Answer
🧪 Methane Gas Final Pressure Calculation
Problem Summary
A methane gas sample undergoes the following changes:
- Initial Temperature: −11.0 °C
- Final Temperature: 10.0 °C
- Initial Pressure: 3.3 atm
- Volume increases by 45.0%
Step 1: Convert Temperatures to Kelvin
T₁ = −11.0 + 273.15 = 262.15 K
T₂ = 10.0 + 273.15 = 283.15 K
T₂ = 10.0 + 273.15 = 283.15 K
Step 2: Express Volume Change
V₂ = 1.45 × V₁
Step 3: Apply the Combined Gas Law
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Rearranged: P₂ = (P₁ × T₂) / (T₁ × V₂/V₁)
Rearranged: P₂ = (P₁ × T₂) / (T₁ × V₂/V₁)
P₂ = (3.3 × 283.15) / (262.15 × 1.45) = 934.395 / 380.1175 ≈ 2.46 atm
Step 4: Round Final Answer
✅ Final Answer: P₂ ≈ 2.5 atm (rounded to 2 significant digits)
Key Concepts
- Increasing temperature tends to increase pressure.
- Increasing volume tends to decrease pressure.
- The combined gas law accounts for simultaneous changes in pressure, volume, and temperature.
- In this case, the volume increase has a slightly greater effect than the temperature rise, resulting in a net pressure decrease.