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Potassium sulphate is isomorphous with potassium chromate which contains $26.79 \%$ by weight of chromium. Find out the atomic weight of chromium. ( $K=39$, $O=16)$

SOLUTION :

Formula of potassium sulphate : $K _{2} SO _{4}$

and hence formula of pot. chromate : $K _{2} CrO _{4}$

Let the atomic wt. of $Cr$ be $x$. Then mol. wt. of

$K _{2} CrO _{4}=39 \times 2+x+4 \times 16=142+x$

$\therefore(142+x)$ g potassium chromate contains $x g Cr$

$\therefore 100 g$ potassium chromate contains $\frac{x \times 100}{142+x} g$

Given that $\%$ of $C r=26 \cdot 79, \therefore \frac{100 x}{142+x}=26 \cdot 79$

or, $\quad 100 x=26 \cdot 79(142+x)=26 \cdot 79 x+3804 \cdot 18$

or, $\quad x(100-26 \cdot 79)=3804 \cdot 18, x=\frac{3804 \cdot 18}{73 \cdot 21}=51 \cdot 96$

Hence, atomic wt. of chromium $= 5 1 . 9 6$.

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