Question

Question #14f66

Answer 1

Here's what I got.

Explanation:

Your starting point here will be the rate law for a second-order and a third-order reaction, respectively.

As you know, the rate law for a given reaction establishes a relationship between the rate of the reaction, the rate constant, and the concentrations of the reactants.

• Second-order reaction

For a second-order reaction, the rate law takes the form

`color(blue)("rate" = k * ["A"] * ["B"])" "`, where

`k` - the rate constant

SIDE NOTE Since your goal here is to determine the units of the rate constant, you don't have to worry about having

`"rate" = k * ["A"]^2`

since the units will come out the same regardless if you have one reactant or two reactants.

Now, the rate of a reaction is a measure of the change in concentration of partial pressure of the reactants (or products) per unit of time.

In your case, the units for the rate of a reaction will be

`color(blue)("M"/"s" = "mol"/("L" * "s") = "mol L"^(-1)"s"^(-1)) ->` for concentrations

`color(blue)("kPa"/"s" = "kPa s"^(-1)) ->` for partial pressures

So, rearrange the rate law equation to find the units of `k`

`k = "rate"/(["A"] * ["B"]) = (color(red)(cancel(color(black)("mol"))) color(red)(cancel(color(black)("L"^(-1)))) "s"^(-1))/(color(red)(cancel(color(black)("mol"))) color(red)(cancel(color(black)("L"^(-1)))) * "mol L"^(-1)) = color(green)("L mol"^(-1)"s"^(-1))`

and

`k = "rate"(["A"] * ["B"]) = (color(red)(cancel(color(black)("kPa"))) "s"^(-1))/(color(red)(cancel(color(black)("kPa"))) * "kPa") = color(green)("kPa"^(-1)"s"^(-1))`

• Third-order reaction

For a third-order reaction, the rate law could look like this

`color(blue)("rate" = k * ["A"] * ["B"] * ["C"])`

This time, the units of the rate constant will be

`k = "rate"/(["A"] * ["B"] * ["C"]) = (color(red)(cancel(color(black)("mol"))) color(red)(cancel(color(black)("L"^(-1)))) "s"^(-1))/(color(red)(cancel(color(black)("mol"))) color(red)(cancel(color(black)("L"^(-1)))) * "mol L"^(-1) * "mol L"^(-1))`

`k = color(green)("L"^(2) "mol"^(-2)"s"^(-1))`

and

`k = "rate"/(["A"] * ["B"] * ["C"]) = (color(red)(cancel(color(black)("kPa"))) "s"^(-1))/(color(red)(cancel(color(black)("kPa"))) * "kPa" * "kPa") = color(green)("kPa"^(-2)"s"^(-1))`