For many purposes we can treat methane (CH4) as an ideal gas at temperatures above its boiling point of –161. °C. Suppose the temperature of

Answer

Methane Gas Volume Change

🧪 Problem Statement

Methane (CH₄) behaves as an ideal gas at temperatures above −161°C. Suppose the temperature of a sample of methane gas is raised from −78.0°C to −58.0°C, and the pressure is decreased by 15%.

Determine whether the volume increases, decreases, or stays the same, and calculate the percentage change in volume.

🔁 Step 1: Apply the Combined Gas Law

Using the combined gas law:

(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
⇒ V₂ / V₁ = (P₁ / P₂) × (T₂ / T₁)
  

🌡️ Step 2: Convert Temperatures to Kelvin

• T₁ = -78.0°C + 273.15 = 195.15 K
• T₂ = -58.0°C + 273.15 = 215.15 K

⚖️ Step 3: Apply Pressure Change

Pressure is decreased by 15%:

P₂ = 0.85 × P₁ ⇒ P₁ / P₂ = 1 / 0.85 ≈ 1.176
  

🧮 Step 4: Plug into the Equation

Compute the volume ratio:

V₂ / V₁ = (1 / 0.85) × (215.15 / 195.15)
        ≈ 1.176 × 1.102 ≈ 1.297
  

📊 Step 5: Calculate Percentage Change

% Change = (1.297 - 1) × 100 = 29.7%
  

This outcome aligns with expectations: when temperature increases and pressure decreases, an ideal gas expands.