# a). Rate constant k for first order reaction has been found to be 2.54 x 10^‐3 s^‐1 . Calculate its three fourth life.

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a). Rate constant k for first order reaction has been found to be 2.54 x 10‐3 s‐1 . Calculate its three fourth life.

b). A reaction is first order in A and second order in B.

(i) Write the differential rate equation.

(ii) How is the rate affected on increasing the concentration of B three times?

(iii) How is the rate affected when the concentrations of both A and B are doubled?

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(a) k = $\frac{2.303}{t}$ log $\frac{[R]_o}{[R]}$

For three-forth of the reaction to take place,

[R] = $\frac{[R]_o}{[4]}$ or $\frac{[R]_o}{[R]}$ = 4

Substituting the vale in the rate equation, we have

2.54 x 10-3$\frac{2.303}{t}$log 4

or t = $\frac{2.303}{2.54}$ x 103 x 0.6021 = 5.46 x 102s

b) (i) dx/dt = k [A][B]2

(ii) 9 times

(iii) 8 times