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SOLUTION:

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{1.20 atm} \\ & V_1 = \text{2.50 L} \\ & T_1 = 25^{\circ}\text{C} = \text{298 K} \\ & P_2 = \text{0.00300 atm} \\ & T_2 = -23^{\circ}\text{C} = \text{250 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{(\text{2.50 L})(\text{1.20 atm})(\text{250 K})}{(\text{0.00300 atm})(\text{298 K})} \\ & = \boxed{\text{839 L}} \end{aligned}[/tex]

Hence, the final volume of the balloon is 839 L.

[tex]\\[/tex]

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