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Standard XII

Chemistry

Stoichiometric Calculations

A 20.0 cm...

Question

A $20.0$ ${c m}^{3}$ mixture of $C O$ , $C H_{4}$ and $H e$ gases is exploded by an electric discharge at room temperature with excess of oxygen. The volume of contraction is found to be $13$ ${c m}^{3}$ . A further contraction of $14$ ${c m}^{3}$ occurs when the residual gas is treated with $K O H$ solution. The composition of $C O$ in the mixture in terms of volume percentage is:

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Solution

Let volume of $C O, C H_{4}$ and $H e$ be $a, b$ and $c$ respectively.

Given, $∴ a + b + c = 20 . . . (i)$

The reactions are:

$C O + \frac{1}{2} O_{2} \to C O_{2}$

$C H_{4} + 2 O_{2} \to C O_{2} + 2 H_{2} O$

$∴$ Volume of $C O_{2}$ formed $(a + b)$ $=$ $14 . . . (i i)$

By Eqs. (i) and (ii) , $c = 6$

Also, an initial volume of the mixture -final volume after sparking $= 13$

$a + b + c + V_{O_{2}} - [a + b + c + V_{O_{2}}] = 13$

$∴ V_{O_{2}}$ used $= 13$

or, $\frac{a}{2} + 2 b = 13$

or, $a + 4 b = 26 . . . (i i i)$

$∴ a = 10, b = 4$

$∴$ % of $C O$ $= \frac{10}{20} \times 100 = 50$ %

% of $C H_{4} = \frac{4}{20} \times 100 = 20$ %

% of $H e$ = $\frac{6}{20} \times 100 = 30$ %

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