College

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, [tex]P^0_{\text{water}} = 42.2 \text{ mmHg}[/tex].)

Answer :

Answer:

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

Final answer:

To calculate the mass of urea to be dissolved in water, we can use Raoult's law. The mass of urea needed is approximately 502.65 grams.

Explanation:

To calculate the mass of urea that should be dissolved in water to produce a solution with a certain vapor pressure, we can use Raoult's law. According to Raoult's law, the vapor pressure of a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent. The mole fraction of the solvent can be found using the equation:

Mole fraction of solvent (water) = moles of water / total moles of solute

Since urea is the solute and water is the solvent, we can rewrite the equation as:

Mole fraction of water = moles of water / moles of urea + moles of water


To find the moles of water in 175 g of water, we divide the given mass by the molar mass of water. The molar mass of water is approximately 18 g/mol. Then, we can use the mole fraction of water and the vapor pressure of water to calculate the vapor pressure of the solution. Setting that equal to the given vapor pressure, we can solve for the moles of urea needed. Finally, we can convert moles of urea to grams using the molar mass of urea, which is approximately 60 g/mol. The resulting mass will be the mass of urea that should be dissolved in 175 g of water to produce the desired solution.

  1. Mass of water = 175 g
  2. Molar mass of water = 18 g/mol
  3. Molar mass of urea = 60 g/mol
  4. Moles of water = mass of water / molar mass of water = 175 g / 18 g/mol = 9.7222 mol
  5. Moles of urea + moles of water = moles of water / mole fraction of water
  6. Moles of urea + 9.7222 mol = 9.7222 mol / (42.2 mmHg / 38.1 mmHg)
  7. Moles of urea = (9.7222 mol / (42.2 mmHg / 38.1 mmHg)) - 9.7222 mol = 8.3776 mol
  8. Mass of urea = moles of urea * molar mass of urea = 8.3776 mol * 60 g/mol = 502.65 g


Learn more about Raoult's law here:

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