The first-order isomerization of cis -but-2-ene to trans -but-2-ene was studied

Question

The first-order isomerization of cis-but-2-ene to trans-but-2-ene was studied at 723 K. The Arrhenius pre-exponential factor, A, was found to be 6.1×10^13 s?1 and the activation energy, Ea is 260 kJmol?1.

A) What is the rate constant at 723 K?

Express your answer using two significant figures.

B)

If the temperature of a pure sample of cis-but-2-ene was increased to 723 K, how long would it take for 47.0 % of the sample to isomerize?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)

using,

lnk = lnA - Ea/RT

with,

k = rate constant

Ea = activation energy

A = preexponential factor

R = gas constant

T = temperature

feeding values,

lnk = ln(6.1 x 10^13) - 260 x 10^3/8.314 x 723

k = 1.00 x 10^-5 s-1

B) [A]o = 100

[A] = 100-47 = 53

Using,

time (t) = (ln[A]o - ln[A])/k

So time taken to isomerize 47% sample

t = (ln(100) - ln(53))/1.00 x 10^-5

= 6.35 x 10^4 s

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