The rate constant, k, for a first-order reaction is equal to 6.2 × 10^-4 s^-1. Half-life?

Question

The rate constant, k, for a first-order reaction is equal to 6.2 × 10-4 s-1. What is the half-life for the reaction?

1. a. 8.0 × 102 s

2. b. 4.3 × 10-4 s

3. c. 1.1 × 103 s

4. d. 1.6 × 103 s

How?

Answer 1

Half life of a 1st order reaction is ln(2)/k. Where k is the rate constant.

dN/dt = -k*N

dN/N = -k*dt

integrate both sides with limits

ln(N2/N1) = -k*(t2-t1)

for N2 = 0.5*N1, ln(1/2) = -k*(t - 0) where t is half life and considering t1 = 0 for N1

so ln(1/2) = -ln(2)

so ln(2) = k*t

t = ln(2)/k. and ln(2) = 0.693

so t = 0.693/k

t = 0.693/(6.2 × 10^-4 s^-1) = 1117.74 sec

so (c) is correct