Question

Determine the rate law and the value of k for the following reaction using the data provided.

2 NO(g) + O₂(g) ? 2 NO₂(g)

[NO]i (M)	[O2]i (M)	Initial Rate (M-1s-1)
0.030	0.0055	8.55 x 10-3
0.030	0.0110	1.71 x 10-2
0.060	0.0055	3.42 x 10-2

	Rate = 57 M-1s-1[NO][O2]
	Rate = 3.1

Answer 1

The reaction is 2NO(g) + O₂(g) 2NO₂(g)

Let the rate law be r = k [NO] ^m [O₂] ⁿ    

From the table the rate law for the three readings will be as follows:

reading (1)    ------> 8.55 x 10^-3 = k (0.030 ) ^m (0.0055)ⁿ                          ------------------------- (1)

reading (2)    ------> 1.71 x 10^-2 = k (0.030 ) ^m (0.0110)ⁿ                          ------------------------- (2)

reading (3)    ------> 3.42 x 10^-2 = k (0.060 ) ^m (0.0055)ⁿ                          ------------------------- (3)

Eqn (3) / Eqn (1) becomes

                                      

                                              m = 2

Eqn (2) / Eqn (1) becomes

                                      

                                                  n = 1

So rate law becomes r = k [NO] ² [O₂] ¹   

                              r = k [NO] ² [O₂]

Substitute the values of r, [A] & [B] from reading (1) we get

          8.55 x 10^-3 = k (0.030 )² (0.0055)

                       k = 1.7 x 10³ M^-2s^-1