For a first-order reaction R P at a given temperature, k is the rate constant. For this reaction, at the given temperature, the concentrations of R and P at a time t are [R] and [P], respectively. The correct graphical representation(s) for this reaction is(are)
- [figure]
- [figure]
- [figure]
- [figure]
Answer
(3) [figure], (4) [figure]
Solution
For first order: [R]=[R]0e-kt, [P]=[R]0(1-e-kt).
(A) [P] rises with decreasing slope (concave down) and levels off at [R]0; the concave-up curve is wrong.
(B) d[R]dt=-k[R] is negative, a line of negative slope; the plotted positive line is wrong.
(C) d[P]dt=k[R]0e-kt decays exponentially with t: correct.
(D) k is independent of time at a given temperature: correct.
Answer: (C), (D)