To solve the problem of finding the temperature of a gas when its pressure is reduced at constant volume, we can use the ideal gas law and the relationship between pressure and temperature. Let's break this down step-by-step. ### Step 1: Understand the Ideal Gas Law The ideal gas law is given by the equation: \[ PV = nRT \] Where: - \( P \) = pressure of the gas (in atm) - \( V \) = volume of the gas (in liters) - \( n \) = number of moles of gas - \( R \) = ideal gas constant (0.0821 L·atm/(K·mol)) - \( T \) = temperature of the gas (in Kelvin) ### Step 2: Use the Relationship Between Pressure and Temperature Since the volume is constant, we can use the relationship derived from the ideal gas law that relates pressure and temperature: \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \] Where: - \( P_1 \) and \( T_1 \) are the initial pressure and temperature. - \( P_2 \) and \( T_2 \) are the final pressure and temperature. ### Step 3: Identify the Given Values From the problem: - Initial pressure, \( P_1 = 9 \) atm - Initial temperature, \( T_1 = 0°C = 273K \) (we convert Celsius to Kelvin by adding 273) - Final pressure, \( P_2 = 3 \) atm - Final temperature, \( T_2 \) is what we need to find. ### Step 4: Rearranging the Equation We can rearrange the equation to solve for \( T_2 \): \[ T_2 = T_1 \times \frac{P_2}{P_1} \] ### Step 5: Substitute the Values Now, we substitute the known values into the equation: \[ T_2 = 273K \times \frac{3 \text{ atm}}{9 \text{ atm}} \] ### Step 6: Calculate \( T_2 \) Now, we perform the calculation: \[ T_2 = 273K \times \frac{1}{3} \] \[ T_2 = 273K \times 0.3333 \] \[ T_2 = 91K \] ### Conclusion The final temperature of the gas when the pressure is reduced to 3 atm at constant volume is **91K**. ### Explanation of Other Options - **Option B (273K)**: This is the initial temperature of the gas, not the final temperature after the pressure change. - **Option C (300K)**: This value does not relate to the calculations based on the pressure change and is not derived from the ideal gas law. - **Option D (91°C)**: This is a misinterpretation of the temperature in Kelvin. 91K is equivalent to -182°C, not 91°C. ### Revision Summary - Use the ideal gas law to relate pressure and temperature. - Convert Celsius to Kelvin when necessary. - At constant volume, use the ratio of pressures to find the new temperature. - Always check the units and conversions to avoid common pitfalls. The correct answer is **A. 91K**.