Question

At 300K and 1atm, 15ml of gaseous hydrocarbon requires 375ml air containing 20% ${{O}_{2}}$ by volume for complete combustion. After combustion the gases occupy 330ml. Assuming that the water formed is in liquid form and the volumes were measured at same temperature and pressure, the formula of hydrocarbon is,
(A) ${{C}_{3}}{{H}_{8}}$
(B) ${{C}_{4}}{{H}_{8}}$
(C) ${{C}_{4}}{{H}_{10}}$
(D) ${{C}_{3}}{{H}_{6}}$

Answer 1

Hint: Find out the volume of oxygen present in air. Find out the ratio between volume of oxygen and hydrocarbon. Write down the complete combustion of each of the given compounds.

Complete step by step solution:
Let’s have a look at the question. Volume of gaseous hydrocarbon used for combustion is 15ml.
375ml air having 20% ${{O}_{2}}$ is required. That means, $375\times \dfrac{20}{100}=75ml$.
So, the volume of oxygen required for combustion is 75ml.
If we obtain a ratio of volume of oxygen required for combustion to that of hydrocarbon used in combustion we get, $\dfrac{Volume\,of\,oxygen}{Volume\,of\,hydrocarbon}=\dfrac{75}{15}=5:1$
We know that complete combustion of a hydrocarbon leads to emission of carbon dioxide gas and water. Let us write the complete combustion reactions for each of the compounds given in the question.
(A) ${{C}_{3}}{{H}_{8}}+5{{O}_{2}}\to 3C{{O}_{2}}+4{{H}_{2}}O$
(B) ${{C}_{4}}{{H}_{8}}+6{{O}_{2}}\to 4C{{O}_{2}}+4{{H}_{2}}O$
(C) $2{{C}_{4}}{{H}_{10}}+13{{O}_{2}}\to 8C{{O}_{2}}+10{{H}_{2}}O$
(D) $2{{C}_{3}}{{H}_{6}}+9{{O}_{2}}\to 6C{{O}_{2}}+6{{H}_{2}}O$
So, from the above reaction we can conclude that the ratio of hydrocarbon to oxygen which is 1:5 is followed in only the first reaction (A).
${{C}_{3}}{{H}_{8}}+5{{O}_{2}}\to 3C{{O}_{2}}+4{{H}_{2}}O$
Water is in a liquid phase. 15ml of propane ${{C}_{3}}{{H}_{8}}$ on combustion will give $3\times 15=45ml\,C{{O}_{2}}$
Total volume of air except oxygen is $375-75=300ml$
So, the total volume that should be occupied by gases after combustion should be $300+45=345ml$. But according to the question, it is 330ml. That is because some amount of carbon dioxide will remain dissolved in water and thus, volume will decrease slightly.

Hence, the correct answer is option (A) ${{C}_{3}}{{H}_{8}}$


Note: Combustion reactions have a lot of applications in our daily life. Burning of fossil fuels emits water, heat and carbon dioxide. This heat energy runs the motor vehicles, aeroplanes, rockets. In ships, coal is used. Combustion of coal also gives thermal energy which is used to run the ship. In thermal power plants and for cooking using natural gas, LPG or wood, heat energy comes from combustion reactions only.