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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] New post 07 Aug 2005, 20:00
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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: the-rate-of-a-certain-chemical-reaction-is-directly-90119.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Dec 2013, 02:01, edited 1 time in total.
Added the OA.
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 [#permalink] New post 07 Aug 2005, 20:11
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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 [#permalink] New post 08 Aug 2005, 06:01
But the question does say the relationship between A and B is multiplication.
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 [#permalink] New post 08 Aug 2005, 07:14
does inversely proportion suggest when B increase, the reaction speed decrease - in essense it is equivalent to a division.
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 [#permalink] New post 08 Aug 2005, 09:47
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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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 [#permalink] New post 15 Aug 2005, 13:31
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] New post 03 Dec 2013, 08:36
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Re: The rate of a certain chemical reaction is directly [#permalink] New post 04 Dec 2013, 02:01
Expert's post
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: the-rate-of-a-certain-chemical-reaction-is-directly-90119.html
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Re: The rate of a certain chemical reaction is directly [#permalink] New post 04 Dec 2013, 02:02
Expert's post
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: the-rate-of-a-certain-chemical-reaction-is-directly-90119.html


DS problems about this concept:
the-amount-of-coal-a-train-burns-each-mile-is-directly-93667.html
in-a-certain-business-production-index-p-is-directly-63570.html

PS problems about this concept:
a-is-directly-proportional-to-b-when-a-8-b-88971.html
in-a-certain-formula-p-is-directly-proportional-to-s-and-80941.html

Hope it helps.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: The rate of a certain chemical reaction is directly   [#permalink] 04 Dec 2013, 02:02
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