Ideal Gas Equation

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What is the gas equation?

\[pV = nRT\]

This is the ideal gas equation

It can be used for gases, to find the amount of a substance in moles

The symbols represent:

P : Pressure - in pascals (Pa)

V: Volume - in metres cubed (\(m^3\))

n: Number of moles

R: The gas constant - 8.31 - in joules per mole per kelvin (\(J mol^{-1} K{-1}\))

T: Temperature - In Kelvins (K)

Temperature can be converted from degrees Celsius to Kelvin by adding 273 to the degrees Celsius value.

Example: 0°C becomes 273K

A change in temperature of one degree Celsius is the same amount as a change in temperature of one Kelvin - the scales simply measure from different points.

It is important that you use the SI units stated above (making any necessary conversions), otherwise your calculations will not give you the correct answers.

You are not expected to remember the value of R.

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Example 1

A 0.4g sample of gas has a volume of 58.5\(\boldsymbol {cm^3}\), measured at a a temperature of 30°C. It has a molar mass of 160 \(\boldsymbol{gmol^{-1}}\).

What pressure is this measurement taken at?

\( n = \frac{m}{M} \text{ -To calculate the number of moles} \)

\( n = \frac{0.4}{160}=0.0025mol\)

\(V= 58.5 cm^{3} = 58.5 \times 10^{-6} m^{-3} \)

\( T = 30 + 273 = 303K \)

\( p = \frac{nRT}{V} = \frac{0.025 \times 8.31 \times 303}{ 5.5 \times 10^{-6}}= 107.7 \times 10^{3} Pa \)

\( \therefore \text{Pressure=107.7kPa} \)