keep the reaction

[sanju09]

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. 25
B. 32
C. 36
D. 40
E. 44

OA D

[moutar]

Take a = conc of A, b = conc of B and R = rate.

Then R = k(a^2)/b

Increasing b by 100% is the same as doubling

We need to find x in the equation (i.e. the inc/dec of A):
k(a^2)/b = k(xa)^2/2b

Divide by ka^2 and multiply by b

1 = x^2/2
x = sqrt (2)
= 1.415

Therefore increse in A is approx 40% = D

[Vemuri]

Take a = conc of A, b = conc of B and R = rate.

Then R = k(a^2)/b

Increasing b by 100% is the same as doubling

We need to find x in the equation (i.e. the inc/dec of A):
k(a^2)/b = k(xa)^2/2b

Divide by ka^2 and multiply by b

1 = x^2/2
x = sqrt (2)
= 1.415

Therefore increse in A is approx 40% = D

Hi moutar,

Whatever you explained just over my head. Can you please explain or make it easier to understand?

Also, if (concentration of A)^2 is inversely proportional to concentration of B, don't you think any increase in B should reduce the concentration of A to maintain the balance? All the answer choices are positive & this makes me think that maybe I did not understand the question.

[moutar]

R is directly proportional to the square of a.
i.e. R = ca^2 (where c is some constant)

R is inversely proportional to b.
i.e. R = d/b (where d is some constant)

Putting these together gives R = ka^2/b (k is a combination of d and c)

So for an increase of b, a would have to increase by the square root of the factor for R to stay the same.

Anything else?

[Vemuri]

R is directly proportional to the square of a.
i.e. R = ca^2 (where c is some constant)

R is inversely proportional to b.
i.e. R = d/b (where d is some constant)

Putting these together gives R = ka^2/b (k is a combination of d and c)

So for an increase of b, a would have to increase by the square root of the factor for R to stay the same.

Anything else?

Thanks moutar. It makes perfect sense to me now. Maybe a good night's sleep & your patient explanation did the trick