To determine the pressure of the gas after the change in volume and temperature, we can use the combined gas law:
[tex]\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \][/tex]
Here:
- \( P_1 \) = initial pressure = \( 338 \, \text{mm Hg} \)
- \( V_1 \) = initial volume = \( 0.225 \, \text{L} \)
- \( T_1 \) = initial temperature in Kelvin = \( 72^\circ \text{C} \) converted to Kelvin
- \( V_2 \) = final volume = \( 1.50 \, \text{L} \)
- \( T_2 \) = final temperature in Kelvin = \( -15^\circ \text{C} \) converted to Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
[tex]\[ T_1 = 72 + 273.15 = 345.15 \, \text{K} \][/tex]
[tex]\[ T_2 = -15 + 273.15 = 258.15 \, \text{K} \][/tex]
Next, we'll rearrange the combined gas law to solve for the final pressure \( P_2 \):
[tex]\[ P_2 = \frac{P_1 V_1 T_2}{V_2 T_1} \][/tex]
Plugging in the given values:
[tex]\[ P_2 = \frac{338 \, \text{mm Hg} \times 0.225 \, \text{L} \times 258.15 \, \text{K}}{1.50 \, \text{L} \times 345.15 \, \text{K}} \][/tex]
Now, let's simplify and calculate:
[tex]\[ P_2 = \frac{19,669.3875}{517.725} \approx 37.92 \, \text{mm Hg} \][/tex]
Thus, the pressure of the gas in the flask is approximately \( 37.9 \, \text{mm Hg} \).
Therefore, the correct answer is:
b. [tex]\( 37.9 \, \text{mm Hg} \)[/tex]
