H2 Chemistry 3 - The Gaseous State: Ideal Gas Calculation and Real Gas Deviation

Step 1 - State the problem

A sample of nitrogen gas occupies a volume of two point four six cubic decimetres at twenty-seven degrees Celsius and one point zero one times ten to the five pascals.

Step 1 - State the problem

Calculate the amount of nitrogen in moles using the ideal gas equation.

Step 1 - State the problem

Then explain why nitrogen deviates from ideal behaviour at high pressures.

Step 2 - Apply the ideal gas equation

The ideal gas equation is P V equals n R T.

Step 2 - Apply the ideal gas equation

Rearrange for n: n equals P V divided by R T.

Step 2 - Apply the ideal gas equation

The gas constant R is eight point three one four joules per kelvin per mole.

Step 2 - Apply the ideal gas equation

Make sure all units are SI: pressure in pascals, volume in cubic metres, temperature in kelvin.

Step 3 - Substitute and calculate

Substitute the values: n equals one point zero one times ten to the five, times two point four six times ten to the minus three, divided by eight point three one four times three hundred.

Step 3 - Substitute and calculate

The numerator is two hundred and forty-eight point four six.

Step 3 - Substitute and calculate

The denominator is two thousand four hundred and ninety-four point two.

Step 3 - Substitute and calculate

n equals zero point zero nine nine six moles, which rounds to zero point one zero zero moles.

Step 4 - Explain deviations from ideal behaviour

An ideal gas assumes that molecules have negligible volume and no intermolecular forces.

Step 4 - Explain deviations from ideal behaviour

At high pressures, the volume of the nitrogen molecules becomes significant compared to the container volume.

Step 4 - Explain deviations from ideal behaviour

At low temperatures, the weak van der Waals forces between nitrogen molecules become significant relative to their kinetic energy.

Step 4 - Explain deviations from ideal behaviour

Both effects cause the gas to deviate from P V equals n R T.

Step 5 - State the final answer and common pitfall

The amount of nitrogen is zero point one zero zero moles.

Step 5 - State the final answer and common pitfall

Nitrogen deviates from ideal behaviour at high pressures because molecular volume becomes significant, and at low temperatures because intermolecular attractions reduce the pressure exerted on the walls.

Step 5 - State the final answer and common pitfall

Common mistake: forgetting to convert temperature to kelvin or volume to cubic metres.

Step 5 - State the final answer and common pitfall

Always check your units before substituting into P V equals n R T.