a given sample.

Given number of atoms= 2.31x10²³atoms

we know one mole of any element contains 6.022×10²³ atoms which is also called Avogadro number

mole =given number of atoms ÷ 6.022×10²³(Avogadro number)

Substituting the values

mole= 2.31x10²³÷ 6.022×10²³

mole = 0.38 moles of SrF[tex]_2[/tex]

mass of SrF[tex]_2[/tex]= moles of SrF[tex]_2[/tex] × Molar mass of SrF[tex]_2[/tex]

mass of SrF[tex]_2[/tex]= 0.38  × 106.6184

mass of SrF[tex]_2[/tex] = 40.51 g

Therefore, 40.51 g is the mass of 2.31x10²³ formula units of SrF[tex]_2[/tex].

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Calcular la masa de Mg que se necesita hacer reaccionar con CuSO4 para formar 1.89 g de Cu2O según la siguiente ecuación: Mg + CuSO4 + H2O MgSO4 + Cu2O + H2

Answers

Answer:

0.642 g

Explanation:

La ecuación balanceada es:

2Mg + 2CuSO₄ + H₂O → 2MgSO₄ + Cu₂O + H₂

Primero convertimos 1.89 g de Cu₂O en moles, usando su masa molar:

1.89 g ÷ 143.09 g/mol = 0.0132 mol Cu₂O

Después convertimos moles de Cu₂O en moles de Mg, usando los coeficientes estequiométricos:

0.0132 mol Cu₂O * [tex]\frac{2molMg}{1molCu_2O}[/tex] = 0.0264 mol Mg

Finalmente convertimos moles de Mg en gramos, usando la masa molar de Mg:

0.0264 mol Mg * 24.305 g/mol = 0.642 g

Numbers 15-21

HELP PLEASE!!

Answers

I wish I could help you, but I cannot see your paper. Please re-upload so I can help you : )
Re upload the pic I can’t see it ://

A reaction yields 6.26 grams of a CuCl2. What is the percent yield of CuCl2 if the theoretical yield is 18.81g?
% Yield = (Actual Yield/Theoretical Yield) x 100

Answers

Answer:

33% yield

Explanation:

6.26/18.81 =0.33280170122 = 33%

Which two elements on the periodic table share the same period and are both gases?

A. Hydrogen and Helium

B. Fluorine and Bromine

C. Lithium and Potassium

D. Xenon and Argon

Answers

A
Hydrogen and Helium are the only elements in the periodic table that share the same period and are based

The particles of a substance lose energy and change from
a disordered structure with large distances between the particles to
a loosely ordered state.
Which change of state is described?

Answers

Answer:

A Liquid

Explanation:

structure with large distance (gas) than goes to a loosely ordered state (liquid)

I hope this helps

which statement best describes the reflection of a wave?

Answers

The best statement that describes the reflection of a wave is: When a wave reflects off a surface, it retains its characteristics and changes direction.

A wave is defined as a disturbance that moves through space and matter with the transfer of energy from one place to another. When the wave moves from one medium to another, it reflects off the surface. Reflection of a wave is described as the change in the direction of the wave when it bounces back from the surface on which it strikes.

When a wave reflects off a surface, the angle of incidence is equal to the angle of reflection, which is known as the law of reflection. The normal line, which is perpendicular to the surface, splits the incident and reflected waves at the point of incidence. The angle between the normal line and the incident wave is the angle of incidence, and the angle between the normal line and the reflected wave is the angle of reflection.

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A compound is found to be made up of 3.21 g Carbon and 1.02 g Oxygen. Determine the percent composition from this data?

Answers

Given :

A compound is found to be made up of 3.21 g Carbon and 1.02 g Oxygen.

To Find :

The percent composition from this data.

Solution :

We know, percentage composition is given by :

[tex]\%mass = \dfrac{mass}{mass of compound}\times 100[/tex]

So, percentage composition of Carbon is :

[tex]\%Carbon = \dfrac{3.21}{3.21+1.02}\times 100\\\\\%Carbon = \dfrac{3.21}{4.23}\times 100\\\\\%Carbon = 75.89 \%[/tex]

Since, compound is made up of Carbon and Oxygen.

So, %Oxygen is ( 100 - 75.89 )% = 24.11%

Hence, this is the required solution.

