The Ideal Gas Equation (DP IB Chemistry: SL): Revision Note

Calculate the volume, in dm³, occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.

Answer:

• Step 1: Rearrange the ideal gas equation to find volume of the gas

$V=\frac{nRT}{P}$

• Step 2: Convert into the correct units and calculate the volume the oxygen gas occupies

P = 220 kPa = 220 000 Pa

n = 0.781 mol

R = 8.31 J K^-1 mol^-1

T = 21 ^oC = 294 K

$V=\frac{0.781\mathrm{mol}\times 8.31\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mol}\times 294\mathrm{K}}{220000\mathrm{Pa}}$

V = 0.00867 m³

V = 8.67 dm³

Many students make mistakes converting between cm³ and m³ in gas law problems.

• 1 m³ = 1,000,000 cm³ (because 100 × 100 × 100 = 10⁶)

• So:

  • To convert m³ to cm³, multiply by 10⁶

  • To convert cm³ to m³, divide by 10⁶ (or multiply by 10⁻⁶)

Always check units before using the ideal gas equation, it requires volume in m³

Calculate the pressure of a gas, in kPa, given that 0.20 moles of the gas occupy 10.1 dm³ at a temperature of 25 ^oC.

Answer:

• Step 1: Rearrange the ideal gas equation to find the pressure of the gas

$P=\frac{nRT}{V}$

• Step 2: Convert to the correct units and calculate the pressure

n = 0.20 mol

V = 10.1 dm³ = 0.0101 m³ = 10.1 x 10^-3 m³ 

R = 8.31 J K^-1 mol^-1

T = 25 ^oC = 298 K

$P=\frac{0.20mol\times 8.31J{K}^{-1}mo{l}^{-1}\times 298K}{10.1\times {10}^{-3}{m}^3}$

P = 49 037 Pa = 49 kPa (2 sig figs)

Calculate the temperature of a gas, in ^oC, if 0.047 moles of the gas occupy 1.2 dm³ at a pressure of 100 kPa.

Answer:

• Step 1: Rearrange the ideal gas equation to find the temperature of the gas

$T=\frac{PV}{nR}$

• Step 2: Convert to the correct units and calculate the pressure

n = 0.047 mol

V = 1.2 dm³ = 0.0012 m³ = 1.2 x 10^-3 m³ 

R = 8.31 J K^-1 mol^-1

P = 100 kPa = 100 000 Pa

$T=\frac{100000\times 1.2\times {10}^{-3}{m}^3}{0.047mol\times 8.31J{K}^{-1}mo{l}^{-1}}$

T = 307.24 K

T = 34.24 ^oC = 34 ^oC  (2 sig figs)

A flask of volume 1000 cm³ contains 6.39 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.

Calculate the molar mass of the gas.

Answer:

• Step 1: Rearrange the ideal gas equation to find the number of moles of gas

$n=\frac{PV}{RT}$

• Step 2: Convert to the correct units and calculate the number of moles of gas

P = 300 kPa = 300 000 Pa

V = 1000 cm³ = 0.001 m³ = 1.0 x 10^-3 m³ 

R = 8.31 J K^-1 mol^-1

T = 23 ^oC = 296 K

      n = 0.12 mol

• Step 3: Calculate the molar mass using the number of moles of gas

$\mathrm{molar}\mathrm{mass}=\frac{\mathrm{mass}}{\mathrm{moles}}$

$M=\frac{6.39\mathrm{g}}{0.12\mathrm{mol}}=\mathbf{53}\mathit{g}\mathit{m}\mathit{o}{\mathit{l}}^{\mathbf{-}\mathbf{1}}\left(2\mathrm{sig}\mathrm{figs}\right)$

To calculate the temperature in Kelvin, add 273 to the Celsius temperature, eg. 100 ^oC is 373 Kelvin.