Question

Calculate the vapor pressure of a solution of 0.99 mol of cholesterol in 5.4 mol of toluene at 32°c. pure toluene has a vapor pressure of 41 torr at 32°c. (assume ideal behavior.)

Answer 1

Explanation:

No. of moles of cholesterol solute, $n_{1}$ = 0.99 mol

No. of moles of toulene solvent, $n_{2}$ = 5.4 mol

Hence, total number of moles of solution will be as follows.

                  n = $n_{1} + n_{2}$

                     = 0.99 mol + 5.4 mol

                     = 6.39 mol

Therefore, mole fraction of cholestrol solute ($\chi_{1}$) is as follows.

                = $\frac{\text{no. of moles of chloesterol}}{\text{Total number of moles of solution (n)}}$  

     $\chi_{1}$ = $\frac{0.99 mol}{6.39 mol}$

                      = 0.154

Vapor pressure of pure toulene solvent ($p^{o}$) = 41 torr

Vapor pressure of solution = P

Hence, formula to calculate relative lowering of vapor pressure is as follows.

     Relative lowering of vapor pressure = $\frac{p^{o} - P}{p^{o}}$

As per relative lowering of vapor pressure colligative property, the relative lowering of vapor pressure is equal to the mole fraction of solute.

Hence,     $\frac{p^{o} - P}{p^{o}}$ = $\chi_{1}$

               $\frac{41 torr - P}{41 torr}$ = 0.154

                         41 torr - P = 6.314

                                      P = 34.686 torr

or,                                      = 35 torr

Therefore, we can conclude that vapor pressure of the solution is 35 torr.

Answer 2

We can get the vapor pressure of the solution from this formula:
Pv(solu) = n P°v
when n is the mole fraction of toluene so we can get by substitution in this formula: 
n = moles of toluene / (moles of cholesterol + moles of toluene)
   = 5.4 / ( 0.99 + 5.4) = 0.85
so by substitution in vapor pressure formula:
∴ Pv(solu) = 0.85 *41 = 34.85 atm