here are several factors that affect the rate of a reaction. These factors inclu

Question

here 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.

i) A certain reaction has an activation energy of 64.0 kJ/mol and a frequency factor of A1 = 8.20×1012 M1s1 . What is the rate constant, k, of this reaction at 22.0 C ?

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

Figure 1:

ii)

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, x is 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

Solution :-

Given data

Ea = 64.0 kJ/mol = 64000 J/ mol

Temperature = 22.0 C +273 = 295 K

Frequency factor = 8.20*1012 M-1s-1

Calculate the rate constant K= ?

Formula

K = Ae-Ea/RT

Lets put the values in the formula

K = 8.20*1012 M-1s-1 * e(-64000 J per mol *K / 8.314 J per K*mol * 295 K )

K = 38.12

Part 2

Given data

K1 = 109 M-1 s-1 and T1 = 352 K

K2 = 185 M-1s-1 and T2 = 426 K

Now lets calculate the activation energy using the Arrhenius equation

ln[[K2]/[k1]] = Ea/R [(1/T1)- (1/T2)]

Lets put the values in the formula and calculate the activation energy

ln[[K2]/[k1]] = Ea/R [(1/T1)- (1/T2)]

ln[[185]/[109]] = Ea /8.314 J per mol*K [(1/352)-(1/426)]

0.529 = Ea/8.314 J per mol*K * 0.000493

Ea = (0.529*8.314 J/mol*K) / 0.000493

Ea = 8912 J

Lets convert Joule to kJ

8912 J * 1 kJ/ 1000 J = 8.912 kJ/mol

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