Questions: A gas has a volume of 36.0 L and a pressure of 750 torr when the temperature is 10 °C. What is the pressure if the volume changes to 15.0 L and the temperature changes to 78°C, if the amount of gas stays the same? Express your answer using three significant figures.

Solution Steps

We are given the initial and final conditions of a gas:

• Initial volume, \( V_1 = 36.0 \, \text{L} \)
• Initial pressure, \( P_1 = 750 \, \text{torr} \)
• Initial temperature, \( T_1 = 10^\circ \text{C} \)
• Final volume, \( V_2 = 15.0 \, \text{L} \)
• Final temperature, \( T_2 = 78^\circ \text{C} \)

To use the ideal gas law, temperatures must be in Kelvin: \[ T_1 = 10 + 273.15 = 283.15 \, \text{K} \] \[ T_2 = 78 + 273.15 = 351.15 \, \text{K} \]

The combined gas law is given by: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] We need to solve for \( P_2 \): \[ P_2 = \frac{P_1 V_1 T_2}{T_1 V_2} \]

Substitute the known values into the equation: \[ P_2 = \frac{750 \, \text{torr} \times 36.0 \, \text{L} \times 351.15 \, \text{K}}{283.15 \, \text{K} \times 15.0 \, \text{L}} \]

Perform the calculation: \[ P_2 = \frac{750 \times 36.0 \times 351.15}{283.15 \times 15.0} \] \[ P_2 = \frac{9474300}{4247.25} \approx 2230.6 \, \text{torr} \]

Final Answer