Given that 0.10 mol of nitrogen gas undergoes two processes, which of the following statements about the final pressure of the gas is correct if the volume doubles and the temperature remains constant?

• A. The final pressure remains the same as the initial pressure.
• B. The final pressure is four times the initial pressure.
• C. The final pressure is half the initial pressure.
• D. The final pressure is twice the initial pressure.

Answer: (C)

Verified step by step guidance

1. Identify the gas law that relates pressure (P), volume (V), and temperature (T) for a fixed amount of gas. Since the temperature remains constant and the amount of gas does not change, use Boyle's Law, which states that \(P_1 \times V_1 = P_2 \times V_2\).
2. Define the initial conditions: let the initial pressure be \(P_1\) and the initial volume be \(V_1\). The final volume is given as twice the initial volume, so \(V_2 = 2 \times V_1\).
3. Apply Boyle's Law to find the final pressure \(P_2\): rearrange the equation to solve for \(P_2\), giving \(P_2 = \frac{P_1 \times V_1}{V_2}\).
4. Substitute the known value of \(V_2\) into the equation: \(P_2 = \frac{P_1 \times V_1}{2 \times V_1}\).
5. Simplify the expression to find the relationship between \(P_2\) and \(P_1\): \(P_2 = \frac{P_1}{2}\). This shows that the final pressure is half the initial pressure.