Answer:
rate = k [A] [B] ³
Explanation:
Set up a table with the data given in the question to study the dependence of the reaction rate on the concentrations of reactants.
[A] [B] [C] Rate Experiment #
0.4 1.2 0.7 2.32 x 10⁻³ (1)
1.3 1.2 0.9 7.54 x 10⁻³ (2)
0.4 4.1 0.8 9.25 x 10⁻² (3)
1.3 1.2 0.2 7.54 x 10⁻³ (4)
The rate law will have the form : rate = k [A] ^x [B] ^y [C] ^z
Comparing experiments (2) and (4) we have to conclude that the rate is zero order with respect to [C] since keeping [A] and [B] the same and varying [C] did not change the rate (i.e ,no dependence on [C]) .
Now we know the rate law has the form rate = k [A] ^x [B] ^y
Comparing (1) and (4) we keep [B] constant and increase [A] by a factor of 1.3/.4 = 3.25 and the rate increased by a factor of 0.00754 / 0.00232 =3.25, so we can conclude that the rate law is first order with respect to [A]
Finally, comparing (1) and (3) while keeping [A] constant increasing [B] by a factor of 4.1/1.2 = 3.416, the rate increased by a factor of 0.0925/0.00232 = 40, it is not entirely clear the dependence with respect to [B] .
In this case we can always set up the following equation which is obtained by dividing equation (3) by (1)
(4.1 / 1.2)^x = 0.0925/0.00232
taking natural log to both sides of the equation
x ln 3.4167 = ln 40
x = 3.69/1.23 = 3
So the dependence with respect to [C] is three.
The rate law is :
rate = k [A] [B] ³
