Question

The pressure of a gas at the triple point of water is 1.50 atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?

Answer 1

The pressure of a gas at the temperature at which CO2 solidifies cannot be determined with the provided information. Additional data is needed regarding the conditions under which CO2 solidifies, specifically its pressure, as the phase change would render the ideal gas laws inapplicable.

Step-by-step explanation:

The question revolves around the behaviour of a gas under various conditions and relates this to certain specific points on a phase diagram. The student is given the initial conditions of a gas at the triple point of water (0.01°C, 0.006 atm) and is asked to find the pressure of the gas at the temperature at which CO2 solidifies. The temperature at which CO2 solidifies, under normal atmospheric pressure is -78.5°C; however, the pressure at which it solidifies is not provided, thus this temperature change implies a phase change as well, which would render the gas laws inapplicable as they only apply to gases.

If we were to ignore the phase change that occurs when CO2 solidifies and simply consider the temperatures, we could use Charles' Law to relate the volume and temperature of the gas, but this is not possible without assuming the gas remains in a gaseous state. Nevertheless, Charles' Law and a pressure-temperature relationship in the context of gases can usually be represented by the ideal gas law: P1/T1 = P2/T2, where P is pressure and T is absolute temperature (in Kelvin). Given we do not have enough data to perform this calculation for this scenario, we cannot determine the pressure without additional information about the CO2 phase change.

Answer 2

The pressure of a gas at the triple point of water is 1.50 atm, which means it is at the temperature and pressure where water can exist as a solid, liquid, and gas simultaneously.

To find the pressure of the gas at the temperature at which CO2 solidifies, we need to know the triple point of CO2. The triple point of CO2 is -56.6°C and 5.1 atm.

If the volume of the gas remains unchanged, then its pressure will change with a change in temperature. Using the ideal gas law, PV = nRT, we can find the new pressure of the gas:

P1V1 = P2V2

At the triple point of water:

P1 = 1.50 atm

V1 = V (unchanged)

T1 = 0.01°C (triple point of water)

At the triple point of CO2:

P2 = 5.1 atm

V2 = V1 (unchanged)

T2 = -56.6°C

Using the ideal gas law and solving for P2:

P2 = P1(T2/T1)

P2 = 1.5 x (-56.6+273.15) / (0.01+273.15)

P2 = 0.818 atm

Therefore, the pressure of the gas at the temperature at which CO2 solidifies is 0.818 atm.