There are several factors that affect the rate of a reaction. These factors incl

Question

There are several factors that affect the rate of a reaction. These factors include temperature, activation energy, steric factors (orientation), and also collision frequency, which changes with concentration and phase. All the factors that affect reaction rate can be summarized in an equation called the Arrhenius equation:

k=AeEa/RT

where k is the rate constant, A is the frequency factor, Ea is the activation energy, R=8.314 J/(molK) is the universal gas constant, and T is the absolute temperature.

Part A

A certain reaction has an activation energy of 67.0 kJ/mol and a frequency factor of A1 = 6.30×1012 M1s1 . What is the rate constant, k, of this reaction at 23.0 C ?

Express your answer with the appropriate units. Indicate the multiplication of units explicitly either with a multiplication dot (asterisk) or a dash.

The linear form of the Arrhenius equation

The Arrhenius equation can be rearranged to a form that resembles the equation for a straight line:

lnky==(EaR)m(1T)x++lnAb

where y is lnk, m is the slope or EaR, xis 1T, and b is the y-intercept or lnA. The linearity of this equation is illustrated graphically in the image.(Figure 1)

Part B

An unknown reaction was observed, and the following data were collected:

Determine the activation energy for this reaction.

Express your answer with the appropriate units.

Explanation / Answer

Part 1: K = Ae-E/RT

A = 6.30e12
E=67000 J
R = 8.3145
T = 296 K

K = (6.30e12)e-67000/(8.3145 x 296)
K = 9.47

Part 2: ln(k1/k2) = (E/R) x (1/T2 - 1/T1)
k1 = 109
k2 = 185
T2 = 426
T1 = 352

ln(109/185) = (E/8.3145) x (1/426 - 1/352)
E = 8912.9 J = 8.9129 KJ

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