For a first-order reaction, the half-life is constant. It depends only on the ra

Question

For a first-order reaction, the half-life is constant. It depends only on the rate constant k and not on the reactant concentration. It is expressed as t1/2=0.693/k For a second-order reaction, the half-life depends on the rate constant and the concentration of the reactant and so is expressed as t1/2=1/k[A]0.

Part A: A certain first-order reaction (A-->products) has a rate constant of 4.80x10^-3 s^-1 at 45 degrees Celsius. How many minutes does it take for the concentration of the reactant, [A], to drop to 6.35% of the original concentration?

Part B: A certain second-order reaction (B-->products) has a rate constant of 1.45x10^-3 M^-1 x s^-1 at 27 degrees celsius and an initial half-life of 300 s. What is the concentration fo the reactant B after one half-life?

Explanation / Answer

Part A

K = 2.303/t log(a/a-x)

4.8*10-3   = 2.303/t log100/100-6.35

0.0048      = 2.303/t log100/93.65

0.0048       = 2.303*0.0285/t

t                  = 2.303*0.0285/0.0048 = 13.67sec

Part B:

[ B ]= 1/kt1/2

          = 1/1.45*10^-3*300

         = 1/0.435

          = 2.298M

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