1. Pressure in gases

The ideal gas equation relates pressure, volume, temperature and amount of gas. It is important to use the SI units of all the variables in the equation, the gas constant is 8.31 J K⁻¹ mol⁻¹, one mole is Avogadro constant = 6.02 × 10²³, the temperature needs to be given in kelvin (K). The absolute temperature in K can be found by adding 273.15 to the temperature in °C.

There are three specific cases for the ideal gas equation. When only pressure and volume are changing, it is called Boyle’s law and yields p₁V₁ = p₂V₂. When only pressure and temperature are changing, it is called Gay-Lussac’s law and yields p₁/T₁ = p₂/T₂. When only volume and temperature are changing, it is called Charles’ law and yields V₁/T₁ = V₂/T₂. # 1

16 moles of hydrogen occupy a volume of 5.2 dm³ at a pressure of 112 kPa. Using the ideal gas equation, calculate the temperature in kelvins.

5.2 dm³ = 0.0052 m³
112 kPa = 112000 Pa
pV = nRT
T = pV/nR
T = (112000 × 0.0052)/(16 × 8.31) = 4.38 K (3 s. f.)

4.38 K # 2

How many moles does a sample of gas with a volume of 0.57 m³ at 101000 Pa and 300 K contain?

pV = nRT
n = pV/RT
n = (101000 × 0.57)/(8.31 × 300) = 23 mol (2 s. f.)

23 mol # 3

Use the ideal gas equation and the information provided in the image to calculate how many molecules of the gas there are in the flask.

pV = nRT
n = pV/RT
n = (90000 × 0.045)/(8.31 × 312) = 1.56 mol (3 s. f.)

1.56 mol # 4

Provide and equation for Charles’ law that relates initial volume V₁, initial temperature T₁, final volume V₂ and final temperature T₂.

Charles’ law can be derived from the ideal gas law and yields V₁/T₁ = V₂/T₂.

V₁/T₁ = V₂/T₂ # 5

Using the ideal gas equation, calculate the volume of 2 moles of a gas at a temperature of 290 K and a pressure of 103000 Pa.

pV = nRT
V = nRT/p
V = (2 × 8.31 × 290)/103000 = 0.047 m³ (2 s. f.)

0.047 m³ End of page