razorback wrote:Quite baffled...
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 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
OA: D
R is directly proportional to A² means that as R increases, A² increases by a proportional amount:
R/A² = k.
In the equation above, if R doubles, then A² must double, so that the value of R/A² is always equal to the constant k.
R is inversely proportional to B means that as R increases, B decreases by a proportional amount:
RB = k.
In the equation above, if R doubles, then B must be halved, so that the value of RB is always equal to the constant k.
Thus, the problem above describes the following relationship:
R = A²/B.
In the equation above:
R/A² is always equal to B and RB is always equal to A².
Given R=A²/B, we can plug in values.
Plug A=10 and B=1 into R=A²/B:
Then R = 10²/1 = 100.
If B doubles and R is unchanged, we get:
100 = A²/2
200 = A²
A = √200 = 10√2 ≈ 14.
A increases from 10 to 14.
Percent increase in A = Difference/Original = 4/10 = 40%.
The correct answer is
D.
It would be wise to remember the following:
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