Question

For the reaction 2 NO + O2 + M -> NO2 + M, the rate constant...

  1. For the reaction 2 NO + O2 + M -> NO2 + M, the rate constant at 300 K is

k(300 K) = 6*109 1/(M2 s) and the rate constant at 1000 K is

k(1000 K) = 3*1010 1/(M2 s). Calculate the Arrhenius parameters and the order of the reaction.

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Answer #1

K (300K) = 6*109 M-2 s-1

K (1000 K) = 3*1010 M-2 s-1.

From logarithm expression of Arrhenius equation

ln \frac{K_2}{K_1} = -  \frac{E_a}{R} ( \frac{1}{T_2} - \frac{1}{T_1})

Or,

ln ( 3*1010/6*109) = - \frac{E_a}{8.314} ( \frac{1}{1000} - \frac{1}{300})

Or, 1.609 = - \frac{E_a}{8.314} * ( -0.002333)

Or, Ea = (1.609 *8.314)/(0.002333)

Or, Ea = 5733 J/mole .

Again.

K = A * e- Ea/RT

At T = 300 K, K = 6*109

So, 6*109 = A * e-{5733/(8.314*300)}

Or,6*109 = A * 0.1004

Or, A = ( 6*109/0.1004) = 59.76*109 = 5.976*1010

.

Rate = K * [A]n

Or, K = Rate/[A]n

[A] is concentration of reactant.

Hence, General unit of rate constant (K)

= (M)1-n s-1.

Where , n = order of the reaction.

In the given problem

Unit is M-2s-1

So, 1-n = -2

Or, n = 1+2= 3.

Therefore , order of the reaction is 3.

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