132-02 201820/0eh -1459489-dt-content-rid-13598452 7courses/CHEM 17. Which of th

Question

132-02 201820/0eh -1459489-dt-content-rid-13598452 7courses/CHEM 17. Which of the following represents the equation for a first-order half-life? A. t12 KAlo 0.693 B. t1/2 = [A C. t1/2= 2k 2k D. t1/2- [Alo E. t1/2 AL [Alo 18. Which of the following represents the equation for a zero-order half-life? A, t1/2=k(Alo 0.693 B, t1/2 =-k 2k Alo E, 112-A Alo 19·The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 M. What is the rate constant for this reaction? A. 1.0x 10-2 M-1s-1 B. 4.5× 10-2 M-1s-1 C. 9.7 x 10-2 M-1s-1 D. 2.2 x 10-2 M-1s-1 E. 3.8% 10-2 M-1s-1 20. For a reaction, what generally happens if the temperature is increased? A. a decrease in k occurs, which results in a faster rate B. a decrease in k occurs, which results in a slower rate C. an increase in k occurs, which results in a faster rate D. an increase in k occurs, which results in a slower rate E there is no change with k or the rate

Explanation / Answer

[A]=[A]oe?kt

The half-life (t1/2) is a timescale on which the initial population is decreased by half of its original value, represented by the following equation.

[A]=[A]o/2

After a period of one half-life, t=t1/2 we can write

[A]1/2? / [A]o=1/2=e?kt1/2

Taking logarithms of both sides yields

ln0.5=?k

Solving for the half-life, we obtain the simple relation

t1/2 = (ln2) / k ? 0.693 / k

?18 [A] = 1/2[A]o

? Using the integrated form of the rate law, we can develop a relationship between zero-order reactions and the    half-life.

  [A]=[A]o? kt

   Substitute

1/2[A]o=[A]o?kt

Solve for t1/2

t1/2=[A]o/2k

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