Answer: The vapor pressure of the solution at [tex]25^0C[/tex] is 137 torr
Explanation:
As the relative lowering of vapor pressure is directly proportional to the amount of dissolved solute.
The formula for relative lowering of vapor pressure will be,
[tex]\frac{p^o-p_s}{p^o}=i\times x_2[/tex]
where,
[tex]\frac{p^o-p_s}{p^o}[/tex]= relative lowering in vapor pressure
i = Van'T Hoff factor = 1 (for non electrolytes)
[tex]x_2[/tex] = mole fraction of solute =[tex]\frac{\text {moles of solute}}{\text {total moles}}[/tex]
Given : 13.06 g of napthalene is present in 100 g of solution, thus (100-13.06) g = 86.94 g of hexane
moles of solute (napthalene) = [tex]\frac{\text{Given mass}}{\text {Molar mass}}=\frac{13.06g}{128g/mol}=0.102moles[/tex]
moles of solvent (hexane) = [tex]\frac{\text{Given mass}}{\text {Molar mass}}=\frac{86.94g}{86g/mol}=1.01moles[/tex]
Total moles = moles of solute (napthalene) + moles of solvent (hexane) = 0.102 + 1.01 = 1.112
[tex]x_2[/tex] = mole fraction of solute (napthalene) =[tex]\frac{0.102}{1.112}=0.0917[/tex]
[tex]\frac{151-p_s}{151}=1\times 0.0917[/tex]
[tex]p_s=137torr[/tex]
Thus the vapor pressure of the solution at [tex]25^0C[/tex] is 137 torr
