Question

What are the units of k in the following expression: rate = k [A][B]?s-1M-1s-1M-2s-1M

Answer 1

Answer : The unit of 'k' of the given expression will be,
`M^(-1)s^(-1)`

Explanation:

Rate of reaction : It is defined as the rate of change in concentration of reactant or product with respect to time.

The given rate expression is,

`Rate=k[A][B]`

From this expression we conclude that the power of concentration of reactant A and B are 1, 1. That means it is a second order reaction.

The formula for determining the unit of 'k' is:

`\text{Unit}=((Concentration)^(1-n))/(Time)`

where, n = order of reaction

The unit of concentration is, M or mole/L

The unit of time is, second or 's'.

When n = 0

The unit of 'k' =
`((M)^(1-0))/(s)=Ms^(-1)`

When n = 1

The unit of 'k' =
`((M)^(1-1))/(s)=s^(-1)`

When n = 2

The unit of 'k' =
`((M)^(1-2))/(s)=M^(-1)s^(-1)`

and so on.....

Therefore, the unit of 'k' of the following expression is,
`M^(-1)s^(-1)`

Answer 2

Rate of the reaction is represented as

Rate=k[A][B]

Rate represents change in product concentration with time that has a unit Ms- Whereas concentration of each reactant can be represented as M . so the expression will become:

Ms-1=k[M][M]

k=M-1 s-1.