Hey selango,
So, let's set variables for each of the quantities:
r = rate of reaction
A = concentration of A
B = concentration of B
We know that r goes up proportionally as A^2 goes up and B goes down. So you can create an equation like this:
r = k * (A^2 / B)
where k is some constant.
Now, saying that the concentration of chemical B is increased by 100% is really a fancy way of saying that it's doubled (i.e. B becomes 2B). Now, we have to figure out what has to happen to A in order for the rate to remain the same...
r = k * (A^2 / B)
If B becomes 2B, then the denominator has been multiplied by 2, which means numerator has to be multiplied by 2 as well to keep the rate equal. So the quantity A^2 has to be become 2A^2.
You get this by multiplying A by sqrt(2):
A^2 / B
= [sqrt(2)*A]^2 / 2B
= 2A^2 / 2B
= A^2 / B
Multiplying by sqrt(2) is multiplying by roughly 1.414. If you didn't know that offhand, you could estimate it by using perfect squares. Since 14^2 = 196, that means 1.4^2 = 1.96. Since 2 is just slightly above 1.96, you know that sqrt(2) is just slightly above 1.4
Multiplying by 1.414 represents an increase of about 41.4 percent. Choose D
Last edited by
Rich@VeritasPrep on Thu Jun 17, 2010 3:53 am, edited 1 time in total.
Rich Zwelling
GMAT Instructor, Veritas Prep
