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Following is the rate expression.

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

How much rate will be increased if concentration of [A] quadrupled.

Rate = k [A]

^{1/2}[B]

^{3/2}

Concentration of A is quadrupled, then the new concentration of A

_{1}= 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, x

^{1}

^{/n}= nth root of x]

And, [1]

^{3/2 }= ($\sqrt[2]{1}$)

^{3}(because, x

^{m/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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