At 25 degrees Celsius the vapour pressure of pure benzene is 93.9 torr. When nonvolatile solvent is dissolved in benzene, the vapour pressure of benzene is lowered to 91.5 torr. What are the concerntration of solute and solvent expressed in mole fractions
To find the concentration of solute and solvent expressed as mole fractions, we need to use Raoult's law.
Raoult's law states that the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
Let's assume that the solvent is benzene (B) and the solute is the nonvolatile substance (S). We are given the following information:
Vapor pressure of pure benzene (P°B) = 93.9 torr
Vapor pressure of benzene with solute (PB) = 91.5 torr
Now, let's calculate the mole fraction of benzene and solute.
Mole fraction of benzene (XB) is given by:
XB = PB / P°B
XB = 91.5 torr / 93.9 torr ≈ 0.9749
Mole fraction of solute (XS) can be calculated using the fact that the total mole fraction of a solution is always 1. Therefore:
XS = 1 - XB
XS = 1 - 0.9749 ≈ 0.0251
So, the concentration of solute expressed as a mole fraction is approximately 0.0251, and the concentration of the solvent expressed as a mole fraction is approximately 0.9749.
To find the concentration of the solute and solvent expressed in mole fractions, we can apply Raoult's law.
According to Raoult's law, the vapor pressure of a solvent in a solution is proportional to its mole fraction in the solution. The equation is given as:
P_total = P_solute + P_solvent
Where:
P_total is the total vapor pressure of the solution
P_solute is the vapor pressure of the solute
P_solvent is the vapor pressure of the solvent
Based on the information given:
P_total = 91.5 torr (vapor pressure of the solution)
P_solute = ?
P_solvent = 93.9 torr (vapor pressure of pure benzene)
We can rearrange the equation to solve for P_solute:
P_solute = P_total - P_solvent
P_solute = 91.5 torr - 93.9 torr
P_solute = -2.4 torr
Since the vapor pressure cannot be negative, it suggests that the solute does not contribute significantly to the overall vapor pressure of the solution. It is a nonvolatile component.
Now, let's calculate the mole fractions of the solute (X_solute) and the solvent (X_solvent):
X_solute = n_solute / n_total
X_solvent = n_solvent / n_total
Where:
n_solute is the number of moles of the solute
n_solvent is the number of moles of the solvent
n_total is the total number of moles in the solution
Since we have no information about the number of moles, assume we have 1 mole of the solvent:
X_solvent = 1 / (1 + n_solute)
To find the mole fraction of the solute, we can use the fact that the sum of mole fractions in a solution is equal to 1:
X_solute + X_solvent = 1
Solving these equations will give us the values for the mole fractions of the solute and solvent.
Pbenzene-Psoln = Xsolute*Pobenzene
Solve for Xsolute
Then Xbenzene + Xsolute = 1.000
Post your work if you get stuck.