Question

# Gaseous mixture of propane and butane of volume 3L on complete combustion produces 10L of $C{{O}_ {2}}$ under the standard conditions of temperature and pressure. The ratios of volumes of propane to butane is:(a) 1:2(b) 2:1(c) 3:2(d) 3:1

Hint: Combustion is the process in which the substances react with excess of oxygen resulting in the formation of carbon dioxide and water. First, find the volume of butane and propane through writing their combustions reactions and then find their ratios.

Propane is a three carbon atom chemical compound belonging to the category of the alkanes and have the molecular formula as ${{C}_{3}}{{H}_{8}}$($C{{H}_{3}}C{{H}_{2}}C{{H}_{3}}$) and butane is a four carbon atom chemical compound also belongs to the category of alkanes and have the molecular formula as ${{C}_{4}}{{H}_{8}}$($C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}$).
By the term combustion, we mean that the chemical substances react with the excess of oxygen to give carbon dioxide and water.
The total volume of mixture of propane and butane is 3L.
So, let's consider the volume of propane is v litre.
And the volume of butane is 3-v litre.
Now, both propane and butane react with oxygen to give carbon dioxide and water.
Combustion reactions of both propane and butane are as under:
${{C}_ {3}} {{H}_ {8}} (s)+5{{O}_ {2}} (g)\to 3C{{O}_ {2}} (s)+4{{H}_ {2}} O(l)$
1 mol 3 moles
v L 3vL -----------(1)
v liters of propane produce 3v litres of carbon dioxide.
${{C}_ {4}} {{H}_ {10}} (s)+\dfrac {13}{2} {{O}_ {2}} (g)\to 4C{{O}_ {2}} (s)+5{{H}_ {2}} O(l)$
1 mol 4 mol
(3-v) L 4(3-v) L -----------(2)
(3-v) L of butane produces 4(3-v) L litres of carbon dioxide.
As, we have been knowing that complete combustion of butane and propane produces 10L of $C{{O}_ {2}}$, then from equations (1) and (2), we get:
3vL + 4(3-v) L =10L
3v + 12 -4v = 10
12- v= 10
v= 12-10
v=2
So, the volume of propane is: vL
= 2L
Similarly, the volume of butane is: (3-v) L
= (3-2)
=1
Now calculate, the ratio of propane to butane which is:
Ratio= $\dfrac {2}{1}$
Hence, the ratio of propane to butane is 2:1.

So, option (b) is correct.

Note: While calculating the ratio, donâ€™t write ratio of butane to propane instead we have been asked the ratio of propane to butane. So, read the statement carefully.