For many purposes we can treat methane (CH4) as an ideal gas at temperatures above its boiling point of -161. C. suppose the temperatyre of a sample of methane is raised from 35.0 C to 81.0 C, and at the same time the pressure is decreeased by 10.0%
Answer
🧪 Methane Gas Volume Change Using the Combined Gas Law
Objective:
To determine how the volume of methane gas changes when temperature increases and pressure decreases.
Given:
- Initial temperature: T₁ = 35.0°C = 308.15 K
- Final temperature: T₂ = 81.0°C = 354.15 K
- Pressure decreases by 10%: P₂ = 0.90 × P₁
Step 1: Use the Combined Gas Law
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Rearranged to solve for the volume ratio:
V₂ / V₁ = (T₂ / T₁) × (P₁ / P₂)
Step 2: Substitute the Values
V₂ / V₁ = (354.15 / 308.15) × (1 / 0.90)
≈ 1.1493 × 1.1111 ≈ 1.28
≈ 1.1493 × 1.1111 ≈ 1.28
Step 3: Calculate Percentage Change
Volume increase = (1.28 − 1) × 100% = 28.0%
✅ Final Answer:
The volume of methane gas increases by approximately 28.0%.
Key Concepts:
- Combined Gas Law: accounts for simultaneous changes in temperature and pressure.
- Increased temperature causes gas to expand.
- Decreased pressure also causes gas to expand.
- In this case, both effects lead to a net increase in volume.