IMAT Chemistry · States of Matter and Gas Laws

Pressure Units and the Gas Laws

For a fixed amount of gas, pressure and volume are inversely proportional at constant temperature, and each is directly proportional to the kelvin temperature when the other is held fixed.

All States of Matter and Gas Laws notes

Why this matters

This is the most asked page of the chapter. The 2018, 2023 and 2024 papers asked how the pressure of a gas in a rigid container changes when it is heated, which needs kelvin; the 2026 paper asked about volume and pressure at constant temperature, and the 2024 paper asked which value is not equal to 1 atm.

Concept 1 of 4: Units of pressure and their values for one atmosphere

Gas pressure comes from molecules hitting the walls of their container. It is measured in many units for historical reasons: pascals from physics, millimetres of mercury from the barometer, bars and millibars from weather maps. They all describe the same thing, so you only need the value of 1 atm in each one.

Definition

The SI unit is the pascal: $1\ \text{Pa} = 1\ \text{N/m}^2$ . A kilopascal is $10^3\ \text{Pa}$ .
Standard atmospheric pressure: $1\ \text{atm} = 101\,325\ \text{Pa} = 101.325\ \text{kPa}$ .
$1\ \text{bar} = 10^5\ \text{Pa}$ , so 1 atm is about 1.013 bar or 1013 millibar. A millibar equals a hectopascal (hPa).
A barometer's column of mercury is 760 mm tall at 1 atm: $1\ \text{atm} = 760\ \text{mmHg} = 760\ \text{torr}$ .

Unit	Symbol	Value of 1 atm
Pascal	Pa	101 325 Pa
Kilopascal	kPa	101.325 kPa
Bar	bar	1.01325 bar
Millibar (hectopascal)	mbar or hPa	1013.25 mbar
Millimetre of mercury	mmHg	760 mmHg
Torr	Torr	760 torr

Learn 101.3 kPa and 760 mmHg; the others follow from the prefixes.

Practice this conceptself-check · 4 quick reps

1 atm is 101.3 kPa, not 1013 kPa

The number 1013 belongs to millibars (or hectopascals): 1 atm is 1013 mbar = 101.3 kPa. A value of 1013 kPa is ten atmospheres. Watch which prefix goes with which number.

Concept 2 of 4: Boyle's law: pressure and volume at constant temperature

Squeeze a gas into half the volume and each molecule has half as far to travel between hits on the walls, while the same number of molecules now hit a smaller area. The wall gets hit twice as often per square metre, so the pressure doubles. The molecules are not moving any faster, because the temperature has not changed.

Definition

Boyle's law: for a fixed amount of gas at constant temperature (an isothermal change), the pressure is inversely proportional to the volume.

$PV$ stays constant: double the volume and the pressure halves; reduce the volume to a third and the pressure triples.
A graph of $P$ against $V$ is a curve (a hyperbola); a graph of $P$ against $1/V$ is a straight line through the origin.
Any pressure and volume units work, as long as the same units are used on both sides.

Boyle's law

P_1 V_1 = P_2 V_2

$P_1, V_1$ pressure and volume before the change
$P_2, V_2$ pressure and volume after the change (same temperature, same amount of gas)

Worked example

A syringe holds 60 cm³ of air at 100 kPa. The outlet is sealed and the plunger is pushed in slowly, so the temperature stays constant, until the volume is 24 cm³. What is the new pressure?

Practice this conceptself-check · 3 quick reps

Inverse proportion, not a direct decrease

When the volume increases at constant temperature, the pressure decreases in inverse proportion: double the volume, half the pressure, so

PV

is constant. Decreasing in direct proportion would mean

P/V

is constant, which is not true. The temperature does not change in an isothermal process.

Concept 3 of 4: Charles's law and Gay-Lussac's law: the effect of temperature

Heat a gas and its molecules move faster, hitting the walls harder and more often. If the container is rigid, the pressure rises. If the pressure is held constant, for example by a free piston, the gas expands instead. In both cases the change is proportional to the kelvin temperature, because that is what the kinetic energy follows.

