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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

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Answer:

D. 40 % increase  

Step-by-step explanation:

r = k[A]²/[B]

The rate is inversely proportional to [B]. If [B] is doubled, the rate is halved.

We must double this rate to get back to the original.

The rate is directly proportional to [A]².

2 = [A]₂/[A]₁²     Take the square root of each side

√2 = [A]₂/[A]₁     Multiply each side by [A]₁

[A]₂ = √2[A]₁

[A]₂ = 1.41[A]₁

We must increase [A] by 41 %.

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