Biphenyl, C12H10, is a nonvolatile, nonionizing solute that is soluble in benzene, C6H6. At 25 °C, the vapor pressure of pure benzene is 100.84 torr. What is the vapor pressure of a solution made from dissolving 17.5 g of biphenyl in 28.8 g of benzene?

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To determine the vapor pressure of the solution, we need to apply Raoult's law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent.

First, we need to calculate the number of moles of biphenyl and benzene in the solution:

The molar mass of biphenyl (C₁₂H₁₀) can be calculated as follows:
- The molar mass of carbon (C) is 12.01 g/mol.
- There are 12 carbon atoms in biphenyl, so the mass of carbon in biphenyl is 12.01 g/mol × 12 = 144.12 g/mol.
- The molar mass of hydrogen (H) is 1.008 g/mol.
- There are 10 hydrogen atoms in biphenyl, so the mass of hydrogen in biphenyl is 1.008 g/mol × 10 = 10.08 g/mol.
- Adding the masses of carbon and hydrogen, we get the molar mass of biphenyl: 144.12 g/mol + 10.08 g/mol = 154.2 g/mol.

To calculate the number of moles of biphenyl, divide the given mass of biphenyl (17.5 g) by its molar mass:
Number of moles of biphenyl = 17.5 g / 154.2 g/mol.

The molar mass of benzene (C₆H₆) is:

- The molar mass of carbon (C) is 12.01 g/mol.
- There are 6 carbon atoms in benzene, so the mass of carbon in benzene is 12.01 g/mol × 6 = 72.06 g/mol.
- The molar mass of hydrogen (H) is 1.008 g/mol.
- There are 6 hydrogen atoms in benzene, so the mass of hydrogen in benzene is 1.008 g/mol × 6 = 6.048 g/mol.
- Adding the masses of carbon and hydrogen, we get the molar mass of benzene: 72.06 g/mol + 6.048 g/mol = 78.1 g/mol.

To calculate the number of moles of benzene, divide the given mass of benzene (28.8 g) by its molar mass:
Number of moles of benzene = 28.8 g / 78.1 g/mol.

Now that we have the number of moles of biphenyl and benzene, we can calculate their mole fractions in the solution:

Mole fraction of biphenyl = moles of biphenyl / total moles.
Mole fraction of benzene = moles of benzene / total moles.

Using the mole fractions and Raoult's law, we can calculate the vapor pressure of the solution:

Vapor pressure of the solution = mole fraction of benzene × vapor pressure of pure benzene.

Substituting the values, we can compute the solution's vapor pressure.