Answer
🧪 Methane Gas Volume Change with Temperature and Pressure Reduction
Problem Overview
A methane gas sample undergoes the following changes:
- Temperature decreases from 76.0 °C to 59.0 °C
- Pressure decreases by 10.0%
Determine if the volume increases or decreases, and calculate the percentage change in volume.
Step 1: Convert Temperatures to Kelvin
T₁ = 76.0 + 273.15 = 349.15 K
T₂ = 59.0 + 273.15 = 332.15 K
T₂ = 59.0 + 273.15 = 332.15 K
Step 2: Apply Pressure Change
P₂ = 0.90 × P₁ (10% decrease)
Step 3: Use the Combined Gas Law
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
V₂ / V₁ = (T₂ / T₁) × (P₁ / P₂)
V₂ / V₁ = (T₂ / T₁) × (P₁ / P₂)
V₂ / V₁ = (332.15 / 349.15) × (1 / 0.90)
≈ 0.9513 × 1.1111 ≈ 1.057
≈ 0.9513 × 1.1111 ≈ 1.057
Step 4: Calculate Percentage Change
Percentage change = (1.057 − 1) × 100 = 5.7% ≈ 6%
✅ Final Answer:
The volume of methane gas increases by approximately 6%.
Key Concepts:
- Lower temperature tends to decrease volume.
- Lower pressure allows gas to expand.
- In this case, the effect of reduced pressure outweighs the cooling effect.
- Therefore, there is a net increase in volume.