Rate&Percentage

[Akansha]

The rate of a reaction is directly proportional to the square of the concentration of
A and inversely proportional to concentration of B. If B increases by 100%,
which of the following is closest to the % change in concentration of A required
to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase

OA is D

Can anyone help me with this?

[Anurag@Gurome]

The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%,
which of the following is closest to the % change in concentration of A required
to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase

OA is D

Can anyone help me with this?

Let rate of reaction = r, so r α A² and r α 1/B
The, r α A²/B or r = k(A²/B)
Let the new concentration of A = A', and new concentration of B = B'
Now rate remains unchanged means rate is the same, so k(A²/B) = k[(A')²/(B')]
B is increased by 100% means B becomes double, which means B' = 2B
So, k(A²/B) = k[(A')²/(2B)]
A² = (A')²/2 or (A')² = 2A²
So, A' = A√2
Since √2 = 1.414, so A' = 1.4A, which implies there is 40% increase.

The correct answer is D.

[aftableo2006]

40%increase in concentration of A