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A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (i) doubled (ii) reduced to half?

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A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (i) doubled (ii) reduced to half?

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Let the concentration of the reactant be [A] = a

Rate of reaction, R = k [A]2 = ka2

(i) If the concentration of the reactant is doubled, i.e. [A] = 2a, then the rate of the reaction would be

R' = k(2a)2

= 4ka2

= 4R

Therefore, the rate of the reaction would increase by 4 times.

(ii) If the concentration of the reactant is reduced to half, i.e. [A] = \(\frac{1}{2}\)a, then the rate of the reaction would be

R' = k\((\frac{1}{2}a)^2\)

= \(\frac{1}{4}ka^2\)

= \(\frac{1}{4}R\)

Therefore, the rate of the reaction would be reduced to \(\frac{1}{4}^{th}\).

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