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Chemical Kinetics and Nuclear Chemistry question

2020 · 7 Jan · Shift 2 · Q15
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Chemical Kinetics and Nuclear Chemistry question

2020 · 7 Jan · Shift 2 · Q15

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1
For the reaction 2H2H_2H2​(g) + 2NONONO(g) →\to→ N2N_2N2​(g) + 2H2OH_2OH2​O(g) the observed rate expression is, rate = Kf[NONONO]2[H2H_2H2​]. The rate expression for the reverse reaction is :
  1. A
    Kb[N2N_2N2​][H2OH_2OH2​O]
  2. B
    Kb[N2N_2N2​][H2OH_2OH2​O]2/[H2H_2H2​]
  3. C
    Kb[N2N_2N2​][H2OH_2OH2​O]2/[NONONO]
  4. D
    Kb[N2N_2N2​][H2OH_2OH2​O]2
View written solutionFree

Correct answer: B

  1. Given reaction

2H2(g)+2NO(g)→N2(g)+2H2O(g)2H_2(g) + 2NO(g) \rightarrow N_2(g) + 2H_2O(g)2H2​(g)+2NO(g)→N2​(g)+2H2​O(g)

Observed forward rate law:

rf=Kf[NO]2[H2]r_f = K_f[NO]^2[H_2]rf​=Kf​[NO]2[H2​]

We need the rate law for the reverse reaction.

  1. Write the reverse reaction

N2(g)+2H2O(g)→2H2(g)+2NO(g)N_2(g) + 2H_2O(g) \rightarrow 2H_2(g) + 2NO(g)N2​(g)+2H2​O(g)→2H2​(g)+2NO(g)

Let its rate law be:

rb=Kb[N2]a[H2O]b[H2]c[NO]dr_b = K_b[N_2]^a[H_2O]^b[H_2]^c[NO]^drb​=Kb​[N2​]a[H2​O]b[H2​]c[NO]d

We determine this using equilibrium condition.

  1. Use equilibrium condition

At equilibrium,

rf=rbr_f = r_brf​=rb​

So,

Kf[NO]2[H2]=rbK_f[NO]^2[H_2] = r_bKf​[NO]2[H2​]=rb​

Also, from equilibrium constant expression for the reaction,

Kc=[N2][H2O]2[H2]2[NO]2K_c = \frac{[N_2][H_2O]^2}{[H_2]^2[NO]^2}Kc​=[H2​]2[NO]2[N2​][H2​O]2​

Rearranging,

[NO]2=[N2][H2O]2Kc[H2]2[NO]^2 = \frac{[N_2][H_2O]^2}{K_c[H_2]^2}[NO]2=Kc​[H2​]2[N2​][H2​O]2​

Substitute into forward rate law at equilibrium:

rf=Kf[H2][NO]2r_f = K_f[H_2][NO]^2rf​=Kf​[H2​][NO]2

rf=Kf[H2]([N2][H2O]2Kc[H2]2)r_f = K_f[H_2]\left(\frac{[N_2][H_2O]^2}{K_c[H_2]^2}\right)rf​=Kf​[H2​](Kc​[H2​]2[N2​][H2​O]2​)

rf=KfKc[N2][H2O]2[H2]r_f = \frac{K_f}{K_c}\frac{[N_2][H_2O]^2}{[H_2]}rf​=Kc​Kf​​[H2​][N2​][H2​O]2​

Since at equilibrium rb=rfr_b = r_frb​=rf​, we get

rb=Kb[N2][H2O]2[H2]r_b = K_b\frac{[N_2][H_2O]^2}{[H_2]}rb​=Kb​[H2​][N2​][H2​O]2​

where Kb=KfKcK_b = \frac{K_f}{K_c}Kb​=Kc​Kf​​.

  1. Match with options

The reverse rate expression is:

Kb[N2][H2O]2/[H2]K_b[N_2][H_2O]^2/[H_2]Kb​[N2​][H2​O]2/[H2​]

So the correct option is B.

  1. Check all options
  • A: Kb[N2][H2O]K_b[N_2][H_2O]Kb​[N2​][H2​O] → missing one [H2O][H_2O][H2​O] and denominator [H2][H_2][H2​]; incorrect.
  • B: Kb[N2][H2O]2/[H2]K_b[N_2][H_2O]^2/[H_2]Kb​[N2​][H2​O]2/[H2​] → correct.
  • C: Kb[N2][H2O]2/[NO]K_b[N_2][H_2O]^2/[NO]Kb​[N2​][H2​O]2/[NO] → wrong denominator; incorrect.
  • D: Kb[N2][H2O]2K_b[N_2][H_2O]^2Kb​[N2​][H2​O]2 → missing denominator [H2][H_2][H2​]; incorrect.

Therefore, Option B is correct.

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