Air contains `21%` oxygen by volume. Calculate the theoretical volume of air which will be required for burning completely 500 cubic ft of acetylene gas `(C_(2) H_(2))`All volumes are measured under the same conditions of temperature and pressure.

Explanation

`underset(2 "vol")(2C_(2) H_(2)) + underset(5 "vol")(5 O_(2)) rarr underset(4 "vol")(4 CO_(2)) + underset(2 "vol")(2 H_(2) O)` (Steam)
Here, the ratio of the reacting molecules and those of the products is taken as the ratio of their volumes. This is in accordance with Avogadro's hypothesis-equal to volumes of all gases under similar conditions of temperature and pressure contain equal number of molecules or its reverse, namely, equal number of molecules under similar conditions of temperature and pressure occupy equal volumes, is equally true.) The ratio by volumes of reactants and products is apparently simple.
According to the above equation:
2 volumes of acetylene require 5 volumes of `O_(2)` for combustion.
`:. 500 cu`. ft. of acethlene will require `O_(2)`
` = (5 xx 500)/(2) = 1250 cu.ft`.
Hence, the quantity of air required
`= (100 xx 1250)/(21) = 5952.38 cu.ft`.