Given:
Mass of urea = 30g
Mass of water = 90g

To find:
Vapour pressure of the solution at 100°C

Solution:
1. Calculation of moles of urea and water:
The number of moles of a substance can be calculated using the formula:
Moles = Mass / Molar mass

The molar mass of urea (CO(NH2)2) is calculated as follows:
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of N = 14.01 g/mol
Molar mass of H = 1.01 g/mol

Molar mass of urea = (12.01 * 1) + (16.00 * 1) + (14.01 * 2) + (1.01 * 4) = 60.06 g/mol

The number of moles of urea can be calculated as:
Moles of urea = 30g / 60.06 g/mol = 0.4999 mol

The molar mass of water (H2O) is calculated as follows:
Molar mass of H = 1.01 g/mol
Molar mass of O = 16.00 g/mol

Molar mass of water = (1.01 * 2) + 16.00 = 18.02 g/mol

The number of moles of water can be calculated as:
Moles of water = 90g / 18.02 g/mol = 4.995 mol

2. Calculation of the total moles of the solution:
Total moles of the solution = Moles of urea + Moles of water = 0.4999 mol + 4.995 mol = 5.4949 mol

3. Calculation of the mole fraction of urea:
Mole fraction of urea = Moles of urea / Total moles of the solution = 0.4999 mol / 5.4949 mol = 0.0909

4. Calculation of the vapour pressure of the solution:
The vapour pressure of a solution can be calculated using Raoult's Law, which states that the vapour pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapour pressure of the pure solvent.

Vapour pressure of water at 100°C = 760 mmHg

Vapour pressure of the solution = Mole fraction of water * Vapour pressure of water
= (1 - Mole fraction of urea) * Vapour pressure of water
= (1 - 0.0909) * 760 mmHg
= 0.9091 * 760 mmHg
= 690.92 mmHg

Therefore, the vapour pressure of the solution at 100°C is 690.92 mmHg.