2 N 2 O 5 (g) ---> 4 NO 2 (g) + O 2 (g) rate= k[N2O5] p For different Initial ra

Question

2 N2O5(g) ---> 4 NO2(g) + O2(g)

rate= k[N2O5]p

For different Initial rates:

[N2O5] Initial Rate
0.093 M 4.84 x 10^4 M s-1
0.186 M 9.67 x 10^4 M s-1
0.279 M 1.45 x 10^3 M s-1

So it implies
4.84 x 10^4 = k[0.093]p
9.67 x 10^4 = k[0.186]p
1.45 x 10^3 = k[0.279]p

"By dividing we get p value
1.997 = 2p => p = 1
=> k = 5.2 x 10^-3 [N2O5]"

^ Where I made it bold, I don't understand the math involved when the chegg expert said "By dividing we get p value, 1.997 = 2p => p = 1, => k = 5.2 x 10^-3 [N2O5]"

----

how did he figure out k value? p value?

Explanation / Answer

2 N2O5(g) ---> 4 NO2(g) + O2(g)

rate = k[N2O5]p

Plug the values in the given tabular form to the above rate law we get,

1st values    4.84 x 104 = k[0.093]p              ----------(1)

1st values    9.67 x104 = k[0.186]p              ----------(2)

(2) / (1) gives 2p = 2

                      p = 1

Plug the value of p in (1) we have 4.84 x 104 = k[0.093]1

                                                              k = 520.4x103

Therefore the value of p = 1 & the value of k = 520.4x103

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