Question

For the chemical reaction $N_{2 (g)} +3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$ the correct option is :

• A. $-\frac{d\left[N_{2}\right]}{dt}=\frac{1}{2}\frac{d\left[NH_{3}\right]}{dt}$
• B. $3\frac{d\left[H_{2}\right]}{dt}=2\frac{d\left[NH_{3}\right]}{dt}$
• C. $-\frac{1}{3}\frac{d\left[H_{2}\right]}{dt}=2\frac{d\left[NH_{3}\right]}{dt}$
• D. $-\frac{d\left[N_{2}\right]}{dt}=2\frac{d\left[NH_{3}\right]}{dt}$

Answer 1

The Correct Option is A

 To solve this question, we need to understand the concept of reaction rates and how they relate to the stoichiometry of the chemical reaction provided. The chemical reaction given is:

\(N_{2 (g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}\)

In a balanced chemical reaction, the rate of consumption of reactants and the rate of formation of products are related by the stoichiometric coefficients in the chemical equation. For this reaction, the stoichiometric coefficients are 1 for \(N_2\), 3 for \(H_2\), and 2 for \(NH_3\).

The rate of reaction can be expressed in terms of the rate of change of concentration of any of the reactants or products. According to the stoichiometry, the rate expressions can be written as:

• \(-\frac{d[N_2]}{dt} = \frac{1}{1} \times \text{Rate of reaction}\)
• \(-\frac{d[H_2]}{dt} = \frac{1}{3} \times \text{Rate of reaction}\)
• \(\frac{d[NH_3]}{dt} = \frac{1}{2} \times \text{Rate of reaction}\)

From these expressions, we can relate the rate of change of concentrations as follows:

• \(-\frac{d[N_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt}\)
• (Not valid due to stoichiometry mismatch)

Now, comparing the given options with our derived expressions:

• \(-\frac{d[N_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt}\): This is correctly derived from the stoichiometry, matching option 1.
• \(3\frac{d[H_2]}{dt} = 2\frac{d[NH_3]}{dt}\): This option is incorrectly derived from the stoichiometry, as it does not correctly account for the rate relationship between \(H_2\) and \(NH_3\).
• : This is incorrect per stoichiometry, incorrectly relating \(N_2\) to \(NH_3\).

Thus, the correct option is: \(-\frac{d[N_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt}\)