Confused on parts B,C,D and E? Consider the chemical reaction below: SO_2(g) + N
ID: 995715 • Letter: C
Question
Confused on parts B,C,D and E? Consider the chemical reaction below: SO_2(g) + NO_2(g) rightarrow SO_2(g) + NO_2(g) Use the experimental data below to determine the rate law. Show your work. What is the value of the rate constant for this reaction? Show your work and include units. In experiment number 1, how long will it take for the concentration of SO_2 to decrease by 50% of its initial concentration? Show your work. The following mechanism for this reaction was proposed: Step 1: SO_2(g) + SO_2(g) rightarrow SO(g) + SO_3(g) SLOW Step 2: SO(g) + NO_3(g) rightarrow SO_2(g) + NO_2(g) FAST What is the rate law for the overall reaction according to this mechanism? Is the mechanism proposed in part d) plausible for this reaction? Explain in detail.Explanation / Answer
Let the rate law r= K[SO2]a[ NO2]b, where a and b are order of the reaction with respect to SO2 and NO2 respectively.
From experiment-1
3.3*10-4= K[ 0.042]a [0.17]b (1)
From experiment-2
5.3*10-3 = K[0.17]a [0.17]b (2)
Eq.2/Eq.1 gives
5.3*10-3/3.3*10-4 = (0.17/0.042)a
4a =16 and a=2
From experiment-3
3.3*10-4 = K[0.042]a [0.46]b (3)
Eq.3/Eq.1 gives
1= (0.46/0.17)b , b=0
So the rate becomes r= K[SO2]2 (4)
from experiment-1, 3.3*10-4 = K[0.042]2, K= 0.1871/M.sec
now the rate r = -d[SO2]/dt= 0.1871*[SO2]2
-d[SO2]/dt= 0.1871[SO2]2
this on integration gives
1/[SO2] = 1/[SO2]0 +0.1871t
[SO2] is concentration of SO2 any time t and [SO2]0 is initial concentration
Given [SO2]=0.5[SO2]0 ( The concentration will have to drop to 50% of its initial concentration)
Therefore
1/0.5[SO2]0 =1/[SO2]0 +0.1871t
1/[SO2]0= 0.1871t
1/0.042= 0.1871t
And time t= 127.2556 sec
The mechanism proposed is
Step 1: SO2(g) +SO2(g)-----à SO(g) +SO3(g) slow
Step 2: SO(g) +NO2(g) ----à SO2(g) + NO2(g) Fast
The overall rate -d[SO2]/dt= K1[SO2]2- K2[SO] [NO2]
K1 ans K2 are rate constant.
In a series of steps, the rate determining step will be the slowest step and hence the first step is the rate determining step and accordingly
-d[SO2]/dt= K1[SO2]2
hence the given mechanism is plausible for the reaction.