Question

What are the units of the rate constant for a thirdorder reaction?

Short answer

The units of the rate constant for a thirdorder reaction are \(M^{-2}T^{-1}\).

Step-by-step solution

Understanding reaction rates

Reaction rate can also be expressed in terms of the decrease in the concentration of one of the reactants or the increase in the concentration of one of the products during a unit of time.

Expressing reaction rates in terms of reactant concentration and rate constant

The rate of reaction can be expressed as the change in molar concentration of the reactant in a unit time and mathematically, Rate = \(-\frac{d[\text{{Reactant}}]}{dt}\) where \([\text{{Reactant}}]\) is the molar concentration of the reactant. For a third order reaction, Rate = \(k[\text{{Reactant}}]^3\) where k is the rate constant.

Determining units of the third order rate constant

From the equation in Step 2, we infer that the dimensions of the rate constant 'k' can be determined by using the dimensional analysis. The dimension of 'Rate' is \([M T^{-1}]\), 'M' being the molar concentration and 'T' being the time. So, the unit of 'k' for third order reactions should be \(M^{-2}T^{-1}\)