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.)

We should dissolve 62.5 grams of urea

Explanation:

Step 1: Data given

mass of water = 175 grams

Temperature = 35.0 °C

Vapor pressure of solution = 38.1 mmHg

Vapor pressure of water = 42.2 mmHg

Step 2: Calculate mol fraction H2O

Mol fraction H2O = 38.1 mmHg / 42.2 mmHg

Mol fraction H2O = 0.903

Step 3: Calculate mol fraction urea

mol fraction urea = 1 - 0.903 = 0.097

Step 4: Calculate moles H2O

Moles H2O = 175 grams / 18.02 g/mol

Moles H2O = 9.71 moles H2O

Step 5: Calculate moles urea

moles urea = x

x / (9.71 + x) = 0.097

x = 1.04 moles urea

Step 6: Calculate mass urea

mass urea = 1.04 moles * 60.06 g/mol = 62.5 grams of urea

We should dissolve 62.5 grams of urea

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