The units of a rate constant for zero, first, and second order reactions are given in the textbook. If the time units are minutes, what would you expect the units to be for a third order reaction?
1) 1/min^3
2) mol^2/L^2-min
3) L/mol-min^2
4) L^2/mol^2-min
5) L^2/mol^2-min^2
I think that the answer is L/mol-min^2. Is this correct?
I don't think so.
rate = k(A)^3 so
k = rate/(A)^3
Plug in mol/L*min for rate and plug in moles^3/L^3 for A^3 and go through the algebra.
To determine the units for a third-order reaction, we can use the rate equation for a third-order reaction:
Rate = k[A]^3
In this equation, [A] represents the concentration of the reactant A, and k is the rate constant.
Now, let's analyze the units for each term in the rate equation.
The unit for Rate will depend on the units of the concentrations of reactant A divided by the time. Since the time units are minutes, the unit for Rate will be mol/L-min.
The unit for [A] is mol/L since it represents concentration. Taking [A] to the power of 3 gives us (mol/L)^3.
To find the units for the rate constant k, we need to cancel out the units of [A] and time (min), so that the overall units of the rate equation are mol/L-min.
By rearranging the equation, we get:
k = Rate / [A]^3
Substituting the units, we get:
k = (mol/L-min) / (mol/L)^3
Canceling out the moles and volume units, we have:
k = 1 / (L^2-min)
Therefore, the units for the rate constant of a third-order reaction are L^-2-min^-1, which is option 3) L/mol-min^2.
So your answer is correct!