Ideal gas equation and moles questions

1) If I have 40 moles of a gas at a pressure of 56000 Pa and a volume of 2 m³, what is the temperature?

P V = n R T Rearrange to get T on its own, divide both sides by n R

T = P V

n R

T = 56000 x 2

40 x 8.31

T = 337 K

2) If I have an unknown quantity of gas at a pressure of 120000 Pa, a volume of 31 dm³, and a temperature of 360 k, how many moles of gas do I have?

Convert units to SI units first: V = 31 x 10^-3 m³

P V = n R T Rearrange to get n on its own, divide both sides by RT

n = P V

R T

n = 120000 x 31 x 10^-3

8.31 x 360

n = 1.24 moles

3) If I contain 3 moles of gas in a container with a volume of 60 dm³ and at a temperature of 400 K, what is the pressure inside the container?

Convert units to SI units first: V = 60 x 10^-3 m³

P V = n R T Rearrange to get P on its own, divide both sides by V

P = n R T

V

P = 3 x 8.31 x 400

60 x 10^-3

P = 166200 Pa

4) If I have 7.7 moles of gas at a pressure of 9 kPa and at a temperature of 56 ⁰C, what is the volume of the container that the gas is in?

Convert units to SI units first: P = 9 x 10³ Pa T = 56 + 273 = 329 K

P V = n R T Rearrange to get V on its own, divide both sides by P

V = n R T

P

V = 7.7 x 8.31 x 329

9 x 10³

V = 2.34 m³

5) An unknown gas weighs 34g and occupies 6.7 dm³ at 200 kPa and 245K. What is its relative molecular mass?

To calculate Mr from mass, you need moles from the ideal gas equation first:

Convert units to SI units first: V = 6.7 x 10^-3 m³ P = 200 x 10³

P V = n R T Rearrange to get n on its own, divide both sides by RT

n = P V

R T

n = 200 x 10³ x 6.7 x 10^-3

8.31 x 245

n = 0.658 moles

now use these moles in the mass / moles formula:

Mr = mass

n

Mr = 34

0.658

Mr = 51.7g mol^-1

6) What is the volume of 23g of argon gas at 1 ^oC and a pressure of 200 kPa?

You cannot calculate volume directly from a mass so mass must be converted to moles to use in the gas equation first

n = mass

Ar

n = 23

39.9

n = 0.576

now use these moles in the ideal gas equation:

Convert units to SI units first: P = 200 x 10³ Pa T = 1 + 273 = 274 K

P V = n R T Rearrange to get V on its own, divide both sides by P

V = n R T

P

V = 0.576 x 8.31 x 274

200 x 10³

V = 6.56 x 10^-3 m³

7) Calculate the mass of a sample of carbon dioxide which occupies 20 dm³ at 27 ^oC and 100 kPa.

To calculate mass you’ll need moles, n from the ideal gas equation first:

Convert units to SI units first: V = 20 x 10^-3 m³ P = 100 x 10³ T = 27 + 273 = 300

P V = n R T Rearrange to get n on its own, divide both sides by RT

n = P V

R T

n = 100 x 10³ x 20 x 10^-3

8.31 x 300

n = 0.802 moles

now use these moles in the mass / moles formula to calculate mass:

mass = n x Mr

mass = 0.802 x 44

mass = 35.3 g

8) Calculate the relative molecular mass of a gas if a 500 cm³ sample at 20 ^oC and 100 kPa has a mass of 0.66 g.

To calculate Mr from mass, you need moles from the ideal gas equation first:

Convert units to SI units first: V = 500 x 10^-6 m³ P = 100 x 10³ T = 20 + 273 = 293

P V = n R T Rearrange to get n on its own, divide both sides by RT

n = P V

R T

n = 100 x 10³ x 500 x 10^-6

8.31 x 293

n = 0.0205 moles

now use these moles in the mass / moles formula:

Mr = mass

n

Mr = 0.66

0.0205

Mr = 32.1 g mol^-1