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Chemical Kinetics and Nuclear Chemistry question

2022 · 27 Jul · Shift 1 · Q15
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Chemical Kinetics and Nuclear Chemistry question

2022 · 27 Jul · Shift 1 · Q15

JEE MainChemistryChemical Kinetics and Nuclear ChemistryNumerical+4 / −1

2NO+2H2→N2+2H2O2 \mathrm{NO}+2 \mathrm{H}_{2} \rightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}2NO+2H2​→N2​+2H2​O

The above reaction has been studied at 800∘C800^{\circ} \mathrm{C}800∘C. The related data are given in the table below

Reaction serial number Initial Pressure of H2/kPa{H_2}/kPaH2​/kPa Initial Pressure of NO/kPaNO/kPaNO/kPa Initial rate (−dpdt)/(kPa/s)\left( {{{ - dp} \over {dt}}} \right)/(kPa/s)(dt−dp​)/(kPa/s)
1 65.6 40.0 0.135
2 65.6 20.1 0.033
3 38.6 65.6 0.214
4 19.2 65.6 0.106

The order of the reaction with respect to NO is ‾\underline{\hspace{2cm}}​.

Numerical answer
View written solutionFree

Correct answer: 2

  1. Assume the rate law

    Let the rate be r=k (PNO)m(PH2)nr = k\,(P_{\mathrm{NO}})^m (P_{\mathrm{H_2}})^nr=k(PNO​)m(PH2​​)n where mmm is the order with respect to NO\mathrm{NO}NO and nnn is the order with respect to H2\mathrm{H_2}H2​.

  2. Use experiments where PH2P_{\mathrm{H_2}}PH2​​ is constant

    Compare experiment 1 and 2:

    • In both, PH2=65.6 kPaP_{\mathrm{H_2}} = 65.6\,\text{kPa}PH2​​=65.6kPa
    • PNOP_{\mathrm{NO}}PNO​ changes from 40.040.040.0 to 20.1 kPa20.1\,\text{kPa}20.1kPa
    • Rate changes from 0.1350.1350.135 to 0.033 kPa s−10.033\,\text{kPa s}^{-1}0.033kPa s−1

    So, r1r2=(PNO,1PNO,2)m\frac{r_1}{r_2} = \left(\frac{P_{\mathrm{NO},1}}{P_{\mathrm{NO},2}}\right)^mr2​r1​​=(PNO,2​PNO,1​​)m

    Substitute values: 0.1350.033=(40.020.1)m\frac{0.135}{0.033} = \left(\frac{40.0}{20.1}\right)^m0.0330.135​=(20.140.0​)m

    4.09≈(1.99)m4.09 \approx (1.99)^m4.09≈(1.99)m

  3. Find mmm

    Since 4.09≈224.09 \approx 2^24.09≈22 and 1.99≈21.99 \approx 21.99≈2 therefore m=2m = 2m=2

  4. Conclusion

    The order of the reaction with respect to NO\mathrm{NO}NO is 2\boxed{2}2​

  5. Comparison with stored answer

    Stored correct answer: 222

    Our derived answer matches the stored answer.

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