Under which of the following conditions does the molar volume of a gas decrease according to the ideal gas law?

• A. Increasing pressure while keeping temperature constant
• B. Increasing temperature while keeping pressure constant
• C. Decreasing temperature while keeping pressure constant
• D. Decreasing pressure while keeping temperature constant

Answer: (A)

Verified step by step guidance

1. Recall the ideal gas law: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
2. Molar volume is defined as the volume occupied by one mole of gas, so \(V_m = \frac{V}{n}\). Using the ideal gas law, this can be rewritten as \(V_m = \frac{R \times T}{P}\).
3. Analyze how molar volume changes with pressure and temperature by looking at the formula \(V_m = \frac{R \times T}{P}\). Molar volume is directly proportional to temperature and inversely proportional to pressure.
4. To decrease molar volume, either decrease temperature or increase pressure, while keeping the other variable constant.
5. From the given options, increasing pressure while keeping temperature constant will decrease molar volume according to the ideal gas law.