A sample of gas expands from 1.0 m^3 to 4.0 m^3 at constant temperature and pressure. According to the ideal gas law, what happens to the number of moles of gas in the system?

• A. The number of moles doubles.
• B. The number of moles decreases by a factor of 4.
• C. The number of moles increases by a factor of 4.
• D. The number of moles remains constant.

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 the number of moles, \(R\) is the gas constant, and \(T\) is temperature.
2. Note that the problem states the temperature (\(T\)) and pressure (\(P\)) are constant during the expansion.
3. Since \(P\), \(R\), and \(T\) are constants, the equation simplifies to \(P \times V = n \times \text{constant}\), meaning \(V\) is directly proportional to \(n\) if \(P\) and \(T\) are constant.
4. However, in this problem, the gas expands from 1.0 m\(^3\) to 4.0 m\(^3\) at constant \(P\) and \(T\), so the volume increases by a factor of 4.
5. Because \(P\) and \(T\) are constant, the number of moles \(n\) must remain constant to satisfy the ideal gas law; the increase in volume does not imply a change in \(n\).