Question 11.8: CALCULATING THE VAPOR PRESSURE OF A SOLUTION What is the vap...
CALCULATING THE VAPOR PRESSURE OF A SOLUTION
What is the vapor pressure in mm Hg of a solution made by dissolving 18.3 g of NaCl in 500.0 g of H_{2}O at 70 °C, assuming a van’t Hoff factor of 1.9? The vapor pressure of pure water at 70 °C is 233.7 mm Hg.
STRATEGY
According to Raoult’s law, the vapor pressure of the solution equals the vapor pressure of pure solvent times the mole fraction of the solvent in the solution. Thus, we have to find the numbers of moles of solvent and solute and then calculate the mole fraction of solvent.
First, use molar mass to calculate the number of moles of NaCl and H_{2}O.
Moles of NaCl = 18.3 g NaCl × \frac{1 mol NaCl}{58.44 g NaCl} = 0.313 mol NaCl
Moles of H_{2}O = 500.0 g H_{2}O × \frac{1 mol H_{2}O}{18.02 g H_{2}O} = 27.75 mol H_{2}O
Next, calculate the mole fraction of water in the solution. A van’t Hoff factor of 1.9 means that the NaCl dissociates incompletely and gives only 1.9 particles per formula unit. Thus, the solution contains 1.9 × 0.313 mol = 0.59 mol of dissolved particles and the mole fraction of water is
Mole fraction of H_{2}O = \frac{27.75 mol}{0.59 mol + 27.75 mol} = 0.9792
From Raoult’s law, the vapor pressure of the solution is
P_{soln} = P_{solv} × X_{solv} = 233.7 mm Hg × 0.9792 = 228.8 mm Hg