# Following is the rate expression. Rate = k[A]^1/2[B]^3/2 How much rate will be increased if concentration of [A] quadrupled.

Dear Student

Rate = k [A]1/2 [B]3/2

Concentration of A is quadrupled, then the new concentration of A1 =  4 [A]

Rate will increase by ???

Thus, the new rate will be, R' = k [(4 x [A]1/2) [B]3/2]

= [4]1/2 [1]3/2 x [​k [A]1/2 [B]3/2] = $\sqrt[2]{4}$ x($\sqrt[2]{1}$)3 x R [Because R = k [A]1/2 [B]3/2]

Also,  [4]1/2$\sqrt[2]{4}$ (because, x1/n = nth root of x]
And, [1]3/2 = ($\sqrt[2]{1}$)3 (because, xm/n = ($\sqrt[n]{x}$)m

So, R' = 2 x 1 x R = 2R

Therefore, Rate will increase by a factor of 2.

Regards

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