Answer:
The amount of a nonelectrolytic solute that has to be dissolved in 28.9 moles to change the vapor pressure of benzene by 17.9 is 6.31 moles.
Explanation:
Let's see how to solve this, step by step applying Raoult's Law (Colligative property).
Pressure solution = χsolvent . Pressure solvent
You have to consider that Pressure in solution is, Pressure Pure - Pressure in Solution (Solute+Solvent). The statement says, that pressure has fallen 17.9%, so let's find out that
100% ....... 94.2 Torr
17.9 % ...... x
16.86 Torr (after the Rule of 3) - This is the value of decline.
So, 94.2Torr - 16.86 Torr = 77.34 Torr
Now the formula
77.34 Torr = 94.2 Torr . X (where x is molar fraction)
x = moles of benzene / moles of benzene + moles of nonelectrolytic solute
77.34 Torr / 94.2 Torr = X
0.821 = moles of benzene / moles of benzene + moles of nonelectrolytic solute
0.821 = 28.9 moles / 28.9 moles + nonelectrolytic
0.821 (28.9 moles + nonelectrolytic) = 28.9 moles
23.72 moles + 0.821 nonelectrolytic = 28.9 moles
0.821 nonelectrolytic = 28.9 moles - 23.72 moles
0.821 nonelectrolytic = 5.18 moles
nonelectrolytic moles = 5.18 / 0.821
nonelectrolytic moles = 6.31
