Question

A reaction gas mixture contains \(50\%\), \(30\%\), \(20\%\) of \(A\), \(B\) and \(C\) by volume, respectively. The mixture undergoes the following reactions.
\[ 1.\quad A+2B \longrightarrow P_1 \] \[ 2.\quad 4P_1+3C \longrightarrow P_2 \] \(P_1\) and \(P_2\) are two products of the reactions. Choose the correct answer if the reaction completes.

• A. \(C\) will be completely exhausted.
• B. \(A\) will be completely exhausted.
• C. \(B\) will not be completely exhausted.
• D. \(P_1\) will be completely exhausted.

Hint:

For gaseous reactions, volume ratios follow the stoichiometric coefficients when temperature and pressure are the same. First find the limiting reactant in each reaction, then decide which species is completely exhausted.

Answer 1

The Correct Option is D

Step 1: Find P\(_1\) produced in reaction 1.
Take 100 units total: A=50, B=30, C=20. Reaction 1 needs A:B = 1:2. With 50 A, max B needed = 100, but only 30 B available. So B is limiting: 30 B reacts with 15 A to give P\(_1\) = 15 units. A remaining = 35.

Step 2: Check reaction 2 for P\(_1\).
Reaction 2 needs 4P\(_1\):3C. With 15 P\(_1\), C needed = \(rac{3}{4} imes15 = 11.25\); C available = 20. So P\(_1\) is the limiting reagent in reaction 2 and is completely exhausted. \[ oxed{P_1 ext{ will be completely exhausted}} \]