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 problem, we need to understand the concept of reaction rates and how they apply to the given chemical equation:

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

The rate of a reaction is related to the change in concentration of a reactant or product with time. For a general reaction aA + bB \rightarrow cC + dD, the rate can be defined as:

\(-\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}\)

This indicates the rate of disappearance of the reactants equals the rate of appearance of the products, adjusted by their stoichiometric coefficients.

Applying this to our given reaction:

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

This gives us three expressions relating the rates of change of reactants and products. Let's analyze the provided options:

1. -5\frac{1}{3}\frac{d[H_2]}{dt} = -\frac{1}{2}\frac{d[NH_3]}{dt}: Incorrect. The negative sign and the coefficients don't match the rate equation relation with H_2.
2. -\frac{d[N_2]}{dt} = 2\frac{d[NH_3]}{dt}: Incorrect. This suggests twice the effect on NH_3 concentration relative to N_2 change, which contradicts stoichiometry.
3. -\frac{d[N_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt}: Correct. This reflects the stoichiometric relation from the balanced equation, where 1 mole of N_2 produces 2 moles of NH_3.
4. 3\frac{d[H_2]}{dt} = 2\frac{d[NH_3]}{dt}: Incorrect. Though the stoichiometric ratio of 3:2 is used, it should match the form of the rate relation derived.

Thus, the correct option is:

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