The table below contains experimental temperatures and rate constants for the ga

Question

The table below contains experimental temperatures and rate constants for the gas phase decomposition of dinitrogen monoxide according to the following reaction: 2N2O (g) ---> 2N2 (g) + O2 (g) From a graphical analysis of the data, it was determined that the activation energy for the reaction is 254 kH/mole and the collision frequency factor is 5.56 x 1012

a) using the analysis above, write the linear form of the Arrhenius equation for this reaction.

b) Calculate the rate constant k, for this reaction at 1085 Kelvin.

Temp (K) 1/T (K-1) k (M-1sec-1) ln k 1125 8.89 x 10-4 1.16 x 101 2.45 1053 9.50 x 10-4 1.67 0.51 1001 9.99 x 10-4 3.80 x 10-1 -0.97 838 1.19 x 10-3 1.10 x 10-3 -6.81

Explanation / Answer

a) The Arrhenius equation is of the form

where k = rate constant; A = collision frequency factor; Ea = activation energy for the reaction and T = temperature of the reaction in Kelvin scale.

Take natural logarithm on both sides to get the linear equation

The equation is of the form y = mx + c where

y = ln k; x = 1/T; c = ln A and the slope of the plot is m = -Ea/R.

Plug in values (given Ea = 254 kJ/mol = (254 kJ/mol)*(1000 J/1 kJ) = 254*1000 J/mol = 2.54*105 J/mol and A = 5.56*1012; therefore, ln A = ln (5.56*1012) = 29.3466 and Ea/R = (2.54*105 J/mol)/(8.314 J/mol.K) = 3.055*104K.

Put ln A = 29.3466 and Ea/R = 3.055*104 K- to write the linear equation as

(ans)

b) Let the value of k at 1085 K be k2. Use the linear form of the equation (put k1 = 1.67 M-1 s-1from the table at T1 = 1053 K). Write the two equations as

Subtract (2) from (1) to get

===>

===>

===>

The reaction rate constant is 0.71 M-1s-1 at 1085 K (ans).

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