292.5 g of NaCl completely dissolves (producing Na + and Cl - ions) in 1.00 kg of water at 25.0°C. The vapor pressure of pure water at this temperature is 23.8 torr. Determine the vapor pressure of the solution?

21.8 torr

Explanation:

Mathematically, the relationship between the mole fraction of the solvent and the vapor pressure of the solution looks like this

Psol = Xsolvent * P°solvent where,

Psol - the vapor pressure of the solution

Xsolvent - the mole fraction of the solvent

P°solvent - the vapor pressure of the pure solvent

So, your goal here is to figure out how many moles of sodium chloride and of water you have in the solution.

To do that, use the two compounds' respective molar masses. For sodium chloride you'll have

292.5g * (1mol NaCl/58.44g) = 5.005 moles of NaCl

Same for water except you first have to convert to grams by multiplying by 1000

1000g * (1 mol H2O/18.015g) = 55.51 moles H2O

Now, the mole fraction of water is equal to the number of moles of water divided by the total number of moles present in the solution.

ntotal = nwater + nNaCl

ntotal = 55.51 + 5.005 = 60.515 moles

The mole faction of water will thus be

Xwater = 55.51 moles/60.515 moles = 0.917

This means that the vapor pressure of the solution will be

Psol = 0.917 * 23.8 torr = 21.8 torr