Question

a solution of sucrose is labeled as 20%[w/w].what would be the mole fraction of each component of the solution

[Ans:- sucrose =0.01297,water=0.987]

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Answer 1

Answer:

20% w/w means 20 gm of sucrose is dissolved in 100 gm of solution(sucrose+water). Let’s sucrose weight is 20 gm then water weight will be 80 gm.

Molar mass of sucrose (C12H22O11)~ 322 gm/mole

Since 322 gm= 1 mole then 20 gm sucrose = 20/322 ~ 0.062 mole

Molar mass of water (H2O) ~ 18 gm/mole

Similarly moles of water = 80/18 ~4.44 mole

Mole fraction of sucrose = moles of sucrose/total mole = 0.062/(4.44+0.062) ~ 0.014 mole

Mole fraction of water = moles of water/total mole = 4.44/(4.44+0.062) ~ 0.986 mole

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Answer 2

Mole fraction:

Mole fraction of a particular component of the solution is the ratio of number of moles of that component present in the solution to the total number of moles of all the components of the solution.

A solution of sucrose in water is labelled as 20% w/w.

It means that 100 g of solution contains 20 g of sucrose and 100−20=80 grams of water. The molar masses of sucrose and water are 342 g/mol and 18 g/mol respectively.

The number of moles of sucrose =

$\sf \frac{20g}{342g / mol} = 0.0585 \: mol$

The number of moles of water =

$\sf \frac{80g}{18g /mol} = 4.444 \: mol$

The mole fraction of sucrose =

$\frac{0.0585}{0.0585 + 4.444} = 0.01299≃0.013$

The mole fraction of water =1−

0.013=0.987