The Ideal Gas Equation (AQA A-Level Chemistry): Revision Notes
1.3.4 The Ideal Gas Equation
The ideal gas equation is a fundamental equation used to relate the properties of an ideal gas. It connects the pressure, volume, temperature, and amount of gas in a system and is essential for calculating unknown quantities in gas-related problems.
The Ideal Gas Equation
Where:
- p = pressure of the gas (measured in Pascals, Pa)
- V = volume of the gas (measured in m³)
- n = number of moles of gas
- R = gas constant (8.31 J/K/mol)
- T = temperature of the gas (measured in Kelvin, K)
Units and Conversions
To use the ideal gas equation correctly, it is crucial that all values are in SI units:
Pressure (p)
Measured in Pascals (Pa).
If pressure is given in atmospheres (atm), convert it using:
Volume (V)
Measured in cubic metres (m³).
Convert from:
- dm³ to m³ by dividing by 1,000:
- cm³ to m³ by dividing by 1,000,000:
Temperature (T)
Always measured in Kelvin (K). Convert from degrees Celsius using: [ T , \text{(K)} = T , \text{(°C)} + 273 ]
Example Calculations Using the Ideal Gas Equation
Example: Calculating the Volume of Gas Question: Calculate the volume occupied by 2 moles of nitrogen gas at a pressure of 100,000 Pa and a temperature of 300 K.
Step 1: Write the ideal gas equation:
Step 2: Rearrange to solve for volume (V):
Step 3: Substitute the known values:
The volume of the gas is 0.0499 m³ (or 49.9 dm³).
Example: Finding the Molar Mass of a Volatile Liquid Question: A sample of a volatile liquid is vaporised, and the following data is obtained: 100 cm³ of vaporised gas at 101,325 Pa, 373 K, and a mass of 0.5 g. What is the molar mass?
Step 1: First, convert 100 cm³ to m³:
Step 2: Use the ideal gas equation to calculate the number of moles of gas (n):
Step 3: Find the molar mass using the formula:
Therefore, the molar mass of the volatile liquid is 153.37 g/mol.
Summary
The ideal gas equation is a powerful tool for relating pressure, volume, temperature, and the number of moles in a gas. By ensuring all units are in SI units, students can confidently rearrange and use the equation to solve for unknowns in gas-related calculations.