If the vapor pressure of an aqueous solution containing 6.00 moles of a nonvolatile solute has a vapor pressure of 19.8 torr, and given that the vapor pressure of water at room temperature is 23.7 tor

Question

If the vapor pressure of an aqueous solution containing 6.00 moles of a nonvolatile solute has a vapor pressure of 19.8 torr, and given that the vapor pressure of water at room temperature is 23.7 torr, how many total moles are present in solution?

Answer 1

This is a problem where a solute is added to water and this then decreases the vapor pressure of the water from what it was when it was pure. The amount it will decrease the vapor pressure is directly related to the mole fraction of the solute (or put another way, the mole fraction of the water).

mole fraction of water x vapor pressure of water = vapor pressure of solution. In equation form it is ...

P_solution = X_solvent x P⁰_solvent

We can solve for X_solvent which is the mole fraction of the water.

X_solvent = P_solution/P^o_solvent

X_solvent = 19.8 torr/23.7 torr = 0.835

Since there are 6.00 moles of solute, we can find total moles present in solution.

x moles water/6.00 moles solute + x moles water = 0.835

x = 30.4 moles of water

Total moles present in solution = 6.00 moles + 30.4 moles = 36.4 moles