In this example problem, we calculate the vapor pressure for a strong electrolyte solution.
The problem reads, "Calculate the vapor pressure of a 5.31 molar sodium chloride solution at 25 degrees Celsius.
The density of the solution is 1.194 grams per milliliter
and the vapor pressure of pure water at 25 degrees Celsius is 23.8 torr. Assume an ideal van't Hoff factor."
Our equation is vapor pressure of a solution equals the mole fraction of the solvent, in this case water,
times the vapor pressure of the pure solvent.
To calculate the mole fraction of water
we'll use the equation mole fraction of water equals moles of water divided by the total moles,
which are the moles of water plus the moles of ions.
We need to be careful in this problem.
Sodium chloride is a soluble ionic compound so it is a strong electrolyte.
We're told to assume an ideal van't Hoff factor,
so we're assuming the sodium chloride has split apart completely into sodium and chloride ions.
Let's start by calculating the mole fraction of water.
We're given the concentration of molarity of sodium chloride.
Molarity is moles of solute divided by liters of solution.
Since we're not given a quantity of solution in this problem, we can make one assumption about the quantity were working with.
I like to make an assumption based on the denominator of the concentration units we're given
because it seems to make the math easier.
So let's assume we have one liter of solution.
We need to calculate the moles of ions and moles of water in that 1 liter of solution.
We can use dimensional analysis to convert one liter of solution to moles of ions
The molarity of NaCl lets us convert from liters of solution to moles of NaCl.
Then we can convert from moles of sodium chloride to moles of ions.
We will produce two moles of ions in solution for every one mole of sodium chloride, assuming an ideal van't Hoff factor.
The actual van't Hoff factor may be lower with ion pairing.
Completing the calculation, we get 10.62 moles of ions.
Next we can focus on calculating the moles of water.
We'll need to use the equation mass of water equals mass of solution subtract mass of sodium chloride.
Once we have the mass of water, we can convert to moles of water.
Using dimensional analysis
we can convert 1 liter of solution into grams of solution using the density of solution and 1 liter equals 1000 milliliters.
We should get 1194 grams of solution.
We can also use dimensional analysis to convert from liters of solution to grams of sodium chloride
using the molarity of sodium chloride and it's molar mass.
We should get 310.3 grams of sodium chloride.
We can plug these values into our equation for the mass of water and we'll get 883.7 grams of water.
Now that we have the mass of water we can convert to moles.
Using dimensional analysis and the molar mass of water, we get 49.05 moles of water.
With both the moles of ions and moles of water, we can now calculate the mole fraction of water.
Plugging in our numbers, we should get 0.822 for the mole fraction of water.
Going back to our equation for the vapor pressure of a solution,
the mole fraction of water, our solvent, times the vapor pressure of pure water 25 degrees Celsius
gives us a vapor pressure of solution of 19.6 torr.