If a gas is compressed isothermally, which of the following statements is true according to the ideal gas law?

• A. The number of moles of the gas must decrease as the volume decreases.
• B. The pressure of the gas decreases as the volume decreases.
• C. The temperature of the gas increases as the volume decreases.
• D. The pressure of the gas increases as the volume decreases.

Answer: (D)

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 number of moles, \(R\) is the gas constant, and \(T\) is temperature.
2. Understand that an isothermal process means the temperature \(T\) remains constant throughout the compression.
3. Since \(T\) is constant and \(n\) (number of moles) does not change during compression, the product \(P \times V\) must remain constant.
4. Therefore, if the volume \(V\) decreases, the pressure \(P\) must increase to keep the product \(P \times V\) constant.
5. Conclude that during isothermal compression, the pressure of the gas increases as the volume decreases, consistent with the ideal gas law.