Question

Calculate the amount of sugar required to make 20%(w/w) sugar solution in 450g of water

Answer 1

Given :-

Volume of solution = 20%

Mass of water = 450g

To find :-

Amount of sugar required.

Solution :-

Mass % = Mass of solute/Mass of sol. x 100

Mass % = 20

Mass of solute = x

Mass of solution

= Mass of water + Mass of sugar

= (450 + x)

On substituting :-

20 = x/(450 + x) x 100

20 = 100x/(450 + x)

20(450 + x) = 100x

9000 + 20x = 100x (Divide by 20)

450 + x = 5x

450 = 4x

x = 450/4

x = 225/2

x = 112.5

∴ Mass of solute = 112.5g

⇒ 112.5g of sugar is required to make 20% sugar solution in 450g of water.

Answer 2

Let that amount of solute (Sugar) be = (x) g

Mass of solvent = 450 g

w/w% of solution = 20%

Formula:-

w/w% of solution = (Mass of Solute) ÷ (Mass of Solution) × 100%

A.T.Q.,

(x)/(450 + x) × 100 = 20

$\longrightarrow$ (100x)/(450 + x) = 20

$\longrightarrow$ 100x = 20x + 9000

$\longrightarrow$ 80x = 9000

$\longrightarrow$ x = 112.5 g (Answer)