Gas Laws/Stoichiometry Chemistry Questions

Question

A gas has a volume of 450 mL at 35 degrees C. If the volume changes to 400 mL, what is the new

temperature (give your answer in C)?

What volume of Hydrogen gas at STP may be prepared by the reaction of 7.62 g gallium

(Ga) with an excess of hydrochloric acid (HCl)? Use the following balanced reaction to find

your answer: 2 Ga (s) + 6HCl (aq) → 2GaCl3 (aq) + 3H2

Use the following information for the next 3 questions. Ammonia is converted to ammonium sulfate,

an important fertilizer, by the following reaction

2NH3 (g) + H2SO4 → (NH4)₂SO4 (s)

If 225 kg of ammonium sulfate is to be made in one batch, how many liters of ammonia at

STP are needed?

How many moles of H2SO4 are required?

If the H2SO4 is in the form of a 6.00 M solution, what volume of this solution is needed

(provide your answer in liters)?

A bacterial culture isolated from sewage produced 34.5 mL of methane, CH4, at 30.0 degrees C and

749 mm Hg. What is the volume of methane at STP (0 degrees C, 760 mmHg)?

Helium in a 100-mL container at a pressure of 500 torr is transferred to a container with a

volume of 250 mL. What is the new pressure if no change in temperature occurs?

Prove that the ideal gas law is a version of the combined gas law at STP.

When the pressure in a certain gas cylinder with a volume of 4.5 L reaches 500 atm, the

cylinder is likely to explode. If this cylinder contains 40.0 moles of Argon at 25 degrees C, is it on the

verge of exploding? Calculate the pressure (in atm).

A volume of nitrogen, N2, required for 68.3 seconds to effuse from a hole in a chamber.

Under the same conditions, another gas required 51.6 seconds for the same volume to

effuse. What is the molar weight of this gas?

Thanks in advance for your help. I've finished these questions, I just need some confirmation on whether they are correct or not.

Answer 1

A gas has a volume of 450 mL at 35 degrees C. If the volume changes to 400 mL, what is the new

temperature (give your answer in C)?

Can't answer since we don't know the initial temperature.

What volume of Hydrogen gas at STP may be prepared by the reaction of 7.62 g gallium

(Ga) with an excess of hydrochloric acid (HCl)? Use the following balanced reaction to find

your answer: 2 Ga (s) + 6HCl (aq) → 2GaCl₃ (aq) + 3H₂

7.62 g Ga x 1 mol Ga/69.7 g x 3 mol H₂ / 2 mol Ga = 0.164 mols H₂ produced

0.164 mols H₂ x 22.4 L / mol = 3.67 L of H₂ produced

A bacterial culture isolated from sewage produced 34.5 mL of methane, CH4, at 30.0 degrees C and

749 mm Hg. What is the volume of methane at STP (0 degrees C, 760 mmHg)? Edited answer:

P1V1/T1 = P2V2/T2 and solve for V2: V2 = P1V1T2/P2T1 = (749)(34.5)(273)/(760)(303) = 30.6 mls

When the pressure in a certain gas cylinder with a volume of 4.5 L reaches 500 atm, the

cylinder is likely to explode. If this cylinder contains 40.0 moles of Argon at 25 degrees C, is it on the

verge of exploding? Calculate the pressure (in atm).

PV = nRT and solve for P: (P)(4.5 L) = (40.0 mol)(0.0821 Latm/Kmol)(298K) and P = 217 atm. Therefore it is NOT on the verge of exploding since the pressure is significantly less than 400 atm.

Answer 2

1. A gas has a volume of 450 mL at 35 degrees C. If the volume changes to 400 mL, what is the new temperature (give your answer in C)?

-From the ideal gas law, we know PV=nRT. Without adding or subtracting any gas from the container, we know n is a constant for both conditions (R is as well).

-For the initial conditions (subscript 1):

nR = P₁V₁/T₁

-This nR must be the same as the final conditions (subscript 2):

nR = P₂V₂/T₂

-Thus,

P₁V₁/T₁ = P₂V₂/T₂

-In this problem, we are given:

V₁ = 450mL

T₁ = 35^oC + 273 = 308 K (note: the problem asks for the solution in ^oC, however gas law equations require calculation in Kelvin, then we can subtract 273 and return back to Celsius)

V₂ = 400mL

-And told to find T₂. Let's solve for it from our original equation.

P₁V₁/T₁ = P₂V₂/T₂

flip the equations

T₁/P₁V₁ = T₂/P₂V₂

solve

T₂ = T₁ * P₂ * V₂ / P₁ * V₁

-Missing from what we are given is the initial and final pressure, P₁ and P₂.

-This problem cannot be solved unless we assume pressure remains constant (isobaric process).

If P₁ = P₂ then our equation simplifies to:

T₂ = T₁ * V₂ / * V₁

T₂ = (308 K) * (400mL) / 450mL

T₂ = 274 K

T₂ = 274 K - 273 K

T₂ = 1^oC

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2 . What volume of Hydrogen gas at STP may be prepared by the reaction of 7.62 g gallium

(Ga) with an excess of hydrochloric acid (HCl)? Use the following balanced reaction to find

your answer: 2 Ga (s) + 6HCl (aq) → 2GaCl3 (aq) + 3H2

-This is a simple stoichiometry problem. First, we convert mass of gallium to moles via its molar mass (from the periodic table then use the mole ratio of our gallium and the product in question, H₂ gas.

