Answer
🧪 Methane Gas Volume Change with Temperature and Pressure Changes
Problem Summary
Determine whether the volume of a methane gas sample increases or decreases, and by what percentage, given the following changes:
- Temperature increases from 97.0 °C to 116.0 °C
- Pressure decreases by 10%
Step 1: Convert Temperatures to Kelvin
T₁ = 97.0 + 273.15 = 370.15 K
T₂ = 116.0 + 273.15 = 389.15 K
T₂ = 116.0 + 273.15 = 389.15 K
Step 2: Adjust Pressure
P₂ = 0.90 × P₁
Step 3: Apply the Combined Gas Law
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Rearrange to find volume ratio:
V₂ / V₁ = (T₂ / T₁) × (P₁ / P₂)
Substitute values:
V₂ / V₁ = (389.15 / 370.15) × (1 / 0.90) ≈ 1.0513 × 1.1111 ≈ 1.168
Step 4: Calculate Percentage Change
Percentage Increase = (1.168 − 1) × 100% = 16.8%
✅ Final Answer:
The volume of the methane gas increases by approximately 16.8%.
Key Concepts:
- The ideal gas law (PV = nRT) leads to the combined gas law for comparing two states.
- Rising temperature expands gas volume.
- Lower pressure reduces constraints on gas, allowing further expansion.
- Both changes together lead to a net increase in volume.