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.
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To determine the mole fraction of the solvent in the gas phase, we can use the concept of Raoult's Law.
Raoult's Law states that the partial pressure of a component in a mixture of ideal gases is equal to the vapor pressure of the component multiplied by its mole fraction in the liquid phase.
In this case, we are given the vapor pressures of the solvent at two different temperatures: 50 mm Hg at 25°C and 200 mm Hg at 45°C.
First, we need to calculate the mole fraction of the solvent in the liquid phase at 35°C. We can use the following formula:
X₁ = P₁/P, where X₁ is the mole fraction of solvent in the liquid phase, P₁ is the vapor pressure of the solvent at 25°C, and P is the system pressure.
Given:
P₁ = 50 mm Hg
P = 760 mm Hg
Substituting these values into the formula, we have:
X₁ = 50/760
Simplifying, X₁ ≈ 0.0658
Next, we can use Raoult's Law to calculate the mole fraction of the solvent in the gas phase at 35°C. The mole fraction of the solvent in the gas phase (X₂) can be expressed as:
X₂ = P₂/P, where X₂ is the mole fraction of solvent in the gas phase, P₂ is the vapor pressure of the solvent at 35°C, and P is the system pressure.
To calculate P₂, we can use the ideal gas law:
P₂ = X₁ * P
Substituting the values we have:
P₂ = 0.0658 * 760
Simplifying, P₂ ≈ 50.088 mm Hg
Now, we can calculate X₂:
X₂ = P₂/P
Substituting the values:
X₂ = 50.088/760
Simplifying, X₂ ≈ 0.0658
Therefore, the mole fraction of the solvent in the gas phase at 35°C is approximately 0.0658.