How the volume of a gas changes with pressure and temperature, and what STP means.
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Gas particles move randomly and far apart, so a gas has no fixed shape or volume. Boyle's law: at constant temperature the volume of a fixed mass of gas is inversely proportional to its pressure, so PV = constant and P₁V₁ = P₂V₂. A graph of V against P is a curve (hyperbola); V against 1/P is a straight line.
A gas occupies 6 L at 1 atm. Find its volume at 3 atm (constant temperature).
V₂ = P₁V₁ ÷ P₂ = 1 × 6 ÷ 3 = 2 L.
What happens to the volume when the pressure is halved?
It doubles.
Why does a bicycle pump get hard to push?
Compressing the air raises its pressure as the volume falls.
Charles' law: at constant pressure the volume of a fixed mass of gas is directly proportional to its absolute temperature, V₁/T₁ = V₂/T₂. Absolute temperature in kelvin = °C + 273, and 0 K (−273 °C) is the lowest possible temperature. Always convert to kelvin before using the law.
300 mL of gas at 27 °C is heated to 127 °C at constant pressure. Find the new volume.
T₁ = 300 K, T₂ = 400 K. V₂ = 300 × 400 ÷ 300 = 400 mL.
Convert 0 °C, 100 °C and −273 °C to kelvin.
273 K, 373 K and 0 K.
Why can the Celsius temperature not be used directly in V₁/T₁ = V₂/T₂?
At 0 °C the volume is not zero, so volume is not proportional to °C; it is proportional to kelvin.
Gas volumes depend on temperature and pressure, so they are compared at standard temperature and pressure: 0 °C (273 K) and 760 mm Hg (1 atm). To convert a volume to STP, combine both laws: V₀ = V × (P ÷ 760) × (273 ÷ T). At STP one mole of any gas occupies 22.4 L.
Convert 500 mL of gas at 27 °C and 750 mm Hg to STP.
V₀ = 500 × 750 ÷ 760 × 273 ÷ 300 = 449.01 mL.
State STP values.
273 K (0 °C) and 760 mm Hg (1 atm).
Which law explains why a sealed balloon shrinks in a freezer?
Charles' law: lower temperature reduces the volume at constant pressure.
1. State Boyle's law.
2. State Charles' law.
3. Convert 47 °C to kelvin.
4. A gas has volume 10 L at 2 atm. Find the volume at 5 atm.
5. 300 mL of a gas at 300 K is cooled to 150 K. Find the volume.
6. What is absolute zero?
7. Give the values of STP.
8. What volume does 1 mole of oxygen occupy at STP?
9. Why must temperature be in kelvin in gas calculations?
10. The pressure on 6 L of gas is doubled at constant temperature. State the new volume.