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 a

Answer

Combined Gas Law – Methane Pressure Calculation

🧪 Combined Gas Law: Methane Gas Pressure Problem

1. Problem Summary

We are given a sample of methane gas that undergoes a temperature and volume change. We are to determine the final pressure using the combined gas law.

Given:

• Initial temperature: T₁ = −19.0°C = 254.15 K
• Final temperature: T₂ = 12.0°C = 285.15 K
• Initial pressure: P₁ = 5.6 atm
• Volume decreases by 50%, so V₂ = 0.50 × V₁

2. Formula Used: Combined Gas Law

(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂

Substitute V₂ = 0.50 × V₁ and solve for P₂:

P₂ = (P₁ × T₂) / (T₁ × 0.50)

3. Plug in the Values

P₂ = (5.6 atm × 285.15 K) / (254.15 K × 0.50)
P₂ = 1596.84 / 127.075 ≈ 12.57 atm

✅ Final Answer:

P₂ ≈ 12.6 atm (rounded to 3 significant figures)

4. Key Concepts Recap

This is an application of the combined gas law.

Use Kelvin for temperature in gas law equations.

Decreasing volume increases pressure (inverse relationship).

Rising temperature also increases pressure (direct relationship).