# Solution - Temperature Dependence of the Rate of a Reaction

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#### Question

The rate constant for the decomposition of N2O5 at various temperatures is given below:

 T/°C 0 20 40 60 80 10^5XXK/s^(-1) 0.0787 1.7 25.7 178 2140

Draw a graph between ln and 1/and calculate the values of and Ea. Predict the rate constant at 30º and 50ºC.

#### Solution

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The rate constant for the first-order decomposition of H2O2 is given by the following equation:

logk=14.2-(1.0xx10^4)/TK

Calculate Ea for this reaction and rate constant k if its half-life period be 200 minutes.

(Given: R = 8.314 JK–1 mol–1)

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The rate constant of a first order reaction increases from 4 × 10−2 to 8 × 10−2 when the temperature changes from 27°C to 37°C. Calculate the energy of activation (Ea). (log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)

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(b) Rate constant ‘k’ of a reaction varies with temperature ‘T’ according to the equation:

logk=logA-E_a/2.303R(1/T)

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Explain a graphical method to determine activation energy of a reaction.

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#### Reference Material

Solution for concept: Temperature Dependence of the Rate of a Reaction. For the courses 12th CBSE (Arts), 12th CBSE (Commerce), 12th CBSE (Science), PUC Karnataka Science
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