Guided lesson: The Gas Laws

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1.A fixed mass of gas is compressed slowly at constant temperature. What happens to its pressure?
2.At constant temperature, why does a larger volume give a lower pressure?
3.What is held constant for the pressure–volume relationship to apply as stated?
4.A balloon is placed inside a vacuum chamber and the outside pressure is gradually removed. What happens to the balloon and why?
5.A student compresses a gas very quickly and observes the pressure rise more than expected. What extra effect crept in?
6.State what happens to the pressure of a fixed gas at constant temperature when its volume is halved.
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7.State the two conditions that must hold when relating pressure and volume of a fixed gas.
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8.Explain, using the kinetic model, why the pressure of a gas falls as it is slowly expanded at constant temperature.
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9.A vacuum pump removes air from around a sealed balloon, which swells to twice its size. Sketch the reasoning linking the change in available volume to the change in the trapped gas's pressure.
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2.Pressure and kelvin temperature at constant volume

5.20

Heat a sealed, rigid container of gas and the pressure climbs on the gauge. The molecules are already fast; warmer still, they fly faster, strike harder, and return sooner — a triple intensification of the bombardment.

States of Matter Temperature and Pressure, downloadable IB Chemistry revision notes — At constant volume, an increase in the temperature of the gas increases the pressure due to more collisions on the container walls

Key points

At constant volume, raising the kelvin temperature raises the pressure of a fixed gas.
Hotter molecules have higher average kinetic energy and higher average speeds.
Faster molecules deliver a larger impulse at each wall collision.
Faster molecules also return to the walls sooner, so collisions are more frequent.
Together the harder and more frequent impacts raise the pressure.

First pass

In a rigid sealed box, heating makes the molecules faster, so they smack the walls harder and come back for another hit sooner. Both effects push the pressure up together.

Analogy — Hail upgrading from gravel to golf balls arriving twice as often: the roof feels it on both counts.

Exam pointer — Quote both changes — harder hits AND more frequent hits — because a one-cause answer scores half.

Going deeper

At fixed volume the number density is fixed, so the collision frequency rises only through speed. Mean impulse per collision grows with molecular speed and the round-trip time to a wall falls with it, so the impulse flux — pressure — is proportional to mean kinetic energy, which is proportional to kelvin temperature: the qualitative seed of the pressure law.

Analogy — Shortening a squash court and speeding up the players simultaneously: the walls take a double penalty, pace and frequency compounding.

Exam pointer — Connect to proportionality: pressure rises in step with kelvin temperature at constant volume — the statement the next note quantifies.

Checks

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1.A sealed rigid canister of gas is heated. What happens to the pressure inside?
2.Why do hotter molecules raise the pressure in a fixed volume?
3.Which quantity must be constant for the pressure–temperature relationship as stated?
4.A full aerosol can is thrown onto a bonfire and its internal pressure climbs. What is the most likely outcome, and which law explains it?
5.A gas at 200 K in a rigid box is warmed until the pressure doubles. What temperature has been reached, qualitatively using the proportionality?
6.State what happens to the pressure of a fixed gas at constant volume when its kelvin temperature is increased.
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7.State the two ways in which faster molecules intensify the wall bombardment.
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8.Explain why the pressure–temperature relationship requires the amount of gas to be fixed.
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9.A rigid gas cylinder left in direct sun warms from 300 K to 330 K. Using the qualitative proportionality, state roughly how the internal pressure changes.
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