Answer: To solve this problem, we can use the combined gas law, which relates the initial and final states of a gas sample when pressure, volume, and temperature change while the amount of gas remains constant. The formula for the combined gas law is:
(P1 * V1) / T1 = (P2 * V2) / T2
where:
P1 = initial pressure (in torr)
V1 = initial volume (in cm³)
T1 = initial temperature (in Kelvin)
P2 = final pressure (in torr)
V2 = final volume (in cm³)
T2 = final temperature (in Kelvin)
Let's use the given data and solve for V2:
Given data:
P1 = 750 torr
V1 = 625 cm³
T1 = 20.0°C = 20.0°C + 273.15 (convert to Kelvin) ≈ 293.15 K
P2 = 750 torr
T2 = -80.0°C = -80.0°C + 273.15 (convert to Kelvin) ≈ 193.15 K
Now, plug the values into the combined gas law and solve for V2:
(750 torr * 625 cm³) / 293.15 K = (750 torr * V2) / 193.15 K
Solve for V2:
V2 = (750 torr * 625 cm³ * 193.15 K) / (750 torr * 293.15 K)
V2 = (750 * 625 * 193.15) / 293.15
V2 ≈ 304.69 cm³
The final volume (V2) at -80.0°C and 750 torr is approximately 304.69 cubic centimeters.