The kinetics of the following reaction are studied as a function of temperature.

Question

The kinetics of the following reaction are studied as a function of temperature. The reaction is first-order with respect to each reactant and second-order overall. Graph the data shown above (remember temperature must be in Kelvins) and determination the activation energy (Ea) by taking the slope = Ea/R and calculate the Frequency Factor (A) by setting the y-intercept = ln A. Attach the graph to this problem set. Determine the rate constant at 15 degree C by using the Arrhenius equation and solving for k_1 when T_1 = 15 degree C and k_2 and T_2 may be any other temperature and constant taken from the Table. What is the initial rate of the reaction at 15 degree C if [C_2 H_5 Br] = 0.155 M and [OH^-] = 0.250 M?

Explanation / Answer

(a) drawn below is the Arrendius plot of lnK vs 1/T

slope = Ea/R = 1.0677

Ea = 1.0677 x 8.314 = 8.88 J/mol

y-intercept = lnA = -10.336

A = 3.24 x 10^-5 s-1

(b) Rate constant at T1 = 15 oC = 15 + 273 = 303 K

ln(k2/k1) = Ea/R[1/T1 - 1/T2]

ln(2.85 x 10-4/k1) = 8.88/8.314[1/303 - 1/308]

k1 = 2.85 x 10^-4 L/mol-sec

(c) If,

[C2H5Br] = 0.155 M and [OH-] = 0.250 M

Initial rate = 2.85 x 10^-4 x 0.155 x 0.250 = 1.104 x 10^-5 M/s

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