Calculating the Vapour Pressure of an Aqueous Solution with 5% Urea

Introduction:
The vapour pressure of a liquid is the pressure exerted by its vapour when the liquid and vapour are in equilibrium. The vapour pressure of a liquid is affected by temperature, the presence of solutes, and the intermolecular forces within the liquid.

Calculation:
To calculate the vapour pressure of an aqueous solution with 5% by mass of urea at 298K, we need to use Raoult's law, which states that the vapour pressure of a solution is proportional to the mole fraction of the solvent in the solution. The mole fraction is the number of moles of the solvent divided by the total number of moles of all components in the solution.

First, we need to calculate the mole fraction of water in the solution. Since the solution contains 5% by mass of urea, the remaining 95% is water. We can assume that the density of the solution is the same as that of water, which is approximately 1 g/mL. Therefore, 1000 mL of the solution contains 950 g of water and 50 g of urea.

Next, we need to calculate the number of moles of water and urea in the solution. We can use the molar masses of water (18.015 g/mol) and urea (60.06 g/mol) to convert the masses to moles. The number of moles of water is 950 g / 18.015 g/mol = 52.7 mol, and the number of moles of urea is 50 g / 60.06 g/mol = 0.833 mol.

The mole fraction of water is therefore 52.7 mol / (52.7 mol + 0.833 mol) = 0.984. The mole fraction of urea is 0.016.

Finally, we can use Raoult's law to calculate the vapour pressure of the solution. The vapour pressure of pure water at 298K is 23.75 mmHg. The vapour pressure of the solution is therefore:

vapour pressure = mole fraction of water x vapour pressure of pure water
= 0.984 x 23.75 mmHg
= 23.32 mmHg

Therefore, the vapour pressure of the aqueous solution with 5% by mass of urea at 298K is 23.32 mmHg.

Conclusion:
The presence of solutes in a liquid can lower its vapour pressure, as seen in the calculation above. Raoult's law can be used to calculate the vapour pressure of a solution if the mole fractions of the components are known.