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. Determine the
mole fraction of solvent in the gas phase.

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

Ptotal = Psolvent * Xsolvent

Where:
- Ptotal is the total pressure in the flask
- Psolvent is the vapor pressure of the solvent at the given temperature
- Xsolvent is the mole fraction of the solvent in the gas phase

We can rearrange the equation to solve for Xsolvent:

Xsolvent = Ptotal / Psolvent

Given:
- Psolvent at 25°C = 50 mm Hg
- Psolvent at 45°C = 200 mm Hg
- T = 35°C
- Ptotal is not given

To find Ptotal, we can use the ideal gas law:

Ptotal * V = n * R * T

Where:
- V is the volume of the flask
- n is the total moles of substance in the flask
- R is the ideal gas constant (0.0821 L·atm/(mol·K))

Since the solvent is the only species in the flask, the moles of solvent in the gas phase is equal to the total moles of substance in the flask.

Now, let's calculate the mole fraction of solvent in the gas phase step-by-step:

1. Convert the given vapor pressures from mm Hg to atm:
Psolvent at 25°C = 50 mm Hg ≈ 0.066 atm
Psolvent at 45°C = 200 mm Hg ≈ 0.266 atm

2. Convert the given temperature from Celsius to Kelvin:
T = 35°C + 273.15 = 308.15 K

3. Use the ideal gas law to find Ptotal:
Ptotal * V = n * R * T
Since the flask is closed, the volume is constant, so we can assume V = 1 L:
Ptotal = n * R * T / V
Since the solvent is the only species in the flask, n is the total moles of solvent.
Therefore, n = moles of solvent in the liquid + moles of solvent in the gas
Since the flask is closed, we assume that the total number of moles is constant:
n = moles of solvent in the liquid + moles of solvent in the gas

4. Use the Raoult's Law equation to calculate the mole fraction of the solvent in the gas phase:
Xsolvent = Ptotal / Psolvent

Now, you can calculate the mole fraction of the solvent in the gas phase using the above steps.

To determine the mole fraction of the solvent in the gas phase, we can use Raoult's Law, which states that the vapor pressure of a solution is proportional to the mole fraction of the solvent in the solution.

First, let's determine the vapor pressure of the solvent at 35°C using the given data. The vapor pressure of the solvent at 25°C is 50 mm Hg, and at 45°C is 200 mm Hg.

Now, we can use the following formula to calculate the vapor pressure at 35°C:

P₁/T₁ = P₂/T₂

where P₁ and P₂ are the vapor pressures, and T₁ and T₂ are the corresponding temperatures.

Let's substitute the given values:

50 mm Hg / 25°C = P₂ / 35°C

Solving for P₂, we get:

P₂ = (50 mm Hg / 25°C) * 35°C
P₂ = 70 mm Hg

Now we have the vapor pressure of the solvent at 35°C, which is 70 mm Hg.

To find the mole fraction of the solvent in the gas phase, we need to compare the vapor pressure of the solvent with the total vapor pressure of the solution.

The total vapor pressure of the solution can be calculated by adding the vapor pressures of both the solvent and the other species. However, in this case, the solvent is the only species present in the closed flask, so the total vapor pressure is simply equal to the vapor pressure of the solvent alone, which is 70 mm Hg.

Therefore, the mole fraction of the solvent in the gas phase can be calculated using the formula:

Mole fraction of solvent (in gas phase) = Vapor pressure of solvent / Total vapor pressure
= 70 mm Hg / 70 mm Hg
= 1

So, the mole fraction of the solvent in the gas phase is 1, indicating that all the molecules present in the gas phase are the solvent molecules.