Question

A reaction R --> P has the rate constant, k1 = 2.52 x 10-3 s-1 at 80.0 °C, and activation energy, Ea = 54.6 kJ.mol-1. At 110 °C, what is new rate constant, k2?

4.48 x 10^8

1.33 x10^-3

1.33 x 10^8

1.08 x 10^-1

1.08 x 10^-2

Answer #1

this is the temperature dependent equation for rate constant

k = ko e^(-Ea/RT)

Given

Ea = 54.6 KJ/mol = 54600 J/mol

T1 = 80 C = 80 + 273 = 353 K

k1 = 2.52 * 10^{-3} s^{-1}

T2 = 110 C = 273 + 110 = 383 K

k2 = ?

R = 8.314 J/mol.K

k1 / k2 = ko e^(-Ea/RT1) / ko e^(-Ea/RT2)

k1 / k2 = e^(-Ea/RT1) / e^(-Ea/RT2) = e^(-Ea/RT1+Ea/RT2)

sub known values

2.52 * 10^{-3} s^{-1} / k2 = e^( - (54600 /
(8.314 J/mol.K *353 K) ) + (54600 / (8.314 J/mol.K *383 K) ) )

2.52 * 10^{-3} s^{-1} / k2 = e^(-1.457)

2.52 * 10^{-3} s^{-1} / k2 = 0.2329

k2 = 1.08 * 10^{-2} s^{-1} Answer

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is a constant called the frequency factor, and Ea
is the activation energy for the reaction.
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a constant called the frequency factor, and Ea is
the activation energy for the reaction.
However, a more practical form of this equation is
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constant k and the temperature T in kelvins and
is typically written as
k=Ae−Ea/RT
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