For a first order reaction A arrow B t/min [A]/M 0 0.6500 x 0.0650 20 0.00065 x= ______ min. (Nearest integer)

Question

Quantrex Academy · Accepted Answer

Correct answer: 0

For a first order reaction, the rate constant

k

is given by:

k = \dfrac{1}{t} \ln \dfrac{[A]_0}{[A]_t}

Using the data at

t = 20

min:

k = \dfrac{1}{20} \ln \dfrac{0.6500}{0.00065} = \dfrac{1}{20} \ln 1000 = \dfrac{3}{20} \ln 10

Using the data at

t = x

min:

k = \dfrac{1}{x} \ln \dfrac{0.6500}{0.0650} = \dfrac{1}{x} \ln 10

Equating the two expressions for

k

:

\dfrac{3}{20} \ln 10 = \dfrac{1}{x} \ln 10

\dfrac{3}{20} = \dfrac{1}{x}

x = \dfrac{20}{3} = 6.66...

Rounding to the nearest integer, we get

x = 7

.

Answer:

7

For a first order reaction A arrow B t/min [A]/M 0 0.6500 x 0.0650...