Air contains 21% of oxygen by weight. What weight of air is required to burn 50 grams of coal which contains only 50% combustible material?

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634 g

200 g

317 g

158.5 g

answer is A.

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Detailed Solution

weight of coal = 50grams
percentage of Combustible material in coal = 50%
$weight\;of\;combustible\;material\;in\;coal\;=\;\frac{50}{100}\times 50=25g$

$\large \mathop C\limits_{25g}^{12g} \; + \;\mathop {{O_2}}\limits_{'X'g}^{32g} \; \to C{O_2}$

$\large X\; = \;\frac{{25\; \times \;32}}{{12}}g$
$\large weight\;of\;oxygen\;in\;air\;=\left ( \frac{25\times 32}{12} \right )g$
weight % of oxygen in air = 21%
$\large weight\;of\;air\;required\;=\left ( \frac{25\times 32}{12}{\times \frac{100}{21}} \right )g$
weight of air required = 317g