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 Pressure Calculation Using Combined Gas Law
1. Problem Summary
Determine the final pressure (P₂) of a methane gas sample when:
- Initial temperature T₁ = 18.0°C
- Final temperature T₂ = −20.0°C
- Initial pressure P₁ = 4.4 atm
- Volume increases by 40%
2. Convert Temperatures to Kelvin
T₁ = 18.0 + 273.15 = 291.15 K
T₂ = −20.0 + 273.15 = 253.15 K
T₂ = −20.0 + 273.15 = 253.15 K
3. Apply the Combined Gas Law
The combined gas law is:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Since V₂ = 1.40 × V₁, we substitute and solve for P₂:
P₂ = (P₁ × T₂) / (T₁ × 1.40)
4. Insert Known Values
P₂ = (4.4 atm × 253.15 K) / (291.15 K × 1.40)
P₂ ≈ 1113.86 / 407.61 ≈ 2.73 atm
P₂ ≈ 1113.86 / 407.61 ≈ 2.73 atm
✅ Final Answer:
P₂ ≈ 2.73 atm
5. Key Concepts
- Ideal Gas Law: PV = nRT (combined gas law applies when n and R are constant)
- Volume ↑ → Pressure ↓ (inversely proportional)
- Temperature ↓ → Pressure ↓ (directly proportional)
- Always convert temperatures to Kelvin when using gas laws