We can solve this problem using the combined gas law, which relates the initial and final conditions of a gas sample undergoing a change in temperature, pressure, and volume.
The combined gas law formula is given as:
P1 * V1 / T1 = P2 * V2 / T2
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure
V2 = Final volume
T2 = Final temperature
Given:
Initial volume, V1 = 0.750 mL
Final volume, V2 = 0.750 mL / 2 = 0.375 mL
Initial temperature, T1 = -32.7 °C
Let's denote the final temperature, T2, as the unknown value we are trying to find.
We can rearrange the formula to solve for T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
We need to determine the final pressure, P2, in order to use this formula. However, the problem statement does not provide information about pressure. Without knowing the pressure, we are unable to determine the exact temperature needed to reduce the volume to half of the initial amount. Additional information, such as the pressure, is required to solve this problem.