Question

QUESTION 8 If we start with 1.000 g of strontium-90, 0.908 g will remain after 4.00 yr. This means that the half-life of strontium-90 is A. 3.05 B. 4.40 C.28.8 D. 3.63 E. 41.6

Answer 1

we have:
[Sr]o = 1.0 g
[Sr] = 0.908 g
t = 4.0 yr


use integrated rate law for 1st order reaction
ln[Sr] = ln[Sr]o - k*t
ln(0.908) = ln(1) - k*4
-9.651*10^-2 = 0 - k*4
k*4 = 9.651*10^-2
k = 2.41*10^-2 yr-1

Given:
k = 2.41*10^-2 yr-1
use relation between rate constant and half life of 1st order reaction

t1/2 = (ln 2) / k
= 0.693/(k)
= 0.693/(2.413*10^-2)
= 28.8 yr
Answer: C