Question

For the chemical reaction \(N_2(g)+ 3H_2(g)= 2NH_3(g)\) the correct option is :

• A. \(-\frac13\frac{d[H_2]}{dt}=-\frac12\frac{d[NH_3]}{dt}\)
• B. \(-\frac{d[N_2]}{dt}=2\frac{d[NH_3]}{dt}\)
• C. \(-\frac{d[N_2]}{dt}=\frac12\frac{d[NH_3]}{dt}\)
• D. \(3\frac{d[H_2]}{dt}=2\frac{d[NH_3]}{dt}\)

Answer 1

The Correct Option is C

To solve this question, we need to understand the concept of reaction rates and stoichiometry in the given chemical reaction:

The balanced chemical equation for the reaction is:

\(N_2(g) + 3H_2(g) = 2NH_3(g)\)

This equation tells us that 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas to produce 2 moles of ammonia gas. The reaction rates for each component can be equated using the stoichiometric coefficients.

The rate of change of concentration of different substances is given by their stoichiometric coefficients. For the above reaction:

• The rate of disappearance of \(N_2\) is represented as \(-\frac{d[N_2]}{dt}\).
• The rate of disappearance of \(H_2\) is \(-\frac{d[H_2]}{dt}\), and according to the stoichiometry, it should be three times the rate of disappearance of \(N_2\), i.e., \(-\frac{d[H_2]}{dt} = 3 \times \text{rate of } N_2\).
• The rate of formation of \(NH_3\) is given by \(\frac{d[NH_3]}{dt}\), and it should be twice the rate of disappearance of \(N_2\), i.e., \(\frac{d[NH_3]}{dt} = 2 \times \text{rate of } N_2\).

Thus, we derive the following relationships from stoichiometry:

• -\frac{d[N_2]}{dt} = \frac{1}{2}\frac{d[NH_3]}{dt}
• -\frac{1}{3}\frac{d[H_2]}{dt} = \frac{1}{2}\frac{d[NH_3]}{dt}

Among the provided options, the correct relationship according to these calculations matches:

• - \frac{d[N_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt}

Thus, the correct option is:

- \frac{d[N_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt}