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

pV = nRT

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:

1 \, \text{atm} = 101,325 \, \text{Pa}

Volume (V)

Measured in cubic meters (m³).

Convert from:

dm³ to m³ by dividing by 1,000:

1 \, \text{m³} = 1,000 \, \text{dm³}

cm³ to m³ by dividing by 1,000,000:

1 \, \text{m³} = 1,000,000 \, \text{cm³}

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

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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:

pV = nRT

Step 2: Rearrange to solve for volume (V):

V = \frac{nRT}{p}

Step 3: Substitute the known values:

V = \frac{2 \times 8.31 \times 300}{100,000} = 0.04986 \, \text{m}^3

The volume of the gas is 0.0499 m³ (or 49.9 dm³).

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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:

100 \, \text{cm}³ = 100 \div 1,000,000

= 1 \times 10^{-4} \, \text{m}³

Step 2: Use the ideal gas equation to calculate the number of moles of gas (n):

n = \frac{pV}{RT}

= \frac{101,325 \times 1 \times 10^{-4}}{8.31 \times 373}

= 3.26 \times 10^{-3} \, \text{mol}

Step 3: Find the molar mass using the formula:

M_r = \frac{\text{Mass}}{\text{Moles}}

= \frac{0.5 \, \text{g}}{3.26 \times 10^{-3} \, \text{mol}} = 153.37 \, \text{g/mol}

Therefore, the molar mass of the volatile liquid is 153.37 g/mol.

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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.

The Ideal Gas Equation Simplified Revision Notes for A-Level AQA Chemistry

1.3.4 The Ideal Gas Equation

The Ideal Gas Equation

Units and Conversions

Pressure (p)

Volume (V)

Temperature (T)

Example Calculations Using the Ideal Gas Equation

Summary

500K+ Students Use These Powerful Tools to Master The Ideal Gas Equation For their A-Level Exams.

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