Question

"Compounds A and B react to give a single product, C. Write the rate law for each of the following cases and determine the units of the rate constant by using the units M for concentration and s for time.

a. The reaction is first order in A and second order in B.
b. The reaction is first order in A and second order overall.
c. The reaction is independent of the concentration of A and second order overall.
d. The reaction is second order in both A and B."

Answer 1

The rate laws for each case involve different orders of reactions with respect to reactants A and B, leading to different units for the rate constant k, which are determined based on the orders with respect to each reactant and the overall reaction order.

Step-by-step explanation:

To write the rate law for a reaction where compounds A and B react to give a single product C, you must consider the reaction order with respect to each reactant. The rate law shows the relationship between the concentration of reactants and the rate of the reaction.

Case a.

The reaction is first order in A and second order in B. The rate law is written as:

rate = k [A]1[B]2

For the units of k, using M for concentration and s for time, we get:

Units of k = M-1s-1

Case b.

The reaction is first order in A and second order overall. Since the overall order is 2 and one of them is due to A, the second order must be due to the reactant B. The rate law is:

rate = k [A]1[B]1

Units of k would therefore be M-1s-1.

Case c.

The reaction is independent of the concentration of A and second order overall. The rate law only involves B:

rate = k [B]2

Units of k = M-1s-1

Case d.

The reaction is second order in both A and B. The rate law is:

rate = k [A]2[B]2

For this rate law, units of k are M-3s-1.

Answer 2

Part a: Units of k is
`M^(-2)s^(-1)` where reaction is first order in A and second order in B

Part b: Units of k is
`M^(-1)s^(-1)` where reaction is first order in A and second order overall.

Part c: Units of k is
`M^(-1)s^(-1)` where reaction is independent of the concentration of A and second order overall.

Part d: Units of k is
`M^(-3)s^(-1)` where reaction reaction is second order in both A and B.

Step-by-step explanation:

As the reaction is given as

`A+B \rightarrow C`

where as the rate is given as

`r=k[A]^x[B]^y`

where x is the order wrt A and y is the order wrt B.

Part a:

x=1 and y=2 now the reaction rate equation is given as

`r=k[A]^1[B]^2`

Now the units are given as

`r=k[A]^1[B]^2\\M/s =k[M]^1[M]^2\\M/s =k[M]^(1+2)\\M/s =k[M]^(3)\\M^(1-3)/s =k\\M^(-2)s^(-1) =k`

The units of k is
`M^(-2)s^(-1)`

Part b:

x=1 and o=2

x+y=o

1+y=2

y=2-1

y=1

Now the reaction rate equation is given as

`r=k[A]^1[B]^1`

Now the units are given as

`r=k[A]^1[B]^1\\M/s =k[M]^1[M]^1\\M/s =k[M]^(1+1)\\M/s =k[M]^(2)\\M^(1-2)/s =k\\M^(-1)s^(-1) =k`

The units of k is
`M^(-1)s^(-1)`

Part c:

x=0 and o=2

x+y=o

0+y=2

y=2

y=2

Now the reaction rate equation is given as

`r=k[A]^0[B]^2`

Now the units are given as

`r=k[B]^2\\M/s =k[M]^2\\M/s =k[M]^(2)\\M^(1-2)/s =k\\M^(-1)s^(-1) =k`

The units of k is
`M^(-1)s^(-1)`

Part d:

x=2 and y=2

Now the reaction rate equation is given as

`r=k[A]^2[B]^2`

Now the units are given as

`r=k[A]^2[B]^2\\M/s =k[M]^2[M]^2\\M/s =k[M]^(2+2)\\M/s =k[M]^(4)\\M^(1-4)/s =k\\M^(-3)s^(-1) =k`

The units of k is
`M^(-3)s^(-1)`