Question

40 ml of mixture of \[{{C}_{2}}{{H}_{2}}\] and CO is mixed with 100 ml of \[{{O}_{2}}\]​ gas and the mixture is exploded. The residual gases occupy 104 ml and when these are passed through KOH solution, the volume becomes 48ml. All the volumes are at the same temperature and pressure. Determine the composition of the original mixture.
(A) ${{C}_{2}}{{H}_{2}}=16mL,\text{ CO=24mL}$
(B) \[{{C}_{2}}{{H}_{2}}=23mL,\text{ CO=14mL}\]
(C) ${{C}_{2}}{{H}_{2}}=30mL,\text{ CO=26mL}$
(D) ${{C}_{2}}{{H}_{2}}=33mL,\text{ CO=28mL}$

Answer 1

Hint: Carbon Dioxide is separately formed both by \[{{C}_{2}}{{H}_{2}}\] and by CO as a result of two separate chemical reactions with Oxygen. Try to evaluate what each particular component’s volume would have been.

Complete step by step answer:
Let the original mixture contain x ml of CO and (40-x) ml of \[{{C}_{2}}{{H}_{2}}\]​.
Now, let us try and observe the chemical reactions which result in the production of Carbon Dioxide from the given components.
Therefore, the balanced chemical equation for the production of Carbon Dioxide from \[{{C}_{2}}{{H}_{2}}\]is as shown below.
     \[\underset{(40-x)}{\mathop{{{C}_{2}}{{H}_{2}}}}\,\text{ }+\text{ }\underset{2.5(40-x)}{\mathop{\frac{5}{2}{{O}_{2}}}}\,\text{ }\to \text{ }\underset{2(40-x)}{\mathop{2C{{O}_{2}}}}\,\text{ }+\text{ }{{H}_{2}}O\]
Now, the balanced chemical equation for the production of Carbon Dioxide from CO is as shown below.
     \[\underset{(x)}{\mathop{CO}}\,+\underset{(0.5x)}{\mathop{\frac{1}{2}{{O}_{2}}}}\,\to \underset{(x)}{\mathop{C{{O}_{2}}}}\,\]
Now, we know that the total volume is 104 ml from the given data.
Hence,
\[2(40-x)+x+(100-2.5(40-x)-0.5x=104.\]
On solving this, we get \[x=24~ml.\]
Hence, the volumes of CO and \[{{C}_{2}}{{H}_{2}}\]are 24ml and (40−24) =16 ml respectively.
Therefore, the answer to this question is (A) ${{C}_{2}}{{H}_{2}}=16mL\text{ and CO=24mL}$
So, the correct answer is “Option A”.

Note: Be very careful in understanding the question in that there is a mixture of \[{{C}_{2}}{{H}_{2}}\]and CO and both of the components will react with oxygen, reaction between them will not occur. Please do not get confused between the two as that will lead to a different reaction altogether and lead you towards an incorrect answer.