Question

A gaseous fuel mixture comprising 3 moles of methane and 2 moles of ammonia is combusted in \( X \) moles of pure oxygen in stoichiometric amount. Assuming complete combustion, with only \( {CO}_2 \), \( {H}_2{O} \), and \( {N}_2 \) in the product gases, the value of \( X \) is \_\_\_. \[ 3 \, {CH}_4 + 2 \, {NH}_3 + X \, {O}_2 \rightarrow {Products (CO}_2, \, {H}_2{O}, \, {N}_2{)} \]

• A. 7.5
• B. 5.5
• C. 8.5
• D. 9.5

Hint:

When solving stoichiometric combustion problems, balance the combustion reactions for each reactant and then add the oxygen required. Ensure that all elements are conserved on both sides of the equation.

Answer 1

The Correct Option is A

Step 1: Combustion of methane (CH\(_4\)): \[ {CH}_4 + 2 \, {O}_2 \rightarrow {CO}_2 + 2 \, {H}_2{O} \] For 3 moles of CH\(_4\), the oxygen required will be: \[ 3 \times 2 = 6 \, {moles of O}_2 \] Step 2: Combustion of ammonia (NH\(_3\)): \[ 4 \, {NH}_3 + 3 \, {O}_2 \rightarrow 2 \, {N}_2 + 6 \, {H}_2{O} \] For 2 moles of NH\(_3\), the oxygen required will be: \[ \frac{3}{4} \times 2 = 1.5 \, {moles of O}_2 \] Step 3: Total oxygen required Now, adding the oxygen required for both reactions: \[ 6 \, {moles of O}_2 \, ({from CH}_4) + 1.5 \, {moles of O}_2 \, ({from NH}_3) = 7.5 \, {moles of O}_2 \] Therefore, the total moles of oxygen required for stoichiometric combustion are 7.5 moles. Thus, \( X = 7.5 \).