To solve this problem, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature for a given amount of gas. The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where: P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, T1 and T2 are the initial and final temperatures.
Let's plug in the values we have:
P1 = 700 mmHg V1 = 600 ml T1 = 27 degrees Celsius = 27 + 273.15 = 300.15 K
P2 = 500 mmHg V2 = ? T2 = -20 degrees Celsius = -20 + 273.15 = 253.15 K
Now we can solve for V2:
(700 mmHg * 600 ml) / (300.15 K) = (500 mmHg * V2) / (253.15 K)
(700 * 600) / 300.15 = (500 * V2) / 253.15
420000 / 300.15 = (500 * V2) / 253.15
V2 = (420000 * 253.15) / (300.15 * 500)
V2 ≈ 707.01 ml
Therefore, the volume of the gas at -20 degrees Celsius and 500 mmHg would be approximately 707.01 ml.