Question

NO reacts with Br2 in the gas phase according to the following chemical equation: 2NO(g) +Br2(g)2NOBr(g) It is observed that, when the concentration of Br2 is reduced to 1/3 of its initial value, the rate of the reaction is also reduced to 1/3 of its initial value. When the concentration of NO is multiplied by 3.69, the rate of the reaction increases by a factor of 13.6. (a) Write the rate expression for this reaction, and give the units of the rate constant k, assuming concentration is expressed as mol L-1 and time is in second

Answer 1

a)
`rate=r=k[NO]^(2) [Br_(2)]^(1)`

b)
`k=(1)/(s*M^(2))`

Step-by-step explanation:

First of all you need to indicate the reaction order of each reactant (
`NO` and
`Br_(2)`):

1.
`Br_(2)`

Note that if
`Br_(2)` concentration (
`[Br_(2) ]`) is reduced to 1/3 of its initial value, the rate of the reaction is also reduced to 1/3 of its initial value, it means:

`[Br_(2) ]=1/3` then
`r=1/3`

As the change in the rate of the reaction is equal to the change of the initial concentration of
`Br_(2)`, you could concluded that the reaction is first order with respect to
`Br_(2)`

2.
`NO`

Now, note that if
`NO` concentration (
`[NO]`) is multiplied by 3.69, the rate of the reaction increases by a factor of 13.6. In this case, to know the ratio could be advisable divide the rate of the reaction (13.6) over the factor whereby was multiplied the concentration (3.69), as follows:

`(13.6)/(3.69)=3.69`

As the result is the same factor 3.69 you could concluded that the change of the rate of reaction is proportional to the square of the concentration of A:

`r=[NO]^(2) =3.68^(2) =13.6`

It means that the reaction is second order with respect to
`NO`

3. Rate Expression

Remember that the rate expression of the reactions depend on the concentration of each reactant and its order. In this case we have 2 reactants:
`NO` and
`Br_(2)`, then we have a rate law depending of 2 concentrations, as follows:

`rate=r=k[NO]^(2) [Br_(2)]^(1)`

Note that the expression is the result of the concentration of each reactant raised to its reaction order (previously determined)

Note: I hope that you do not mix up the use of the rates of reaction of each reactant, that is experimentally determined, with the stoichiometric coefficient, are different.

4. Rate constant units (k)

Assuming concentration is expressed as
`(mol)/(L)=M` and time is in second, to find the units of k we need to solve an equation with units and with supporting of the rate equation previously obtained, as follows:

`r=k[NO]^(2) [Br_(2)]^(1)`

Where:

`[r]=[(M)/(s)]`

`[[NO]]=[M]`

`[ [Br_(2)]]=[M]`

Then:

`(M)/(s)=kM^(2) M^(1)`

`(M)/(s)=kM^(3)`

`(M)/(s*M^(3))=k`

The units of the rate constant k are:

`k=(1)/(s*M^(2))`