I am having difficulty trying to figure out how they came about with this answer. It asks to find the pH when it is increased from 1 to 2. Sorry I can't post it. Can anyone help me out please?
Well, it doesn't ask for the pH, it asks to find the rate of formation of Cl- when the pH is increased from 1 to 2. In the passage they state the reaction's rate law as:
Rate = k[ClO3-][Br-][H+]^2
They also state that only H+ changes (pH from 1 to 2), so we can ignore ClO3- and Br-. Remember, going from pH 1 to pH 2 means a
decrease in hydrogen ion concentration (from 0.1 M to 0.01 M). So, we need to find out what happens to the rate of formation of Cl- when the reactant H+ decreases from 0.1 M to 0.01 M.
They tell us that originally the rate is 1 x 10^-2 M/sec. This is proportional to the square of the original H+ concentration. The second rate (which we need to find) is also proportional to the square of the new ion concentration. So, for the two reactions, we have:
1. 1 x 10^-2 = k[ClO3-][Br-](0.1)^2
2. x = k[ClO3-][Br-](0.01)^2
Like I said before, ClO3- and Br- concentrations don't change, so we can ignore them because they will cancel out. The same goes for k. So, at this point, we can say that a rate of 1 x 10^-2 is to (0.1)^2, as a rate of x is to (0.01)^2. This can represented as proportions by:
(1 x 10^-2)
/(0.1)^2 = x / (0.01)^2
Solving for x by cross-multiplying gives us a value of 1 x 10^-4 M/s, which is the correct answer.
Additionally, this can be solved intuitively. If I decrease the concentration of a reactant, and that reactant helps determine the rate of formation of the product, then it follows that the rate of formation of the product will also decrease. Answer choice D is the only one in which the rate of formation of Cl- actually decreases from the original value of 1x10^-2 M/s (A and C are both bigger, and B is the same). This confirms D is the correct answer.
