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 a
Answer
🧪 Methane Gas Volume Change with Temperature and Pressure Increase
Problem Summary
A sample of methane gas experiences the following changes:
- Temperature increases from −30.0 °C to −6.0 °C
- Pressure increases by 15.0%
We are to determine whether the gas volume increases, decreases, or remains constant, and by what percentage.
Step 1: Convert Temperatures to Kelvin
T₁ = −30.0 + 273.15 = 243.15 K
T₂ = −6.0 + 273.15 = 267.15 K
T₂ = −6.0 + 273.15 = 267.15 K
Step 2: Express Pressure Change
P₂ = 1.15 × P₁ (since pressure increases by 15%)
Step 3: Use the Combined Gas Law
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Rearranged: V₂ / V₁ = (T₂ / T₁) × (P₁ / P₂)
Rearranged: V₂ / V₁ = (T₂ / T₁) × (P₁ / P₂)
Substitute known values:
V₂ / V₁ = (267.15 / 243.15) × (1 / 1.15)
≈ 1.0987 × 0.8696 ≈ 0.9554
≈ 1.0987 × 0.8696 ≈ 0.9554
Step 4: Calculate Percentage Change in Volume
Percentage Change = (0.9554 − 1) × 100 = −4.46%
✅ Final Answer:
The volume of the methane gas decreases by approximately 4.5%.
Key Concepts:
- Temperature increase tends to expand gas.
- Pressure increase compresses gas.
- In this case, the effect of increasing pressure dominates the modest temperature rise.
- As a result, the gas volume decreases slightly.