Answer
🧪 Final Pressure of Methane Gas — Ideal Gas Calculation
Problem Statement
A methane (CH₄) gas sample undergoes the following changes:
- Temperature increases from −10.0 °C to 20.0 °C
- Volume decreases by 30.0%
- Initial pressure: 2.2 atm
Determine the final pressure and round your answer to two significant digits.
Step 1: Convert Temperatures to Kelvin
T₁ = −10.0 + 273.15 = 263.15 K
T₂ = 20.0 + 273.15 = 293.15 K
T₂ = 20.0 + 273.15 = 293.15 K
Step 2: Volume Change
Volume decreased by 30% → final volume is:
V₂ = 0.70 × V₁
Step 3: Apply the Combined Gas Law
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
P₂ = (P₁ × T₂) / (T₁ × (V₂ / V₁))
P₂ = (2.2 × 293.15) / (263.15 × 0.70)
P₂ = (P₁ × T₂) / (T₁ × (V₂ / V₁))
P₂ = (2.2 × 293.15) / (263.15 × 0.70)
Step 4: Calculate the Final Pressure
P₂ ≈ 644.93 / 184.205 ≈ 3.50 atm
✅ Final Answer:
P₂ ≈ 3.5 atm (rounded to 2 significant digits)
Concept Summary
- Increasing temperature raises gas pressure.
- Decreasing volume also raises pressure.
- Both effects combine, resulting in a higher final pressure.
- The ideal gas law and its derivative (combined gas law) explain the relationship.