A sample of chalk contained as an impurity, a form of clay which loses $14.5 %$ of its mass of water on prolonged heating. $5$ g of chalk on heating shows a loss of $1.507$ g in mass (due to an evolution of $C O_{2}$ and water). The $%$ of chalk in the sample is:
(to the closest integer)

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Solution

Chalk contains : $C l a y$ + $C a C O_{3}$
$a$ g $b$ g
$a + b = 5 . . . (i)$
On heating, $C a C O_{3} Δ - \to C a O + C O_{2}$
$C l a y Δ - \to L o s e s w a t e r$
Mass loss by $a$ g Clay in form of $H_{2} O = \frac{14.5 \times a}{100}$
Mass loss by $b$ g $C a C O_{3}$ in form of $C O_{2} = \frac{44 \times b}{100}$
$\frac{14.5 \times a}{100} + \frac{44 \times b}{100} = 1.507 . . . (i i)$
By equations (i) and (ii), $a$ $=$ $2.349$ g , $b$ $=$ $2.651$ g
% of $C a C O_{3} = \frac{2.651 \times 100}{5} = 53$

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