sk8ternite 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 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
Please explain, completely lost
When you have really complicated questions, you have to spend extra time understanding the situation. This question is a case in point.
With a basic understanding we can give ourselves a quick 50/50 shot at the point:
"The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present"... so when A goes up, the rate of reaction goes up.
"and [is] inversely proportional to the concentration of chemical B present"... so when B goes up, the rate of reaction goes down.
"If the concentration of chemical B is increased"... we predict, this will
slow down the reaction.
"which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?"... we predict, to counteract the effects of B, we need to
increase the amount of A.
Accordingly, eliminate (a), (b) and (c).
If we want to actually solve, we could pick numbers to do so. We have a percent question, so let's use 100 to keep things simple.
Original: 100A and 100B.
Rate of reaction is proportional to a^2 and inversely proportional to B, so original rate of reaction is:
(100*100) * 1/100 = 100
New: B increases by 100%, so we now have 200B.
Without adding A, new rate of reaction is:
(100*100) * 1/200 = 50
We want to get back to our reaction rate of 100. Let's just plug in a choice to see which one is correct:
If new A is 150 (increase by 50%, choice (e)), new rate of reaction is:
(150*150) * 1/200 = 150*150/200 = 15*15/2 = 225/2 which is greater than 100. Therefore, a 50% increase is TOO MUCH.. eliminate (e), choose (d).
