Question

The Haber reaction for the manufacture of ammonia is: N2 + 3H2 → 2NH3 Without doing any experiments, which of the following can you say MUST be true? Disappearance rate of H2 = 3 (Disappearance rate of N2). The reaction is first order in N2. Reaction rate = -Δ[N2]/Δt. The reaction is not an elementary reaction. Δ[H2]/Δt will have a positive value. Disappearance rate of N2 = 3 (Disappearance rate of H2). The activation energy is positive.

Answer 1

Answer :  The correct statement is, $\text{Rate of disappearance of }H_2=3\times (\text{Rate of disappearance of }N_2)$

Explanation :

The general rate of reaction is,

$aA+bB\rightarrow cC+dD$

Rate of reaction : It is defined as the change in the concentration of any one of the reactants or products per unit time.

The expression for rate of reaction will be :

$\text{Rate of disappearance of A}=-\frac{1}{a}\frac{d[A]}{dt}$

$\text{Rate of disappearance of B}=-\frac{1}{b}\frac{d[B]}{dt}$

$\text{Rate of formation of C}=+\frac{1}{c}\frac{d[C]}{dt}$

$\text{Rate of formation of D}=+\frac{1}{d}\frac{d[D]}{dt}$

$Rate=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}$

From this we conclude that,

In the rate of reaction, A and B are the reactants and C and D are the products.

a, b, c and d are the stoichiometric coefficient of A, B, C and D respectively.

The negative sign along with the reactant terms is used simply to show that the concentration of the reactant is decreasing and positive sign along with the product terms is used simply to show that the concentration of the product is increasing.

The given rate of reaction is,

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

The expression for rate of reaction :

$\text{Rate of disappearance of }N_2=-\frac{d[N_2]}{dt}$

$\text{Rate of disappearance of }H_2=-\frac{1}{3}\frac{d[H_2]}{dt}$

$\text{Rate of formation of }NH_3=+\frac{1}{2}\frac{d[NH_3]}{dt}$

From this we conclude that,

$\text{Rate of disappearance of }H_2=3\times (\text{Rate of disappearance of }N_2)$

Hence, the correct statement is, $\text{Rate of disappearance of }H_2=3\times (\text{Rate of disappearance of }N_2)$