If a radioactive isotope has a half-life of 400 million years, how long will it take for 50% of the material to change to the daughter product?

Answers

If a radioactive isotope has a half-life of 400 million years, it will take 400 million years for 50% of the material to change to the daughter product.

How long it takes for half of the radioactive atoms to decay is known as the half-life of the isotope. A radioactive isotope's half-life is the amount of time it takes for half of the parent material to decay to the daughter product. It's worth noting that a half-life isn't a fixed amount of time for each radioactive isotope.

The following formula can be used to calculate the amount of radioactive isotope remaining after a given period of time:

t=ln(N₀/N) / λ

Where:

t= time elapsedN₀= initial quantity of isotopeN= quantity of isotope after a given timeλ= decay constant

For this problem, we need to solve for the time (t) at which 50% of the radioactive isotope has decayed:

0.5N₀ = N₀ e^(-λt)

0.5 = e^(-λt)

t = ln(0.5) / (-λ)

We know that the half-life of this isotope is 400 million years, which means that λ is equal to:

ln(2) / (400,000,000 years)

λ = 0.00000000017 / year

Substituting that value into the formula:

t = ln(0.5) / (-0.00000000017 / year)

t ≈ 400,000,000 years

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Other Questions
Intro You took out a fixed-rate mortgage for $133,000. The mortgage has an annual interest rate of 10.8% (APR) and requires you to make a monthly payment of $1,284.37. Part 1 Attempt 1/10 for 1 pts. How many months will it take to pay off the mortgage? 0+ decimals Submit Intro You took out some student loans in college and now owe $10,000. You consolidated the loans into one amortizing loan, which has an annual interest rate of 8% (APR). Part 1 Attempt 1/10 for 1 pts. If you make monthly payments of $200, how many months will it take to pay off the loan? Fractional values are acceptable. 0+ decimals Submit Intro You took out a 30-year fixed-rate mortgage to buy a house. The interest rate is 4.8% (APR) and you have to pay $1,010 per month. BAttempt 1/10 for 1 pts. Part 1 What is the original mortgage amount? 0+ decimals Submit An electron is released from rest in a uniform electric field and accelerates to the north at a rate of 137 m/s 2 .Part AWhat is the magnitude of the electric field?Part BWhat is the direction of the electric field?to the westto the southto the northto the east A charity holds a raffle in which each ticket is sold for $35. A total of 9000 tickets are sold. They raffle one grand prize which is a Lexus GS valued at $45000 along with 2 second prizes of Honda motorcycles valued at $9000 each. What are the expected winnings for a single ticket buyer? Express to at least three decimal place accuracy in dollar form (as opposed to cents).Answer: $ On a Saturday night, Husband and Wife simultaneously decide where to go for dinner. The options are Vietnamese restaurant (V) or Thai restaurant (T). If both opt for V, the payoffs are (8,8) to Husband and Wife, respectively. If both opt for T. the payoffs are (7, 5). If Husband chooses V and Wife chooses T, the payoffs are (3, 5). Finally, if Husband chooses T and Wife chooses to V, the payoffs are (5, 7). Choose ALL correct answers: The Nash equilibrium is (V. V); this is a dominant strategy equilibrium. Nash equilibrium is (V. V); this not a dominant strategy equilibrium. The Nash equilibria are (V, V) and (T. T); this is a coordination game. Husband has a dominant strategy. Wife has a dominant strategy. Evaluate 5|x - 21 + 7 when x = -2 Determine which of these characteristics are consistent with debt securities and which are consistent with common stock.a. Its dividends are fixed in amount.b. It has a par, or face, value.c. Failure to pay its dividend does not send the firm into bankruptcy. the path of air resembles the path of blood in the circulatory system. it starts off with bigger tubes, and as it moves in deeper into the lungs, it goes through intensive and extensive branching to reach the site of gas exchange (alveoli). study the anatomy of the lungs and follow the path of air through the respiratory structures. ow to answer this question please (allrequirements)Snow Showers operates a Rocky Mountain ski resort. The company is planning its lift-ticket pricing for the coming ski season. Investors would like to earn a 16% return on the company's $100 million of The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location.Pottery TypeSite TypeMesa VerdeBlack-on-WhiteMcElmoBlack-on-WhiteMancosBlack-on-WhiteRow TotalMesa Top796545189Cliff-Talus766770213Canyon Bench926371226Column Total247195186628Use a chi-square test to determine if site type and pottery type are independent at the 0.01 level of significance.