The vapor pressure of an organic solvent is 50 mm Hg at 25°C and 200 mm Hg at 45°C. The solvent is

the only species in a closed flask at 35°C and is present in both liquid and vapor states. the system pressure is 760mmHg. Determine the
mole fraction of solvent in the gas phase.

I would use the Clausius-Clapeyron equation and solve for delta Hvap. Using that number, then solve for vapor pressure of the organic solvent at 35C (again using the CC equation). Then mole fraction = Psolvent/Ptotal.

To determine the mole fraction of the solvent in the gas phase, we can use Raoult's law.

Raoult's law states that the vapor pressure of a component in a mixture is proportional to its mole fraction in the liquid phase.

The mole fraction of the solvent in the gas phase can be calculated using the following formula:

Mole fraction of solvent in gas phase = Vapor pressure of solvent / System pressure

First, let's determine the vapor pressure of the solvent at 35°C using the given data. The vapor pressure is 50 mm Hg at 25°C and 200 mm Hg at 45°C. We need to interpolate between these two temperatures.

ΔT = 45°C - 25°C = 20°C
Vapor pressure difference = 200 mm Hg - 50 mm Hg = 150 mm Hg

Now, we can calculate the vapor pressure at 35°C:

Vapor pressure at 35°C = 50 mm Hg + (ΔT / 20°C) * Vapor pressure difference
= 50 mm Hg + (10°C / 20°C) * 150 mm Hg
= 50 mm Hg + 75 mm Hg
= 125 mm Hg

Next, we can substitute the values into the formula to determine the mole fraction of the solvent in the gas phase:

Mole fraction of solvent in gas phase = 125 mm Hg / 760 mm Hg
≈ 0.1645

Therefore, the mole fraction of the organic solvent in the gas phase is approximately 0.1645.

To determine the mole fraction of solvent in the gas phase, we can use Raoult's Law.

Raoult's Law states that the vapor pressure of a component in a mixture is equal to the product of the mole fraction of that component in the mixture and its vapor pressure in the pure state.

Let's denote the mole fraction of solvent in the liquid phase as x and the mole fraction of solvent in the gas phase as y. We are given the following information:

Vapor pressure of solvent at 25°C (liquid): 50 mm Hg
Vapor pressure of solvent at 45°C (liquid): 200 mm Hg
System pressure: 760 mm Hg
Temperature: 35°C

To find the mole fraction of solvent in the gas phase, we need to find the vapor pressure of the solvent at 35°C.

First, let's determine the vapor pressure of the solvent at 35°C using the given data. We can interpolate between the vapor pressures at 25°C and 45°C:

Vapor pressure of solvent at 35°C = 50 mm Hg + [(35°C - 25°C) / (45°C - 25°C)] * (200 mm Hg - 50 mm Hg)
= 50 mm Hg + (10°C / 20°C) * (200 mm Hg - 50 mm Hg)
= 50 mm Hg + 0.5 * 150 mm Hg
= 50 mm Hg + 75 mm Hg
= 125 mm Hg

Now that we have the vapor pressure of the solvent at 35°C, we can use Raoult's Law to find the mole fraction of the solvent in the gas phase.

According to Raoult's Law:

50 mm Hg * x + 200 mm Hg * (1 - x) = 125 mm Hg

Rearranging the equation:

50x + 200 - 200x = 125

150 - 150x = 125

-150x = -25

x = -25 / -150

x = 1/6 or approximately 0.1667

Therefore, the mole fraction of solvent in the gas phase is approximately 0.1667.