In: Chemistry
Ozone gas, O3 decomposes into O2 in presence of NO and gaseous O atoms The following data was obtained Determine the experimental rate law for the reaction given the following data and the value for the rate constant
O 3= 2.3 x 10^-4 atm NO = 1.6 x 10^-4 O = 1.5 x 10^-4 rate1 = 2.6 x 10-3
O3 = 2.3 x 10^-4 NO = .8 x 10^-4 O = 1.5 x 10^-6 rate 2 = 1.3 x 10^-3
O 3 = 4.6 x a0^-4 NO = 1.6 x 10^-4 O = 1.5 x 10^-6 rate 3 = 5.2 x 10^-3
O3 = 4.6 x 10^-4 NO = 1.6 x 10^-4 O = 3.0 x 10^-6 rate 4 = 5.2 x 10^-3
Let the rate law of the reaction be
rate = K [03]^a [N0]^b [0]^c
here
k is rate constant
a is order with respect to 03
b is order with respect to NO
c is w.r.t 0
now
conisder condition 1
rate1 = K[03]^a [N0]^b [0]^c
2.6 x 10-3 = K [2.3 x 10-4]^a [1.6 x 10-4]^b [1.5 x 10-4]^c
now
consider condition 2
rate2 = K[03]^a [N0]^b [0]^c
1.3 x 10-3 = K [2.3 x 10-4]^a [0.8 x 10-4]^b [1.5 x 10-4]^c
now
conisder condition 3
rate3 = K[03]^a [N0]^b [0]^c
5.2 x 10-3 = K [4.6 x 10-4]^a [1.6 x 10-4]^b [1.5 x 10-4]^c
now
conisder condition 4
rate4 = K[03]^a [N0]^b [0]^c
5.2 x 10-3 = K [4.6 x 10-4]^a [1.6 x 10-4]^b [3 x 10-4]^c
from the above obtained equations
now divide condition 1 by condition 3
2.6 x 10-3 / 5.2 x 10-3 = K [2.3 x 10-4]^a [1.6 x 10-4]^b
[1.5 x 10-4]^c / K [4.6 x 10-4]^a [1.6 x 10-4]^b [1.5 x
10-4]^c
on solving we get
a =1
now divide condition1/ condition 2
we get
2.6 x 10-3 / 1.3 x 10-3 = K [2.3 x 10-4]^a [1.6 x 10-4]^b [1.5 x 10-4]^c / 1.3 x 10-3 = K [2.3 x 10-4]^a [0.8 x 10-4]^b [1.5 x 10-4]^c
solving we get
b=1
now divide condition 3 / condition 4
5.2 x 10-3 / 5.2 x 10-3 = K [4.6 x 10-4]^a [1.6 x 10-4]^b [1.5 x 10-4]^c / 5.2 x 10-3 = K [4.6 x 10-4]^a [1.6 x 10-4]^b [3 x 10-4]^c
on solving we get
c=0
so the rate law is given by
rate = K [03]^1 [N0]^1 [0]^0
so the rate law is
rate = K [03] [N0]
now
consider condition 1
2.6 x 10-3 = K [ 2.3 x 10-4 ] [1.6 x 10-4 ]
K = 7.065 x 10^4
so
the rate constant = 7.065 x 10^4