(a) What is the level of significance?State the null and alternate hypotheses.H0: Site type and pottery are independent.H1: Site type and pottery are independent.H0:Site type and pottery are not independent.H1: Site type and pottery are independent.H0: Site type and pottery are not independent.H1: Site type and pottery are not independent.H0:Site type and pottery are independent.H1: Site type and pottery are not independent.(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)Are all the expected frequencies greater than 5?YesNoWhat sampling distribution will you use?Student's tnormal uniformchi-squarebinomialWhat are the degrees of freedom?(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?Since the P-value > , we fail to reject the null hypothesis.Since the P-value > , we reject the null hypothesis.Since the P-value , we reject the null hypothesis.Since the P-value , we fail to reject the null hypothesis.(e) Interpret your conclusion in the context of the application.At the 1% level of significance, there is sufficient evidence to conclude that site and pottery type are not independent.At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent. Aladdin is the owner and founder of Genie Limited. Aladdins wife, Jasmine, has a controlling investment in Jafar Limited. Which of the followings describes the relationship between Genie Limited and Jafar Limited?Select one:a. Genie Limited is a related party of Jafar Limited.b. Genie Limited has control over Jafar Limited.c. Genie Limited and Jafar Limited are not related parties.d. No disclosure about transactions with Jafar Limited is required in the financial statements of Genie Limited. Chocoholics Anonymous wants to modernize its production machinery. The company's sales are $9.48 million per year, and the choice of machine won't impact that amount. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis.Machine Amaretto costs $2,290,000 and will last for 4 years. Variable costs are 34 percent of sales, and fixed costs are $159,000 per year.Machine Baileys costs $4,740,000 and will last for 7 years. Variable costs for this machine are 28 percent of sales and fixed costs are $87,000 per year.(a)If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine Amaretto? (Do not round your intermediate calculations.)HINT: In EAC problems you first need to find the NPV. Using this NPV you can then calculate the annuity (annual cost) that has the same present value/cost. The lecture videos include a detailed example of this calculation.(b)If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine Baileys? (Do not round your intermediate calculations.) PLEASE I NEED ANSWER 1-4, CASE QUESTIONS. SHORT ANSWERIS OK. TYMANAGEMENT AT WORK The Road to Leadership "Your title makes you a manager, people decide if you're a leader." -Bill Campbell, Leadership Coach On November 14, 1970, a plane crash took the lives of 37 Consider the following system of differential equations da V = 0, dt dy + 3x + 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( )= a()+ (1) M C where C and C are constants. Give the values of X1, 31, A2 and 32. Enter your values such that A A2- A 9/1 3/2 Input all numbers as integers or fractions, not as decimals. Find the particular solution, expressed as a (t) and y(t), which satisfies the initial conditions (0) = 3, y(0) = -7. y(t) complete and balance the following half-reaction in basic solution cr2o7 cr3 urgent.In long-run equilibrium, perfectly competitive firms will Select one: a. go out of business. b. produce where marginal cost is at its minimum. c. produce where marginal cost equals average total cost. Which is a true statement regarding the general trends in atomic radii?a. Radii increase going down a group.b. Radii increase as atomic number increases.c. Radii increase going across a period. d. Radii decrease going down a group if the tax multiplier is -1.5 and a $200 billion tax increase is implemented, what is the change in gdp, holding all else constant? Why is job satisfaction important in the workplace?can you make it an essay Your client has asked you to prepare two different messages targeting both active and passive audiences for a COVID-19 campaign encouraging people to take their third boaster shots. What kind of messages and media would you use for these two audiences? (6 Marks) Messages form the core of PR campaigns. Describe four variables that influence message believability. (4 Marks) The decision stage in message adoption is a crucial stage in the PR campaigns. Describe five factors that influence peoples evaluation of products or ideas covered in this course. (5 Marks) For each pair of functions below, find the Wronskian and determine if they are linearly independent. = = 2x+3 (1) (2) (3) 41 = 20, y2 = y = x2 +1, y2 = x y1 = ln x, y2 = 0 = =