Gas Laws

Grade 10 · Science · Study Guide

Understand the relationships between pressure, volume, temperature, and amount of gas using Boyle's, Charles's, Gay-Lussac's, and the Ideal Gas Law.

The behavior of gases can be predicted and quantified using a set of fundamental laws discovered through experimentation. These laws describe how gases respond to changes in pressure, volume, temperature, and amount.

Boyle's Law states that at constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂. If you compress a gas, its pressure increases. Charles's Law states that at constant pressure, volume and absolute temperature are directly proportional: V₁/T₁ = V₂/T₂. Temperature must always be in Kelvin (K = °C + 273.15).

Gay-Lussac's Law states that at constant volume, pressure and temperature are directly proportional: P₁/T₁ = P₂/T₂. The Combined Gas Law merges these three: P₁V₁/T₁ = P₂V₂/T₂.

Avogadro's Law states that at constant temperature and pressure, equal volumes of gases contain equal numbers of moles. This leads to the Ideal Gas Law: PV = nRT, where P is pressure (atm), V is volume (L), n is moles, R is the gas constant (0.08206 L·atm/mol·K), and T is temperature in Kelvin. Real gases deviate from ideal behavior at high pressures and low temperatures.

Key terms

Boyle's Law
At constant temperature, pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂
Charles's Law
At constant pressure, volume and absolute temperature of a gas are directly proportional: V₁/T₁ = V₂/T₂
Ideal Gas Law
PV = nRT; relates pressure, volume, moles, and temperature of an ideal gas
STP
Standard Temperature and Pressure: 0°C (273.15 K) and 1 atm; one mole of ideal gas occupies 22.4 L at STP
Kelvin scale
Absolute temperature scale used in gas law calculations; K = °C + 273.15; 0 K is absolute zero
Gay-Lussac's Law
At constant volume, pressure and absolute temperature of a gas are directly proportional: P₁/T₁ = P₂/T₂

Flashcards

Boyle's Law formula
P₁V₁ = P₂V₂ (constant T and n); pressure and volume are inversely proportional
Charles's Law formula
V₁/T₁ = V₂/T₂ (constant P and n); volume and absolute temperature are directly proportional
Combined Gas Law
P₁V₁/T₁ = P₂V₂/T₂; combines Boyle's, Charles's, and Gay-Lussac's Laws
Molar volume at STP
One mole of any ideal gas occupies 22.4 L at 0°C and 1 atm (STP)
Dalton's Law
Total pressure of a gas mixture = sum of partial pressures of all component gases: P_total = P₁ + P₂ + ...
Absolute zero
0 Kelvin (-273.15°C); the theoretical temperature at which all molecular motion ceases
Ideal gas assumptions
Gas particles have negligible volume, no intermolecular forces, elastic collisions, and random motion
Real vs. ideal gas
Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and molecular volume

Questions

  1. A gas occupies 4.0 L at a pressure of 2.0 atm. If the temperature is kept constant and the pressure is reduced to 1.0 atm, what is the new volume?

    1. 2.0 L
    2. 4.0 L
    3. 8.0 L
    4. 1.0 L
    Show answer

    Answer: 8.0 L

    Boyle's Law: P₁V₁ = P₂V₂. (2.0 atm)(4.0 L) = (1.0 atm)(V₂). V₂ = 8.0 L. Reducing pressure at constant temperature doubles the volume

  2. In Charles's Law calculations, temperature must be converted to Kelvin before use.

    Show answer

    Answer: True

    Gas law calculations require absolute temperature. Using Celsius would give nonsensical results (e.g., 0°C would make volume zero in Charles's Law)

  3. The ideal gas law is expressed as PV = nRT, where R is the universal gas constant equal to approximately 0.08206 L·atm/(mol·K), and T must be in ________ units.

    Show answer

    Answer: kelvin

    T in the ideal gas law and all gas laws must be in Kelvin (absolute temperature) to ensure the math works correctly

  4. How many moles of gas are present in a 5.0 L container at 27°C and 2.0 atm pressure? (R = 0.08206 L·atm/mol·K)

    1. 0.41 mol
    2. 0.24 mol
    3. 2.44 mol
    4. 0.407 mol
    Show answer

    Answer: 0.407 mol

    n = PV/(RT) = (2.0 atm × 5.0 L) / (0.08206 × 300 K) = 10.0 / 24.618 ≈ 0.407 mol

  5. A gas at 300 K has a pressure of 1.5 atm. If the temperature is raised to 600 K at constant volume, what is the new pressure?

    1. 0.75 atm
    2. 1.5 atm
    3. 3.0 atm
    4. 6.0 atm
    Show answer

    Answer: 3.0 atm

    Gay-Lussac's Law: P₁/T₁ = P₂/T₂. 1.5/300 = P₂/600. P₂ = (1.5 × 600)/300 = 3.0 atm. Doubling temperature doubles pressure

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