want to find the time, t, so plug these values into the last equation to get = kt + . Simplify this
equation to get 2.5 = kt + 0.5, and kt = 2. To solve for t, you first need to figure out the value of k. You
need to use the first equation to find the value of k, since the value of r in the second equation is never
defined. According to the question, C and R are constants, where C = 4 and R = 8.314. Also according to
the question, Ea = 10,082, and T = 310. Plug all of these values into the first equation to get k =
. Simplify the exponent to get k = 4e−3.9118. Use your calculator to find that k = 4(0.02) = 0.08.
Plug this value into the earlier equation kt = 2 to get 0.08t = 2, and t = 25. The correct answer is 25. Grid
it in!
Notice how the second equation was completely useless in solving this problem. That will happen
occasionally on the SAT, so don’t get distracted by the extraneous information.
Now that we have the value of rate constant k, let’s crack question 38. In question 37, k = 0.08, so if k
triples, the new value for k is 0.08 × 3 = 0.24. According to the information in question 37, [A] 0 = 2, and
according to question 38, t = 50. Plug all of these values into the last equation, which has [A]t in it, to get
= (0.24)(50) + . Simplify the right side of the equation to get = 12.5. Multiply both sides by[A]t to get 1 = 12.5[A]t. Finally, divide both sides by 12.5 to get [A]t. The correct answer is 0.08.