For the reaction, 2 XO + O2 = 2 X02, some data obtained from measurement of the initial rate of reaction at varying concentrations are given below.
run # [XO] [O2] rate,mol L-l s-1
1 0.010 0.010 2.5
2 0.010 0.020 5.0
3 0.030 0.020 45.0
The rate law is therefore
a. rate = k[XO]2 [O2]
b. rate = k[XO][O2]2
c. rate = k[XO][O2]
d. rate = k[XO]2 [O2] 2
e. rate = k[XO]2 / [O2] 2
And your problem is what? You find two sets of data in which XO is the same but O2 is different. Compare the change in concn with rate and determine order from that. Then pick another set where XO is not the same but O2 is the came (in concn), and go through the same procedure.
For example, XO is the same in runs 1 & 2. O2 changes by a factor of 2. The rate changes by a factor of 2 also; therefore the order is 1 with respect to O2 since 2^1 = 2.
Do XO the same way.
To determine the rate law for the given reaction, we need to analyze the effect of changing concentrations on the rate of reaction.
In run #1, the initial concentrations of both XO and O2 are 0.010 M, and the rate of reaction is reported as 2.5 mol L^(-1) s^(-1).
In run #2, the initial concentrations of XO and O2 are the same as run #1, but the rate doubles, becoming 5.0 mol L^(-1) s^(-1).
In run #3, the initial concentration of XO is tripled (0.030 M), while the initial concentration of O2 is the same as run #2, and the rate increases by a factor of 9, becoming 45.0 mol L^(-1) s^(-1).
Considering the data, we can determine the rate law by comparing the effect of changing concentrations on the rate of reaction. Let's analyze the effect of changing [XO] and [O2]:
Effect of Changing [XO]:
- When [XO] is doubled (run #1 to run #2), the rate doubles.
- When [XO] is tripled (run #2 to run #3), the rate increases by a factor of 9 (3^2).
Effect of Changing [O2]:
- When [O2] is doubled (run #1 to run #2), the rate remains the same.
- When [O2] is kept the same (run #2 to run #3), the rate remains the same.
Based on these observations, we can conclude that the rate of reaction is dependent on the square of [XO] and is independent of [O2]. Therefore, the rate law equation can be written as:
rate = k[XO]^2
Comparing this rate law equation with the given options, we can see that the correct answer is:
a. rate = k[XO]^2 [O2] (Option a)