To solve this problem, we can use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its temperature and the heat of vaporization. The equation is as follows:
ln(P2/P1) = (ΔHvap/R) * (1/T1 - 1/T2)
Where: P1 and T1 are the initial pressure and temperature, P2 and T2 are the final pressure and temperature, ΔHvap is the heat of vaporization, R is the ideal gas constant.
Let's plug in the given values and solve for T2:
P1 = 115 torr T1 = 34.9°C = 34.9 + 273.15 = 307.05 K P2 = 760 torr ΔHvap = 40.5 kJ/mol = 40.5 * 1000 J/mol R = 8.314 J/(mol·K)
ln(760/115) = (40.5 * 1000 J/mol / 8.314 J/(mol·K)) * (1/307.05 K - 1/T2)
Now we can rearrange the equation to solve for T2:
(40.5 * 1000 J/mol / 8.314 J/(mol·K)) * (1/307.05 K - 1/T2) = ln(760/115)
Simplifying:
(40.5 * 1000 / 8.314) * (1/307.05 - 1/T2) = ln(760/115)
(4.875 * 10^3) * (1/307.05 - 1/T2) = ln(760/115)
1/307.05 - 1/T2 = ln(760/115) / (4.875 * 10^3)
1/T2 = 1/307.05 - ln(760/115) / (4.875 * 10^3)
Now, we can solve for T2:
T2 = 1 / (1/307.05 - ln(760/115) / (4.875 * 10^3))
T2 ≈ 78.8°C
Therefore, when the pressure is 760 torr, the temperature is approximately 78.8°C.