Question

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.

Need Work shown

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, E_a = (1.609 *8.314)/(0.002333)

Or, E_a = 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.