A particular reactant decomposes with a half-life of 109 s when its initial conc

Question

A particular reactant decomposes with a half-life of 109 s when its initial concentration is 0.324 M. The same reactant decomposes with a half-life of 225 s when its initial concentration is 0.157 M.

Determine the reaction order.

What is the value and unit of the rate constant for this reaction?

So then

A reactant decomposes with a half-life of 171 s when its initial concentration is 0.322 M. When the initial concentration is 0.522 M, this same reactant decomposes with the same half-life of 171 s.

What is the order of the reaction?

What is the value and unit of the rate constant for this reaction?

Explanation / Answer

if concentration = 0.324 M

t(1/2) = 109 s

concentration = 0.157 M

t(1/2) = 225 s

so t(1/2)   is inversly proprotional to concentration

which indicates reaction is second order.

for second order

t1/2  = 1 /K[A]

K = 1/[A]t1/2

K = 1 / 0.324 x 109

K = 1 / 35.316

K = 2.83 x 10-2 M-1s-1

for second order K = M-1 s-1

2) if concentration = 0.322 M

t1/2   = 171 s

concentration = 0.522 M

t1/2   = 171 s

means t1/2  is independent on concentration

it indicates first order reaction.

K = 0.693 / t1/2

K = 0.693 / 171

K = 4.05 x 10-3 s-1

K = s-1

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