Calculate the mass of urea that should be dissolved in 175 g of water at 35°C to produce a solution with a vapor pressure of 38.1 mmHg. (At 35°C, P o water = 42.2 mmHg.)

The mass of urea that dissolved in the solution is 62.72 g

Explanation:

Psol = Xsolvent *Psolvent

Where;

Psol is the vapor pressure of the solution = 38.1 mmHg

Psolvent is the vapor pressure of water = 42.2 mmHg

Xsolvent is the mole fraction of the solvent = ?

Xsolvent = Number of moles of solvent/Total number of moles in the solution

Molar mass of water = 18 g

Number of moles of solvent = 175/18 = 9.722 mols

Let the number of moles of urea present in the solution = n

Xsolvent = Psol/Psolvent

Xsolvent = 38.1 /42.2 = 0.903 mols

Also, Xsolvent = 9.722/(n + 9.722)

              0.903 =  9.722/(n + 9.722)

             0.903(n + 9.722) = 9.722

             0.903n + 8.779 = 9.722

              0.903n  = 9.722 - 8.779

              0.903n  = 0.943

                        n =  0.943/0.903

                         n = 1.0443 mols

Thus, the number of moles of urea present in the solution is 1.0443 mols

Molar mass of urea = 60.06 g/mol

Therefore, the mass of urea that dissolved in the solution = 1.0443 *60.06

mass of urea = 62.72 g

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