Gases — Topic Summary

1 Kinetic Molecular Theory

The kinetic molecular theory (KMT) provides the microscopic explanation for the behaviour of gases. It rests on five core assumptions about gas particles:

Gas particles are in constant, random motion in all directions.
The actual volume of gas particles is negligible compared to the volume of the container — they are treated as point masses.
There are no intermolecular forces between gas particles (neither attractive nor repulsive).
Collisions between gas particles and with container walls are perfectly elastic — kinetic energy is conserved.
The average kinetic energy of gas particles is directly proportional to absolute temperature (KE ∝ T in Kelvin).

💡KMT explains all gas behaviours: Pressure arises from particle collisions with container walls. Temperature measures the average kinetic energy of particles. Volume is the space the particles move through.

What KMT predicts

Observable	Microscopic explanation
Pressure	Constant particle collisions with container walls — more collisions or harder collisions = higher pressure.
Temperature increase	Particles move faster on average — they collide more frequently and with greater force.
Volume increase	More space between collisions — at constant pressure, the container expands so collision rate stays the same.

2 Pressure, Volume & Temperature

The Four Gas Variables

All gas laws relate four variables. Understanding their units is essential before applying any formula.

Variable	Symbol	Common units	Notes
Pressure	P	kPa, atm, mmHg	1 atm = 101.325 kPa = 760 mmHg
Volume	V	L, mL	1 L = 1000 mL
Temperature	T	Kelvin (K), °C	Always convert to Kelvin for gas laws
Amount	n	mol	Used in the Ideal Gas Law

⚠️Temperature MUST be in Kelvin. Converting: K = °C + 273.15. Using Celsius in a gas law will give a wrong answer — always convert first.

Standard Conditions

STP (Standard Temperature & Pressure)

0°C (273.15 K) and 101.325 kPa (1 atm)

SATP (some curricula)

25°C (298.15 K) and 100 kPa

3 Boyle's Law

Boyle's Law describes the inverse relationship between pressure and volume when temperature and the number of moles are held constant. If you compress a gas (decrease V), the pressure rises; expand the container and pressure falls.

💡Why? Compressing a gas forces particles into a smaller space, so they collide with the walls more frequently — pressure increases. Temperature hasn't changed, so particle speed is unchanged.

Boyle's Law

P₁V₁ = P₂V₂ (constant T and n)

Worked Example

✏️

A gas at 150 kPa occupies 4.0 L. Find the volume at 300 kPa (constant T).
P₁V₁ = P₂V₂
150 × 4.0 = 300 × V₂
V₂ = 600 / 300 = 2.0 L
Doubling the pressure halved the volume — inverse relationship confirmed.

Key Points

P and V are inversely proportional: P ∝ 1/V
PV = constant (at fixed T, n)
Temperature does not need to be in Kelvin here (since T is constant, it cancels) — but it is good practice always to note T in K.
Units of pressure must be consistent on both sides; units of volume must be consistent on both sides.

4 Charles's Law

Charles's Law describes the direct relationship between volume and temperature when pressure and moles are held constant. Heating a gas causes it to expand; cooling it causes it to contract.

💡Why? Heating makes particles move faster — they hit the walls harder and more often. At constant pressure, the container walls must expand outward to keep pressure the same, so volume increases.

Charles's Law

V₁ / T₁ = V₂ / T₂ (constant P and n)

⚠️T must be in Kelvin. If you use Celsius, the ratio V/T is meaningless because 0°C does not mean "no temperature." Kelvin's zero is absolute zero — no kinetic energy, no volume.

Worked Example

✏️

A balloon has V = 3.0 L at 20°C. Find its volume at 80°C (constant P).
T₁ = 20 + 273.15 = 293.15 K T₂ = 80 + 273.15 = 353.15 K
V₂ = V₁ × T₂ / T₁ = 3.0 × 353.15 / 293.15 = 3.61 L

5 Gay-Lussac's Law

Gay-Lussac's Law describes the direct relationship between pressure and temperature when volume and moles are held constant (a sealed, rigid container). Heating increases pressure; cooling decreases it.

💡Why? In a fixed container, heating makes particles move faster and collide harder with walls. Since the walls can't move (constant V), the pressure rises instead.

