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Chemical Kinetics

Question
CBSEENCH12010174

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

  log space k equals space l o g space A space minus space fraction numerator E subscript a over denominator 2.303 end fraction open parentheses 1 over T close parentheses

where Ea is the activation energy.

When a graph is plotted for   l o g space k space space V s. space 1 over straight T a straight line with a slope of -4250 K is obtained. Calculate ‘Ea’ for the reaction.

(R = 8.314 JK-1 mol-1)

Solution

log space k space equals space l o g space A space minus fraction numerator E subscript a over denominator 2.303 end fraction open parentheses 1 over T close parentheses
Ea --> Activation energy

 The above equation is like y = mx + c where if we plot y v/s x we get a straight line with slope ‘m’ and intercept ‘c’.

 
So comma space slope space is space equal space to equals space fraction numerator negative straight E subscript straight a over denominator 2.303 end fraction
space equals space space fraction numerator negative straight E subscript straight a over denominator 2.303 end fraction space equals space minus 4250 space straight K space

minus straight E subscript straight a space equals 4250 space straight x space 2.303 space straight x space 8.314 space equals space 81 comma 375.3535 space straight j space mol to the power of negative 1 end exponent

straight E subscript straight a space equals space 81.3753 space KJ space mol to the power of negative 1 end exponent