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Chemical Kinetics and Nuclear Chemistry question

2018 · Shift 0 · Q16
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Chemical Kinetics and Nuclear Chemistry question

2018 · Shift 0 · Q16

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1
At 518oC the rate of decomposition of a sample of gaseous acetaldehyde initially at a pressure of 363 Torr, was 1.00 Torr s–1 when 5% had reacted and 0.5 Torr s–1 when 33% had reacted. The order of the reaction is
  1. A
    0
  2. B
    2
  3. C
    3
  4. D
    1
View written solutionFree

Correct answer: B

  1. Use pressure as concentration
    For a gaseous reaction at constant volume and temperature, pressure is proportional to concentration.
    So we can use r=kPnr = kP^nr=kPn where PPP is the partial pressure of acetaldehyde remaining.

  2. Initial pressure
    Given initial pressure: P0=363 TorrP_0 = 363\ \text{Torr}P0​=363 Torr

  3. Pressure when 5% has reacted
    If 5%5\%5% has reacted, then 95%95\%95% remains: P1=0.95×363=344.85 TorrP_1 = 0.95 \times 363 = 344.85\ \text{Torr}P1​=0.95×363=344.85 Torr Given rate: r1=1.00 Torr s−1r_1 = 1.00\ \text{Torr s}^{-1}r1​=1.00 Torr s−1

  4. Pressure when 33% has reacted
    If 33%33\%33% has reacted, then 67%67\%67% remains: P2=0.67×363=243.21 TorrP_2 = 0.67 \times 363 = 243.21\ \text{Torr}P2​=0.67×363=243.21 Torr Given rate: r2=0.50 Torr s−1r_2 = 0.50\ \text{Torr s}^{-1}r2​=0.50 Torr s−1

  5. Apply rate law ratio
    r1r2=(P1P2)n\frac{r_1}{r_2} = \left(\frac{P_1}{P_2}\right)^nr2​r1​​=(P2​P1​​)n Substitute values: 1.000.50=(344.85243.21)n\frac{1.00}{0.50} = \left(\frac{344.85}{243.21}\right)^n0.501.00​=(243.21344.85​)n 2=(1.4178)n2 = (1.4178)^n2=(1.4178)n

  6. Solve for nnn
    Taking logarithms: n=log⁡2log⁡1.4178n = \frac{\log 2}{\log 1.4178}n=log1.4178log2​ Now, log⁡2≈0.3010,log⁡1.4178≈0.1510\log 2 \approx 0.3010, \quad \log 1.4178 \approx 0.1510log2≈0.3010,log1.4178≈0.1510 So, n≈0.30100.1510≈1.99≈2n \approx \frac{0.3010}{0.1510} \approx 1.99 \approx 2n≈0.15100.3010​≈1.99≈2

  7. Conclusion
    The reaction is second order.

Therefore, the correct option is: B: 2\boxed{\text{B: }2}B: 2​

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