What amount of a nonelectrolytic solute should be dissolved in 28.9 moles of benzene (C₆H₆) at 25°C to change the vapor pressure of benzene by 17.9%? The vapor pressure of pure benzene at 25°C is 94.2 torr.

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