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# The rate of a certain chemical reaction is directly

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SVP
Joined: 21 Jul 2006
Posts: 1508
The rate of a certain chemical reaction is directly [#permalink]

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17 Aug 2008, 07:09
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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 the chemical B present. If the concentration of the 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
Director
Joined: 27 May 2008
Posts: 540

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17 Aug 2008, 07:45
tarek99 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 the chemical B present. If the concentration of the 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

initially A = x
B = y
rate1 = k x^2 / y

A = ?
B = 2y
rate2 = k A^2 / 2y = k x^2 /y
A^2 = (x^2)2
A = 1.414 * x

% change = approx 40% increase....
Director
Joined: 12 Jul 2008
Posts: 514
Schools: Wharton

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17 Aug 2008, 07:55
tarek99 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 the chemical B present. If the concentration of the 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

I get C.

R = A^2/B

R = (x*A)^2/2B
= (x^2)*(A^2)/2B

A^2/B = (x^2)*(A^2)/2B
1 = x^2/2
2 = x ^2
x = sqrt(2) = 1.414

40% increase
Intern
Joined: 07 Jan 2006
Posts: 49

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17 Aug 2008, 07:57
Using numerical values...

RB = A^2

Suppose R = 1, B = 100, and A = 10.

When B is increased by 100%, which means B is now 200, A^2 also needs to be 200 to stay unchanged, which means it's approximately 14 x 14 = 196 (is closer than 15 x 15 = 225) giving no calculator allowed, so it's 10 -> 14 (meaning approximately 140%, or 40% increase).
Retired Moderator
Joined: 18 Jul 2008
Posts: 959

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17 Aug 2008, 10:50
Is there answer 40% increase, or 40% decrease?
Re: PS: Concentration   [#permalink] 17 Aug 2008, 10:50
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