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Step 1: List the given values.
To convert the temperature from degree Celsius to kelvin, add 273 to the temperature expressed in degree Celsius.
[tex]\begin{aligned} & P_1 = \text{750 mmHg} \\ & V_1 = 3.2 \times 10^3 \: \text{L} \\ & T_1 = 20^{\circ}\text{C} = \text{293 K} \\ & P_2 = \text{76 mmHg} \\ & T_2 = -33^{\circ}\text{C} = \text{240 K} \end{aligned}[/tex]
Step 2: Calculate the final volume using combined gas law.
[tex]\begin{aligned} \frac{P_1V_1}{T_1} & = \frac{P_2V_2}{T_2} \\ V_2P_2T_1 & = V_1P_1T_2 \\ \frac{V_2P_2T_1}{P_2T_1} & = \frac{V_1P_1T_2}{P_2T_1} \\ V_2 & = \frac{V_1P_1T_2}{P_2T_1} \\ & = \frac{(3.2 \times 10^3 \: \text{L})(\text{750 mmHg})(\text{240 K})}{(\text{76 mmHg})(\text{293 K})} \\ & = \boxed{2.6 \times 10^4 \: \text{L}} \end{aligned}[/tex]
Hence, the new volume of the balloon will be 2.6 × 10⁴ L.
[tex]\\[/tex]
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