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# The rate of a certain chemical reaction is directly

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The rate of a certain chemical reaction is directly [#permalink]  12 May 2007, 14:56
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%, 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

OA is D
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Re: GMATPrep: chemical reaction [#permalink]  12 May 2007, 17:26
kookoo4tofu wrote:
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%, 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

OA is D

refer here.
http://www.gmatclub.com/phpbb/viewtopic ... t=chemical
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Chemical Reaction [#permalink]  13 May 2007, 20:17
If y is inversely proportional to x, then y = 1/x. If y is equal to the square of x, then y = x^2, of course. Chemical Reaction => CR. I.e., label chemical reaction CR. So, then CR = A^2 / B. So, if B is increased by 100%, then B => 2B. For the Rate of the chemical reaction to stay the same, you need a 2 to appear in the numerator because the denominator is now 2B. So, ( Root(2) * A )^2 is what you need. Distribute the Squre. This results in Root(2)^2 = 2 in the numerator and also A^2 in the numerator: 2 * A^2. The 2 in the numerator and denominator cancel and you are left with what you started with: A^2 / B. So, what you had to increase A by approx 40%..........................Because Root(2) is approx 1.41.
Chemical Reaction   [#permalink] 13 May 2007, 20:17
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