Question number 5
For this kind of reaction, the rate of reaction will look as follows:
rate = k[A]x[B]Y
In this reaction, k is rate constant, while x and y are the order of reaction of A and B respectively.
There are different kinds of orders of reactions: first order, second order, third order, and so forth. In the case the rate is proportional to the concentration f the reactant, then that is known as first orders. Reactants are said to be in second-order when the rate is proportional to the square of concentration. From this understanding, it is easy to deduce the order of reaction from how the initial rate is changing with the concentration of the reactants.
Looking at the first and second row of the data table, the concentration of A does not change. That means that the change in the rate of reaction only depends on the change of concentration of B. [B] is increased from 0.02 to 0.004, while the rate is increasing from 4×10-3 to 1.6×10-2.
The concentration is increasing by a factor of:
0.04/0.02=2
On the other hand, rate is increasing by a factor of:
0.016/0.004= 4
The reaction cannot be first order because the change of the rate is not proportional to change in [B].
The reaction is second order when increase in rate is proportional to squared increase in concentration
4 = 22
Evaluating the two side, you can see that it is true that this is a second order equation.
To find the order of reaction for A, let look at the first and third row of the data table; this is [B] is not changing.
[A] changes by a factor of:
0.8/0.4=2
Rates increase by:
0.032/0.004=8
Comparing the two:
8=23
This means that the order of reactant A is third order.
The overall order of a reaction is the total orders of reactant taking part in the reaction.
Overall order of reaction = 3+2
=5
No that we know order of each reactant, we can rewrite the rate law:
rate= k[A]3[B]2
Rearrange the equation to find the rate constant:
k=rate/(〖[A]〗^3 〖[B]〗^2 ) this is the rearranged rate equation of the reaction
Using the first row, substitute the concentration and rates in the equation
k=(4×10^(-3 ) mol 〖dm〗^(-3) s^(-1))/(〖0.4〗^(3 ) mol 〖dm〗^(-3)×〖0.02〗^2 mol 〖dm〗^(-3) )
Use a calculator to multiply and divide the substitutes
K=156.25 mol-1 dm-3 s-1
Answers:
order of reaction with respect to A = 3
order of reaction with respect to B = 2
overall order of reaction = 5
rate= k[A]3[B]2
K=156.25 mol-1 dm-3 s-1