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The rate of a certain chemical reaction is directly [#permalink]
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07 Aug 2005, 21:00
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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 present is increased by 100 percent, which of the following is closest to the percent change in the 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 OPEN DISCUSSION OF THIS QUESTION IS HERE: therateofacertainchemicalreactionisdirectly90119.html
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Last edited by Bunuel on 04 Dec 2013, 03:01, edited 1 time in total.
Added the OA.



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Let's say here is the formula of how A and B affects the reaction speed:
rate = A^2/B
After the concentration B is increased by 100%, the percentage of B
become 2B, to keep 'rate' the same, need to have A^2 being doubled.
Which means A increased by 2^(1/2) times.
In closest percentage, that is 40% increase
D



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But the question does say the relationship between A and B is multiplication.



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does inversely proportion suggest when B increase, the reaction speed decrease  in essense it is equivalent to a division.



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In general and in full
r = k A^2 / B for some constant k<>0
(Question should also give B<>0)
So we have
r1 = k A1^2 / B1
r2 = k A2^2 / B2
r1 = r2
B2 = (1+100%)B1 = 2B1
k A1^2 / B1 = k A2^2 / B2
A1^2 / B1 = A2^2 / 2B1
2A1^2 = A2^2
(sqrt(2)A1)^2 = A2^2
A1,A2>0
A2 = sqrt(2) * A1
A2 = (1 + 41.4%) * A1
About 40% increase
D



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qpoo wrote: Let's say here is the formula of how A and B affects the reaction speed:
rate = A^2/B
After the concentration B is increased by 100%, the percentage of B become 2B, to keep 'rate' the same, need to have A^2 being doubled. Which means A increased by 2^(1/2) times.
In closest percentage, that is 40% increase
D
plz QPoo could explain why doubled A^2 is to increase it by 2^(1/2) times.
thanks
regards
mandy



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Re: The rate of a certain chemical reaction is directly [#permalink]
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03 Dec 2013, 09:36
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Re: The rate of a certain chemical reaction is directly [#permalink]
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04 Dec 2013, 03:01
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 present is increased by 100 percent, which of the following is closest to the percent change in the 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 NOTE: Put directly proportional in nominator and inversely proportional in denominator. \(RATE=\frac{A^2}{B}\), (well as it's not the exact fraction it should be multiplied by some constant but we can ignore this in our case). We are told that B increased by 100%, hence in denominator we have 2B. We want the rate to be the same. As rate is directly proportional to the SQUARE of A, A should also increase (nominator) by x percent and increase of A in square should be 2. Which means \(x^2=2\) > \(x\approx{1.41}\), which is approximately 40% increase. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}=\frac{2A^2}{2B}\) Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: therateofacertainchemicalreactionisdirectly90119.html
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Re: The rate of a certain chemical reaction is directly [#permalink]
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04 Dec 2013, 03:02
Bunuel 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 present is increased by 100 percent, which of the following is closest to the percent change in the 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 NOTE: Put directly proportional in nominator and inversely proportional in denominator. \(RATE=\frac{A^2}{B}\), (well as it's not the exact fraction it should be multiplied by some constant but we can ignore this in our case). We are told that B increased by 100%, hence in denominator we have 2B. We want the rate to be the same. As rate is directly proportional to the SQUARE of A, A should also increase (nominator) by x percent and increase of A in square should be 2. Which means \(x^2=2\) > \(x\approx{1.41}\), which is approximately 40% increase. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}=\frac{2A^2}{2B}\) Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: therateofacertainchemicalreactionisdirectly90119.html DS problems about this concept: theamountofcoalatrainburnseachmileisdirectly93667.htmlinacertainbusinessproductionindexpisdirectly63570.htmlPS problems about this concept: aisdirectlyproportionaltobwhena8b88971.htmlinacertainformulapisdirectlyproportionaltosand80941.htmlHope it helps.
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Re: The rate of a certain chemical reaction is directly
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