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Chemical Kinetics and Nuclear Chemistry question

2002 · Shift 0 · Q39
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Chemical Kinetics and Nuclear Chemistry question

2002 · Shift 0 · Q39

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1
The differential rate law for the reaction H2H_2H2​ + I2I_2I2​ →\to→ 2HIHIHI is
  1. A
    −d[H2]dt- {{d\left[ {{H_2}} \right]} \over {dt}}−dtd[H2​]​ =−d[I2]dt- {{d\left[ {{I_2}} \right]} \over {dt}}−dtd[I2​]​=−d[HI]dt- {{d\left[ {{HI}} \right]} \over {dt}}−dtd[HI]​
  2. B
    d[H2]dt{{d\left[ {{H_2}} \right]} \over {dt}}dtd[H2​]​ =d[I2]dt{{d\left[ {{I_2}} \right]} \over {dt}}dtd[I2​]​=d[HI]dt{{d\left[ {{HI}} \right]} \over {dt}}dtd[HI]​
  3. C
    12d[H2]dt{1 \over 2}{{d\left[ {{H_2}} \right]} \over {dt}}21​dtd[H2​]​=12d[I2]dt{1 \over 2}{{d\left[ {{I_2}} \right]} \over {dt}}21​dtd[I2​]​=−d[HI]dt- {{d\left[ {{HI}} \right]} \over {dt}}−dtd[HI]​
  4. D
    −2d[H2]dt- 2{{d\left[ {{H_2}} \right]} \over {dt}}−2dtd[H2​]​ =−2d[I2]dt- 2{{d\left[ {{I_2}} \right]} \over {dt}}−2dtd[I2​]​=d[HI]dt{{d\left[ {{HI}} \right]} \over {dt}}dtd[HI]​
View written solutionFree

Correct answer: D

  1. For a reaction aA+bB→cC+dDaA+bB\rightarrow cC+dDaA+bB→cC+dD the rate is written as Rate=−1ad[A]dt=−1bd[B]dt=1cd[C]dt=1dd[D]dt.\text{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}.Rate=−a1​dtd[A]​=−b1​dtd[B]​=c1​dtd[C]​=d1​dtd[D]​.

  2. Given reaction: H2+I2→2HIH_2+I_2\rightarrow 2HIH2​+I2​→2HI Here, stoichiometric coefficients are:

    • for H2H_2H2​: 111
    • for I2I_2I2​: 111
    • for HIHIHI: 222

  3. Therefore, the differential rate law is −d[H2]dt=−d[I2]dt=12d[HI]dt.-\frac{d[H_2]}{dt}=-\frac{d[I_2]}{dt}=\frac{1}{2}\frac{d[HI]}{dt}.−dtd[H2​]​=−dtd[I2​]​=21​dtd[HI]​.

  4. Multiply all terms by 222: −2d[H2]dt=−2d[I2]dt=d[HI]dt.-2\frac{d[H_2]}{dt}=-2\frac{d[I_2]}{dt}=\frac{d[HI]}{dt}.−2dtd[H2​]​=−2dtd[I2​]​=dtd[HI]​.

  5. Compare with options:

    • A: wrong sign for HIHIHI
    • B: all signs wrong
    • C: incorrect coefficients and sign
    • D: matches exactly

Hence, the correct option is D.

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