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# The rate of a certain chemical reaction is directly

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Joined: 13 Aug 2005
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The rate of a certain chemical reaction is directly [#permalink]  27 Aug 2005, 10:04
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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%, which of the following is the 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

Senior Manager
Joined: 29 Nov 2004
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Re: PS - concentrations [#permalink]  27 Aug 2005, 10:41
let us say a = 1, b = 1

Initially cr = 1^2*(1/1) = 1

now b = 2 a = ?, cr is still 1

cr = 1 = a^2*1/2 => a^2 = 2 or a = 1.414..

so aproximately 40% increase (D)

cr
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Re: PS - concentrations [#permalink]  27 Aug 2005, 10:43
yaron 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 the 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

A^2/B = 1 => B = A^2
after 100% increase

we have: X/(2B)=1
X is the new amount of A, X = 2B = 2*A^2 = (2^(1/2)*A)^2
=> represents a 2^(1/2) - 1 increase, closest to 40%

D
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Understood
Thank you all.
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