14.2.2 Second-Order Reactions

Question 1

Second-Order Reactions

Answer 1

• The rate law for a second-order reaction has the general form rate = k[A] 2 . A more useful equation for second-order reactions is 1/[A] t = kt + 1/[A] 0 .
• The half-life (t 1/2 ) of a second-order reaction depends on starting concentration, and is therefore not particularly useful.

Question 2

note

Answer 2

• The rate law for a second-order reaction has the general form rate = k[A] 2 . However, the plot of [A] versus t looks the same for a first-order reaction or a second-order reaction.
• Applying principles of calculus, a more useful equation can be derived: 1/[A] t = kt + 1/[A] 0
• This equation is in the form of a straight line (y = mx + b), where y = 1/[A]t, m = k, x = t, and b = 1/[A] 0 . A plot of 1/[A] t versus t for a second-order reaction can be easily identified as a straight line.
• As for first-order reactions, the rate of second-order reactions can be expressed in terms of half-life (t 1/2 ).
• However, since the half-life for a second-order reaction
  depends on starting concentration, this number is not
  particularly useful.
• If a plot of ln[A] versus t yields a straight line, the reaction is first-order in A.
• If a plot of 1/[A] versus t yields a straight line, the reaction is second-order in A.
• In either case, a plot of [A] versus t will yield a curve.

Question 3

The following data are gathered for the reaction aA -> bB + cC
Time (min) 0 5 10 15 20
[A] (M) 0.10 0.068 0.047 0.032 0.022
ln [A] -2.30 -2.68 -3.06 -2.44 -3.82
1/A^-1 10.0 14.7 21.4 31.3 45.7
Which of the following is equal tot eh rate law for this reaction?

Answer 3

rate = (0.076 min^−1 ) [A]

Question 4

The reaction 2HI → H2 + I2 is second order in [HI] and second order overall. The rate constant of the reaction at 700°C is 1.57 × 10−5 M −1s−1. Suppose you have a sample in which the concentration of HI is 0.75 M. What was the concentration of HI 8 hours earlier?

Answer 4

2.3 M

Question 5

The reaction 2X → Y + Z is second order in [X] and second order overall. The rate constant of the reaction is 0.028 M −1hr−1. Suppose the initial concentration of X is 3.4 M. What percentage of X will remain after a period of 24 hours?

Answer 5

18%

Question 6

The reaction 2J -> K + L is second order in [J] and second order overall. When the concentration of J is 2.9*10^-3 M, its half-life is 27 days. What is the half-life when its concentration is 0.46M?

Answer 6

0.17 days

Question 7

Which of the following graphs correctly represents the relationship between the half-life and [A]0 for a reaction that is second order in [A] and second order overall?

Answer 7

-

Question 8

Suppose the following reaction is second-order in [A].

2A → 2B + C

The initial rate of reaction when [A]0 is 0.24 M is 9.79 × 10−4 M / s. After how many seconds will [A] be 0.12 M?

Answer 8

123 s

Question 9

Which of the following graphs represents a reaction that is second-order in [ M]?

Answer 9

-