Ideal Gas Law

1.5 moles of nitrogen gas is kept at a temperature of 30 °C and 50 kPa of pressure. What volume does the gas occupy? Give your answer to 2 d.p.

[Gas constant = 8.314 J mol^-1 K^-1]

Answer explanation

1) pV = nRT, rearrange to solve for volume: V = nRT/p

2) Convert 30 °C to kelvin: 30 + 273 = 303 K

3) Insert values: V = (1.5 x 8.314 x 303) / 50

4) V =75.57 L

2.2 moles of gas is kept at 400 kPa and -70 °C. What is the volume of this container? Give your answer to 2 d.p.

[Gas constant = 8.314 J K^-1 mol^-1]

Answer explanation

1) Rearrange pV = nRT to solve for V: V = nRT/p

2) Convert °C to Kelvin by adding 273: 273 + -70 = 203 K

3) Insert values to equation:

V = (2.2 x 8.314 x 203) / 400

4) V = 9.28 L

What volume is occupied by 0.02 moles of gas at 500 K and 150 kPa of pressure?

Give your answer to 2 s.f.

[Gas constant = 8.314 J K^-1 mol^-1]

Answer explanation

1) Rearrange pV = nRT to solve for volume: V = nRT/p

2) Insert values into equation:

V = 0.02 x 8.314 x 500 / 150

3) V = 0.055 L

What pressure is exerted by 3 moles of gas stored in a 1 litre balloon at 45 °C? Give your answer to 1 d.p.

[Gas constant R = 8.314 J K^-1 mol^-1]

Answer explanation

1) Rearrange equation to solve for pressure: p = nRT/V

2) Convert °C to K by adding 273: 45 + 273 = 318 K

3) Insert values into equation:

p = (3 x 8.314 x 318) / 1

4) p = 7931.556 -> 7931.6 kPa

What pressure is exerted by 0.33 moles of gas inside a 0.4 dm³ container at 25 °C?

[Gas constant R = 8.314 J K-1 mol-1]

Answer explanation

1) Rearrange equation to solve for pressure: p = nRT/V

2) Convert °C to K by adding 273: 273+25 = 298 K

3) Insert values into equation:

p = 0.33 x 8.314 x 298 / 0.4

4) p = 2043.975 kPa

What pressure is exerted by 0.015 moles of gas inside a 2.0 dm³ container at -20 °C? Give your answer to 2 s.f.

[Gas constant R = 8.314 J K-1 mol-1]

Answer explanation

1) Rearrange equation to solve for p: p = nRT/V

2) Convert °C to K by adding 273: -20 + 273 = 253 K

3) Insert values into equation:

p = 0.015 x 8.314 x 253 / 2

4) p = 15.775 kPa

5) p = 16 kPa (2 s.f.)

A 1.5 L container of gas has a pressure of 30 kPa and a temperature of 10 °C. How many moles are within the container? Give your answer to 3 s.f.

[Gas constant R = 8.314 J K-1 mol-1]

Answer explanation

1) Rearrange pV = nRT to solve for n:

n = pV/RT

2) Convert °C to K by adding 273:

10 + 273 = 283 K

3) Insert values into equation:

n = 30 x 1.5 / 8.314 x 283

4) n = 0.0191 moles (3 s.f.)

A 0.65 L container of oxygen has a pressure of 200 kPa and a temperature of 5 °C. How many grams of oxygen are found within the container? Give your answer to 2 d.p.

[Gas constant R = 8.314 J mol-1 K-1]

Answer explanation

1) Question asks for grams, but need to work out moles first. Rearrange pV = nRT to solve for n:

n = pV/RT

2) Convert °C to K by adding 273:

5 + 273 = 278 K

3) Insert values:

n = 200 x 0.65 / 8.314 x 278

4) n = 0.0562 moles

5) m = nM = 0.0562 x 32 (Oxygen gas is diatomic, so one mole of O₂ has a mass of 32 grams)

6) m = 1.7984g = 1.80 g (2 d.p.)

Calculate the mass of ammonia in a balloon with a volume of 0.03 dm³, a pressure of 100 kPa and a temperature of 25 °C. Give your answer to 1 s.f.

[Gas constant R = 8.314 J mol^-1 K^-1]

Answer explanation

1) Rearrange pV = nRT to solve for n:

n = pV/RT

2) Convert °C to K by adding 273:

25 + 273 = 298 K

3) Insert values:

n = 100 x 0.03/8.314 x 298

4) n = 0.00121 moles

5) A_r (NH₃) = (14 x 1) + (1 x 3) = 17 g/mol

6) 0.00121 x 17 = 0.02 g (1 s.f.)

5)

Calculate the temperature of a vessel containing 10 grams of hydrogen chloride gas with a volume of 0.2 dm³ and a pressure of 350 kPa. Round your answer to the nearest integer.

Answer explanation

1) Rearrange pV = nRT to solve for T:

T = pV/nR

2) Convert grams to moles. First work out molecular mass of HCl:

(1 x 1) + (35.5 x 1) = 36.5 g/mol

3) Work out how many moles of HCl there are:

n = m/M = 10/36.5 = 0.2739 moles

4) Insert values into equation:

T = 350 x 0.2 / 8.314 x 0.2739

T = 30.739

T = 31 K (to nearest integer)