at 25 degrees C liquid A has a vapor pressure of 100.0 torr, while liquid B has a vapor pressure of 200.0 torr. The heat of vaporization of liquid A is 32.0 kJ/mol and that of liquid b is 18.0 kJ/mol. At what celsius temperature will A and B have the same temperature.

I haven't the slighest idea how to solve this. What should I do first? Do I use the clausius-clayperon equation?

I think you stated the problem incorrectly. Do you want the temperature at which the VAPOR PRESSURES are equal? If so, then yes, you do use the Clausius Clapeyron equation. The vapor pressure will be proportional to e(-Hv/RT), where Hv is the heat of vaporization

To solve this problem, we can indeed use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its temperature and heat of vaporization. However, we need to modify the equation slightly to compare the vapor pressures of two different substances at different temperatures. Here's how you can approach it step by step:

1. Write down the Clausius-Clapeyron equation for both substances:
ln(P1/P2) = -(ΔHvap/R)(1/T1 - 1/T2)
where P1 and P2 are the vapor pressures of substances A and B, respectively, ΔHvap is the heat of vaporization, R is the gas constant (8.314 J/(mol K)), T1 is the initial temperature, and T2 is the desired temperature.

2. Rearrange the equations to isolate the temperature terms:
1/T1 - 1/T2 = (R/ΔHvap) * ln(P1/P2)

3. Plug in the given values for liquid A and liquid B:
For liquid A: P1 = 100.0 torr, ΔHvap = 32.0 kJ/mol
For liquid B: P2 = 200.0 torr, ΔHvap = 18.0 kJ/mol

4. Convert the temperatures to Kelvin:
Add 273 to both temperatures in Celsius to convert them to Kelvin.

5. Substitute the values into the equation, and solve for T2:
(1/T1) - (1/T2) = (8.314 J/(mol K) / (32.0 kJ/mol)) * ln(100.0 torr / 200.0 torr)

6. Rearrange the equation to solve for T2:
1/T2 = 1/T1 - [(8.314 J/(mol K) / (32.0 kJ/mol)) * ln(100.0 torr / 200.0 torr)]

7. Solve for T2:
Plug in the value of T1 (25 degrees Celsius + 273 = 298 K) and calculate T2.

This will give you the temperature at which substances A and B have the same vapor pressures.