Definition

For a fixed amount of gas, with the temperature always in kelvin:

Charles's law: at constant pressure, the volume is directly proportional to the temperature: $V/T$ is constant.
Gay-Lussac's law (the pressure law): at constant volume, the pressure is directly proportional to the temperature: $P/T$ is constant.
Both lines, drawn against Celsius temperature, cross zero volume or zero pressure at absolute zero, $-273\ ^\circ\text{C}$ .
Together with Boyle's law they give the combined gas law, for when $P$ , $V$ and $T$ all change.

Charles, Gay-Lussac and the combined gas law

\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \frac{P_1}{T_1} = \frac{P_2}{T_2} \qquad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

$T_1, T_2$ absolute temperatures, in K
$P, V$ pressure and volume, in any units used consistently

Worked example

A sealed aerosol can holds gas at 2.9 atm at 17 °C. It is left in a car where it warms to 87 °C. The volume of the can does not change. What is the new pressure?

Practice this conceptself-check · 4 quick reps

Convert to kelvin before using any gas law ratio

Doubling the Celsius temperature does not double the pressure. To double the pressure of a gas at 50 °C in a rigid container, the kelvin temperature must double, from 323 K to 646 K, which is 373 °C. Answers built on Celsius ratios are always among the options.

Concept 4 of 4: Avogadro's law and the molar volume of a gas

In a gas the molecules are so far apart that their own size hardly matters. So at the same temperature and pressure, the volume depends only on how many molecules there are, not on what they are. A mole of hydrogen and a mole of carbon dioxide take up the same space.

Definition

Avogadro's law: at the same temperature and pressure, equal volumes of gases contain equal numbers of molecules. So $V$ is proportional to the amount $n$ .

The molar volume $V_m$ is the volume of one mole of any (ideal) gas:
at STP, 0 °C and 1 atm, $V_m \approx 22.4\ \text{L/mol}$ (with the newer STP of 0 °C and 1 bar it is 22.7 L/mol);
at RTP, room temperature and 1 atm, $V_m \approx 24\ \text{L/mol}$ (24.0 at 20 °C, 24.5 at 25 °C).
For gases at the same conditions, volume ratios in a reaction equal mole ratios in the equation.

Amount of gas from its volume

n = \frac{V}{V_m}

$n$ amount of gas, in mol
$V$ volume of the gas
$V_m$ molar volume at the stated conditions (22.4 L/mol at STP)

Worked example

How many moles, and what mass, of carbon dioxide (

M = 44\ \text{g/mol}

) are in 5.6 L of the gas at STP?

Practice this conceptself-check · 3 quick reps

Equal volumes mean equal moles, not equal masses

At the same temperature and pressure, 1 L of hydrogen and 1 L of carbon dioxide contain the same number of molecules, but the carbon dioxide is 22 times heavier. Avogadro's law is about the number of particles.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Boyle's law: pressure and volume at constant temperature
Boyle's law
$P_1 V_1 = P_2 V_2$
Charles's law and Gay-Lussac's law: the effect of temperature
Charles, Gay-Lussac and the combined gas law
$\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \frac{P_1}{T_1} = \frac{P_2}{T_2} \qquad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$
Avogadro's law and the molar volume of a gas
Amount of gas from its volume
$n = \frac{V}{V_m}$

Reference tables (1)

Units of pressure and their values for one atmosphere6 rows

Unit	Symbol	Value of 1 atm
Pascal	Pa	101 325 Pa
Kilopascal	kPa	101.325 kPa
Bar	bar	1.01325 bar
Millibar (hectopascal)	mbar or hPa	1013.25 mbar
Millimetre of mercury	mmHg	760 mmHg
Torr	Torr	760 torr

Learn 101.3 kPa and 760 mmHg; the others follow from the prefixes.

Watch out for (4)

1 atm is 101.3 kPa, not 1013 kPa
→ Units of pressure and their values for one atmosphere
Inverse proportion, not a direct decrease
→ Boyle's law: pressure and volume at constant temperature
Convert to kelvin before using any gas law ratio
→ Charles's law and Gay-Lussac's law: the effect of temperature
Equal volumes mean equal moles, not equal masses
→ Avogadro's law and the molar volume of a gas

Drill the past-year questions on this topic

Open the bank with this topic pre-filtered.

Open in the bank