Question

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? a. rate of a chemical reaction b. rate constant for a zero-order rate law c. rate constant for a first-order rate law d. rate constant for a second-order rate law e. rate constant for a third-order rate law

Short answer

a. The units for the rate of a chemical reaction are mol/Ls. b. The units for the rate constant of a zero-order rate law are mol/Ls. c. The units for the rate constant of a first-order rate law are s⁻¹. d. The units for the rate constant of a second-order rate law are L/mol·s. e. The units for the rate constant of a third-order rate law are L²/mol²·s.

Step-by-step solution

a. Units for the rate of a chemical reaction

The rate of a chemical reaction (represented as 'r') is usually expressed as the change in concentration (∆[A]) of the reacting species A over the change in time (∆t). Thus: \(r = \frac{-\Delta{[A]}}{\Delta{t}}\) The units for the change in concentration are moles per liter (mol/L) and time in seconds (s). Therefore, the unit for the rate of a chemical reaction will be in mol/Ls.

b. Units for the rate constant of a zero-order rate law

In a zero-order rate law, the rate of the reaction (r) is directly proportional to the concentration of the reactant [A]^0: \(r = k [A]^0\) Since [A]^0 = 1, the rate constant k has the same units as the rate of reaction. Thus, the units for a zero-order rate constant k are mol/Ls.

c. Units for the rate constant of a first-order rate law

In a first-order rate law, the rate of the reaction (r) is directly proportional to the concentration of the reactant [A]: \(r = k [A]\) To find the units of the rate constant k, we rearrange the equation: \(k = \frac{r}{[A]}\) Since the units of the rate are mol/Ls and the units of the concentration are mol/L, the units for the rate constant k in a first-order rate law are s⁻¹.

d. Units for the rate constant of a second-order rate law

In a second-order rate law, the rate of the reaction (r) is directly proportional to the square of the concentration of the reactant [A]^2: \(r = k [A]^2\) To find the units of the rate constant k, we rearrange the equation: \(k = \frac{r}{[A]^2}\) Since the units of the rate are mol/Ls and the units of the concentration squared are (mol/L)^2, the units for the rate constant k in a second-order rate law are L/mol·s.

e. Units for the rate constant of a third-order rate law

In a third-order rate law, the rate of the reaction (r) is directly proportional to the cube of the concentration of the reactant [A]^3: \(r = k [A]^3\) To find the units of the rate constant k, we rearrange the equation: \(k = \frac{r}{[A]^3}\) Since the units of the rate are mol/Ls and the units of the concentration cubed are (mol/L)^3, the units for the rate constant k in a third-order rate law are L²/mol²·s.