At 298 K, the vapour pressure of water is 23.75 mm Hg. Calculate the vapour pressure at the same temperature over 5% aqueous solution of urea `(NH_2CONH_2)`.

Explanation

A 5% aqueous solution of urea means that out of 100 g
of solution, urea is 5 g and water is 95 g.
Weight of solute (urea), `w_B` - 5g
Weight of solvent (water), `W_A = 95` g
Molar mass of urea, `m_B = 60 g mol^(-1)`
Molar mass of water, `M_A = 18 g mol^(-1)`
Vapour pressure of water, `p_A^@ = 23.75 mm` Hg,
Vapour pressure of solution, `P_A` = ?
According to Raoult.s law, `(p_A^@-P_A)/(p_A^@)=(W_BM_A)/(W_Am_B)`
or `(23.75 – P_A)/(23.75) = (5xx18)(95xx 60)`
or `23.75 – P_A = (5xx18xx23.75)/(96xx60) = 0.375`
or `P_A = 23.75 -0.375 = 23.375`
`:.` Vapour pressure of solution = 23.375 mm Hg.