Biphenyl, C12H10, is a nonvolatile, non ionizing 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 14.3 g of biphenyl in 25.8 g of benzene?
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To calculate the vapor pressure of the solution, we can use Raoult's Law, which states that the vapor pressure of a solution is equal to the vapor pressure of the solvent multiplied by the mole fraction of the solvent in the solution.
First, let's calculate the mole fraction of benzene in the solution. The mole fraction of a component is calculated by dividing the moles of that component by the total moles of all components in the solution.
To calculate the moles of benzene, we need to know its molar mass. The molar mass of benzene (C6H6) is:
6*12.01 g/mol (for carbon) + 6*1.01 g/mol (for hydrogen) = 78.11 g/mol
Now we can calculate the moles of benzene:
moles of benzene = mass of benzene / molar mass of benzene
moles of benzene = 25.8 g / 78.11 g/mol
moles of benzene = 0.3304 mol
Next, let's calculate the moles of biphenyl. We also need to know its molar mass. The molar mass of biphenyl (C12H10) is:
12*12.01 g/mol (for carbon) + 10*1.01 g/mol (for hydrogen) = 154.22 g/mol
Now we can calculate the moles of biphenyl:
moles of biphenyl = mass of biphenyl / molar mass of biphenyl
moles of biphenyl = 14.3 g / 154.22 g/mol
moles of biphenyl = 0.0928 mol
The total moles of the solution can be calculated by adding the moles of benzene and biphenyl:
total moles of solution = moles of benzene + moles of biphenyl
total moles of solution = 0.3304 mol + 0.0928 mol
total moles of solution = 0.4232 mol
Now, we can calculate the mole fraction of benzene in the solution:
mole fraction of benzene = moles of benzene / total moles of solution
mole fraction of benzene = 0.3304 mol / 0.4232 mol
mole fraction of benzene = 0.7802
Finally, we can use Raoult's Law to calculate the vapor pressure of the solution:
vapor pressure of solution = vapor pressure of benzene * mole fraction of benzene
vapor pressure of solution = 100.84 torr * 0.7802
vapor pressure of solution = 78.75 torr
Therefore, the vapor pressure of the solution made from dissolving 14.3 g of biphenyl in 25.8 g of benzene is 78.75 torr.