Question

A particular reactant decomposes with a half-life of 157 s when its initial concentration is 0.372 M. The same reactant decomposes with a half-life of 231 s when its initial concentration is 0.253 M. A.) Determine the reaction order. B)What is the value and unit of the rate constant for this reaction?

Answer 1

t 1/2 proportional to 1/(a^(n-1) where a is the concentration and n is the order

so:

for point 1:

t_{1/2 1} = 1 / (a1^n-1))

for point 2

t_{1/2 2} = 1 / (a2^n-1))

then

t_{1/2 1} / t_{1/2 2} = (a1/a2)^(n-1)

substitute data

157 / 231 = (0.372/0.253) ^ (n-1)

0.679653 = 1.47035 ^(n-1)

ln(0.679653 ) = (n-1)* ln(1.47035 )

ln(0.679653 ) /  ln(1.47035 ) = n-1

n = 1 + ln(0.679653 ) /  ln(1.47035 ) = -0.001744 or 0 oder

b)

since this is 0 order, then

units are M/s o mol per liter per second