Question

An uncatalyzed reaction has a rate of 4.8 x 10-7 s–1 at room temperature (25°C). When an enzyme is added the rate is 3.3 x 104 s–1. If the height of the activation barrier for the uncatalyzed rate is 28.2 kcal/mol, what is the height of the activation barrier for the catalyzed rate? Report your answer in terms of kcal/mol to the nearest tenths. Also, assume the pre-exponential terms for the uncatalyzed and catalyzed reactions are the same.

Answer #1

Arrhenus equation k = A e^{-Ea/RT}

In can be written as

In k1 = In A - Ea1/RT for uncatalysed --- eq (1)

In k2 = In A - Ea2/RT for catalysed ---- eq(2)

Eq(2) - Eq(1) gives,

Ink2 - Ink1 = (-Ea2/RT) + (Ea1/RT)

In(k2/k1) = [Ea1-Ea2]/RT

[Ea1-Ea2] = RT In(k2/k1)

Ea2 = Ea1 - { RT In(k2/k1)}

= 28.2 x 10^{3} - { 1.987
cal/mol/K x 298 K In (3.3 x 10^{4}/ 4.8 x 10^{-7})
}

= 13424 cal/mol

= 13.4 kcal/mol

Ea2 = 13.4 kcal/mol

Therefore,

activation barrier for the catalyzed rate = 13.4 kcal/mol

An uncatalyzed reaction has a rate of 0.0000048 sec–1 at room
temperature (25 °C). When an enzyme is added the rate is 32955
sec–1. If the height of the activation barrier for the uncatalyzed
rate is 27.9 kcal/mol, what is the height of the activation barrier
for the catalyzed rate? Report your answer in terms of kcal/mol to
the nearest tenths. Also, assume the pre-exponential terms for the
uncatalyzed and catalyzed reactions are the same.

If the uncatalyzed reaction proceeds at a rate of 2.6 x 10-5 s-1
and the enzymatic reaction rate is 50 s-1 , what is the difference
in the height of the activation barrier for the enzymatic reaction?
If the average H-bond in the chorismate mutase active site releases
18.5 kJ/mol of energy, how many H-bonds would have to form to
account for the rate enhancement?

A reaction has a rate constant of 1.28×10−4 s−1 at
25 ∘C and 0.226 s−1 at 78 ∘C .
A) Determine the activation barrier for the reaction.
B) What is the value of the rate constant at 16 ∘C
?

If a first order reaction has a rate constant of 4.15 X
10-2 s-1 at a temperature of
24.5oC, what would the value of k be if the reaction
temperature was changed to 52oC given that the
activation energy is 67.8 kJ/mol?

A reaction has a rate constant of 1.22×10−4 s−1 at
26 ∘C and 0.234 s−1 at 75 ∘C .
A) Determine the activation barrier for the reaction.
B)What is the value of the rate constant at 15 ∘C
?

A reaction has a rate constant of 1.21×10^−4 s^(−1) at 26 ∘C and
0.229 s^(−1) at 79 ∘C .
A) Determine the activation barrier for the reaction.
B) What is the value of the rate constant at 16 ∘C ?

The rate constant of a first-order reaction is 0.0032 x
10-4 L/mol *s at 640 K. If the activation energy is
176,406J/mol, calculate the temperature at which is rate constant
is 0.0039 x10 -4 L/mol*s.
Show your work please.

A reaction has a rate constant of 1.26×10−4 s−1 at 28 ∘C and
0.233 s−1 at 79 ∘C .
1.Determine the activation barrier for the reaction. Express
your answer in units of kilojoules per mole.
2. What is the value of the rate constant at 17 ∘C ? Express
your answer in units of inverse seconds.

A reaction has a rate constant of 1.25×10−4 s−1 at 29 ∘C and
0.228 s−1 at 79 ∘C . Part A Determine the activation barrier for
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Part B What is the value of the rate constant at 18 ∘C ? Express
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The rate constant of a first-order reaction is 3.20 × 10−4 s−1
at 350.°C. If the activation energy is 135 kJ/mol, calculate the
temperature at which its rate constant is 9.15 × 10−4 s−1.

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