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CUET · CHEMISTRY · PYQ PAPER 2025

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The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
For an integrated first order reaction, a straight line graph is plotted. The incorrect co-ordinates and resulting slope of the graph are

  1. A \(\log [ R ]\) vs \(t ;\) Slope \(=-k / 2.303\)
  2. B \(\ln \left([ R ]_0 /[ R ]\right)\) vs \(t ;\) Slope \(=k\)
  3. C \(\ln [ R ]\) vs \(t ;\) Slope \(=k\)
  4. D \(\log \left([ R ]_0 /[ R ]\right)\) vs \(t ;\) Slope \(=k / 2.303\)
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Answer & Solution

Correct Answer

(C) \(\ln [ R ]\) vs \(t ;\) Slope \(=k\)

Step-by-step Solution

Detailed explanation

\( \ln[R]_t = \ln[R]_0 - kt \) For \( \ln[R] \) vs \( t \), slope \( = -k \). Option C states slope \( = k \), which is incorrect.
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