To solve the problem of determining the volume of a gas at a new temperature and pressure, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas. The combined gas law is expressed as: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] Where: - \( P_1 \) and \( P_2 \) are the initial and final pressures, - \( V_1 \) and \( V_2 \) are the initial and final volumes, - \( T_1 \) and \( T_2 \) are the initial and final temperatures in Kelvin. ### Step 1: Identify the Initial Conditions At Standard Temperature and Pressure (S.T.P.): - \( V_1 = 30.0 \, \text{dm}^3 \) - \( T_1 = 0^\circ C = 273.15 \, \text{K} \) - \( P_1 = 1 \, \text{atm} = 760 \, \text{mm Hg} \) ### Step 2: Identify the Final Conditions We need to find the volume \( V_2 \) at: - \( T_2 = 91^\circ C = 91 + 273.15 = 364.15 \, \text{K} \) - \( P_2 = 380 \, \text{mm Hg} \) ### Step 3: Rearranging the Combined Gas Law We can rearrange the combined gas law to solve for \( V_2 \): \[ V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} \] ### Step 4: Plugging in the Values Now we can substitute the known values into the equation: \[ V_2 = 30.0 \, \text{dm}^3 \times \frac{760 \, \text{mm Hg}}{380 \, \text{mm Hg}} \times \frac{364.15 \, \text{K}}{273.15 \, \text{K}} \] ### Step 5: Calculating Each Component 1. **Pressure Ratio**: \[ \frac{760}{380} = 2 \] 2. **Temperature Ratio**: \[ \frac{364.15}{273.15} \approx 1.333 \] ### Step 6: Final Calculation Now we can calculate \( V_2 \): \[ V_2 = 30.0 \, \text{dm}^3 \times 2 \times 1.333 \] \[ V_2 = 30.0 \, \text{dm}^3 \times 2.666 \approx 80.0 \, \text{dm}^3 \] ### Conclusion Thus, the volume of the gas at 91°C and 380 mm Hg is approximately **80.0 dm³**. Therefore, the correct answer is **D. 80.0 dm³**. ### Explanation of Other Options - **A. 20.0 dm³**: This option is too low and does not account for the increase in temperature and the decrease in pressure adequately. - **B. 40.0 dm³**: This option is also too low; it does not reflect the significant increase in volume due to the high temperature. - **C. 60.0 dm³**: This option is closer but still underestimates the volume based on the calculations we performed. ### Revision Summary - Use the combined gas law to relate pressure, volume, and temperature. - Convert all temperatures to Kelvin and ensure pressure units are consistent. - Rearrange the formula to solve for the unknown volume. - Carefully calculate each component step-by-step to avoid errors.