High School

The vapor pressure of benzene is 100.0 mmHg at 26.1°C. Calculate the vapor pressure of a solution containing 27.6 g of camphor ([tex]C_{10}H_{16}O[/tex]) dissolved in 98.2 g of benzene. (Camphor is a low volatility solid.)

Provide your answer in mmHg.

Answer :

If the vapor pressure of benzene is 100.0 mmHg at 26.1°C, the vapor pressure of the solution is 87.4 mmHg.

How to calculate vapour pressure

To calculate the vapor pressure of the solution, use Raoult's law, which says the vapor pressure of a solution is proportional to the mole fraction of the solvent in the solution:

P_solution = X_benzene * P_benzene

where

P_solution is the vapor pressure of the solution,

X_benzene is the mole fraction of benzene in the solution, and

P_benzene is the vapor pressure of pure benzene.

To find the mole fraction of benzene, calculate the moles of each component in the solution

moles of benzene = 98.2 g / 78.11 g/mol = 1.257 mol

moles of camphor = 27.6 g / 152.23 g/mol = 0.181 mol

The total moles of the solution is the sum of the moles of benzene and camphor

total moles = 1.257 mol + 0.181 mol

= 1.438 mol

The mole fraction of benzene is the moles of benzene divided by the total moles

X_benzene = 1.257 mol / 1.438 mol

= 0.874

Substituting the given values

P_solution = X_benzene * P_benzene

P_solution = 0.874 * 100.0 mmHg

P_solution = 87.4 mmHg

Therefore, the vapor pressure of the solution is 87.4 mmHg.

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