How many grams of glucose are required to prepare an aqueous solution of glucose having a vapour pressure of 23.324 mm Hg at `25^@ C` in 100 g of water ? The vapour pressure of pure water at `25^@C ` is 23.8 mm Hg.
(Molar mass of glucose `=180 mol ^(-1)`)

Options

A. 20.4
B. 10.3
C. 5.4
D. 7.4

Answer

A

Explanation

Vapour pressure of pure solvent
`=p^@=` 23.8 mm of Hg
Vapour pressure of solution (p) = 23.324 mm of Hg
Thus, difference in vapour pressure `(Deltap)`
`=23.8-23.324`
= 0.476 mm of Hg
`:'" "(Deltap)/p^@=w_B/M_BxxM_A/w_A" ""(for dilute solution)"`
where, `M_A and w_A` are molar and actual masses of solvent respectively.
`M_B and w_B` are molar and actual masses of solute respectively.
Given,
`M_A=18=w_A=100`
`w_B=M_B=180`
`w_B=(DeltapxxM_Bxxw_A)/(p^@xxM_A)`
`=(0.02xx180xx100)/18" "[(Deltap)/p^@=0.476/23.8=0.02]`
Hence, option (a) is the correct answer.