The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical a present and inversely proportional to the concentration of chemical b present. if the concentration of chemical b is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical a required to keep the reaction rate unchanged?
(a) 100 % decrease
(b) 50 % decrease
(c) 40 % decrease
(d) 40 % increase
(e) 50 % increase

increase the concentration of A by 40% approximately.

Explanation:

The rate of reaction is directly proportional to square of the concentration of chemical present A.  the rate of reaction is inversely proportional to concentration of B. Thus we can write it as :

Rate = K [A]²[B]⁻¹

Now if we are increasing the concentration of B by 100% it means we are doubling its concentration.

If we wish to keep the rate of reaction constant we have to increase the concentration of A

Rate =K [A₁]²[B₁]⁻¹ = K [A₂]²[B₂]⁻¹ =K [A₂]²[2B₁]⁻¹

K [A₁]²[B₁]⁻¹ = K [A₂]²[2B₁]⁻¹

[A₁]² = 0.5 X [A₂]²

[A₂] = 1.414 [A₁]

It means we have to increase the concentration of A by 40% approximately.

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