Gay-Lussac's Law

P₁ / T₁ = P₂ / T₂ (constant V and n)

Worked Example

✏️

A sealed container at 25°C has P = 120 kPa. Find P after heating to 75°C.
T₁ = 298.15 K T₂ = 348.15 K
P₂ = P₁ × T₂ / T₁ = 120 × 348.15 / 298.15 = 140.1 kPa

💡Real-world example: a car tyre pressure increases after driving. The friction from the road heats the air inside (constant V) — Gay-Lussac's Law in action.

6 Combined Gas Law

When two or more of P, V, and T change simultaneously (with n constant), use the Combined Gas Law. It is a unification of Boyle's, Charles's, and Gay-Lussac's laws.

Combined Gas Law

P₁V₁ / T₁ = P₂V₂ / T₂ (constant n)

💡The three simpler laws are special cases: set T₁ = T₂ and you get Boyle's. Set P₁ = P₂ and you get Charles's. Set V₁ = V₂ and you get Gay-Lussac's.

Worked Example

✏️

Gas at 100 kPa, 2.0 L, 27°C is compressed to 1.5 L and heated to 127°C. Find new P.
T₁ = 300 K T₂ = 400 K
P₂ = P₁V₁T₂ / (T₁V₂) = 100 × 2.0 × 400 / (300 × 1.5) = 177.8 kPa

7 Ideal Gas Law

The Ideal Gas Law combines all four variables — pressure, volume, moles, and temperature — into a single equation. Use it whenever the problem involves the number of moles (n) or asks you to find moles from other quantities.

Ideal Gas Law

PV = nRT

The Gas Constant R

R (pressure in kPa)

R = 8.314 L·kPa / (mol·K)

R (pressure in atm)

R = 0.08206 L·atm / (mol·K)

⚠️Match R to your pressure units. If P is in kPa, use R = 8.314. If P is in atm, use R = 0.08206. Mixing units is the most common source of error in gas law problems.

Molar Volume at STP

At STP (0°C, 101.325 kPa), one mole of any ideal gas occupies exactly 22.4 L. This is a useful shortcut — memorise it.

Molar volume at STP

1 mol = 22.4 L at 0°C and 101.325 kPa

Worked Example

✏️

Find the volume of 0.50 mol of gas at 25°C and 100 kPa.
T = 25 + 273.15 = 298.15 K R = 8.314 L·kPa/(mol·K)
V = nRT / P = 0.50 × 8.314 × 298.15 / 100 = 12.4 L

8 Dalton's Law of Partial Pressures

In a mixture of gases, each gas exerts its own partial pressure independently, as if the other gases were not present. The total pressure is the sum of all partial pressures.

Dalton's Law

Pₜₒₜₐₗ = P₁ + P₂ + P₃ + …

💡Why? Ideal gas particles don't interact with each other. Each type of molecule bounces around independently and contributes its own collision rate with the walls — so pressures simply add.

Mole Fractions

Mole fraction

χ₁ = n₁ / nₜ = P₁ / Pₜ

Collecting Gas Over Water

When gas is collected by water displacement, the collected gas is a mixture of the desired gas and water vapour. Subtract the water vapour pressure to find the gas pressure alone.

Collecting over water

P☟ₐⸯ = Pₜₒₜₐₗ − Pₕ₂ₒ

💡Water vapour pressure depends on temperature and must be looked up from a table (e.g., at 25°C, Pₕ₂ₒ ≈ 3.17 kPa). Never forget this correction when collecting gas over water.

9 Common Mistakes to Avoid

Mistake	What to do instead
Using Celsius in gas laws	Always convert: K = °C + 273.15. Every gas law formula requires Kelvin.
Using wrong R value	R = 8.314 with kPa; R = 0.08206 with atm. Check your pressure units first.
Boyle's law when T also changes	If two variables change, use the Combined Gas Law — not Boyle's or Charles's alone.
Forgetting Dalton's law over water	Collected gas pressure = total − water vapour pressure at that temperature.
Inconsistent pressure or volume units	Both sides of the equation must use the same units for P and the same units for V.
Applying ideal gas law to real gases	Real gases deviate from ideal behaviour at high pressure and low temperature — the assumptions break down.