7.62g Ga * 1 mol Ga / 69.7g Ga * 3 mol H₂ / 2 mol Ga = 0.164 mol H₂

-Now that we know how many mols of hydrogen gas we produced, we convert to volume using the knowledge at standard temperature and pressure (STP), 1 mol of an ideal gas has a volume of 22.4L (we assume hydrogen gas acts ideally).

Volume H₂ = 0.164mol H₂ * 22.4 L / 1 mol H₂ = 3.67 L

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3. Use the following information for the next 3 questions. Ammonia is converted to ammonium sulfate,

an important fertilizer, by the following reaction

2NH3 (g) + H2SO4 → (NH4)₂SO4 (s)

a) If 225 kg of ammonium sulfate is to be made in one batch, how many liters of ammonia at

STP are needed?

-we solve it just like the previous problem. Ammonium sulfate abbreviated as AS

225 kg AS * 1000g / 1kg * 1 mol AS / 132g AS * 2 mol NH₃ / 1 mol AS * 22.4L NH₃ / 1 mol NH₃

= 7.64 x 10⁴ L of ammonia

b) How many moles of H2SO4 are required?

225 kg AS * 1000g / 1kg * 1 mol AS / 132g AS * 1 mol H₂SO₄ / 1 mol AS = 1700 mol H₂SO₄

c) If the H2SO4 is in the form of a 6.00 M solution, what volume of this solution is needed

(provide your answer in liters)?

6.00M H₂SO₄ = 6.00 mol H₂SO₄ / 1.00L sol H₂SO₄

-use 1700 mol of H₂SO₄ determined earlier

1.00 L sol H₂SO₄ / 6.00 mol H₂SO₄ * 1700 mol H₂SO₄ = 283 L of 6M H₂SO₄ sol

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4. A bacterial culture isolated from sewage produced 34.5 mL of methane, CH4, at 30.0 degrees C and

749 mm Hg. What is the volume of methane at STP (0 degrees C, 760 mmHg)?

-The number of moles stays the same so like the first problem in the set we can arrive at the relation:

P₁ * V₁ / T₁ = P₂ * V₂ / T₂

-We know:

V₁ = 34.5 mL

T₁ = 30.0^oC + 273 = 303 K

P₁ = 749 mm Hg

T₂ = 0^oC + 273 = 273 K

P₂ = 760 mm Hg

-We are asked to find V₂

-Solve for V₂

P₁ * V₁ / T₁ = P₂ * V₂ / T₂

V₂ = T₂ * P₁ * V₁ / T₁ * P₂

V₂ = (273 K) * (749 mm Hg) * (34.5mL) / ( 303 K) * (760 mmHg) = 30.6 mL

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5. Helium in a 100-mL container at a pressure of 500 torr is transferred to a container with a

volume of 250 mL. What is the new pressure if no change in temperature occurs?

-We start with our good friend:

P₁ * V₁ / T₁ = P₂ * V₂ / T₂

-The problem states temperature remains constant (isothermal process), therefore we simplify to:

P₁ * V₁ = P₂ * V₂

-We know:

P₁ = 500 torr

V₁ = 100mL

V₂ = 250mL

-We are asked to find P₂.

P₁ * V₁ = P₂ * V₂

P₂ = P₁ * V₁ / V₂

P₂ = (500 torr) * (100mL) / (250mL) = 200 torr

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6. Prove that the ideal gas law is a version of the combined gas law at STP.

The combined gas law written as:

P₁ * V₁ / T₁ = P₂ * V₂ / T₂

can be re-written for a single condition:

P * V / T = constant

Avogadro's law is not always included but is essential for arriving at the ideal gas law because for all the other laws (PV = constant, V/T = constant, P/T = constant), another variable must be held constant: the number of moles.

Avogadro's law:

V / n = constant

Thus, we combine these to get:

PV/nT = constant

AT STP, P is fixed to 1 atm or 760 mm Hg and temperature is 273 K. If we fix n = 1 mol for simplicity, then V also equals 22.4L

constant = (760mmHg) * 22.4L / 1mol * 273 K = 62.4 mm Hg * L / mol * K

This 'constant' is precisely R, the ideal gas constant.

R = PV/nT

PV = nRT

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7.When the pressure in a certain gas cylinder with a volume of 4.5 L reaches 500 atm, the

cylinder is likely to explode. If this cylinder contains 40.0 moles of Argon at 25 degrees C, is it on the

verge of exploding? Calculate the pressure (in atm).

-We are given:

V = 4.5L

n = 40.0 moles

T = 25^oC + 273 = 298 K

P_explosion = 500 atm

-We are asked to find:

P and compare it to P_explosion

-We have all the variables to use the ideal gas equation

PV = nRT

P = nRT/V = (40.0mol)(0.0821 L * atm / mol * K) * (298 K) / 4.5L

P = 217 atm

This is below below P_explosion = 500 atm, thus it is NOT on the verge of exploding.

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