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. rate of a chemical reaction: \(M/s\) b. rate constant for a zero-order rate law: \(M/s\) c. rate constant for a first-order rate law: \(s^{-1}\) d. rate constant for a second-order rate law: \(M^{-1}s^{-1}\) e. rate constant for a third-order rate law: \(M^{-2}s^{-1}\)

Step-by-step solution

Identifying the required units for the rate of a chemical reaction

The rate of a chemical reaction is given by the change in concentration of a reactant or product per unit time. Since the concentration is expressed in moles/L (M) and time in seconds (s), the units for the rate of a chemical reaction will simply be the concentration units (moles/L) divided by the time units (seconds), resulting in M/s.

Identifying the required units for a zero-order rate law

A zero-order reaction has a rate law in the form of: Rate = k[A]^0, where Rate is the rate of the reaction, k is the rate constant, and [A] is the concentration of a reactant. Since [A]^0 is equal to 1, the rate law simplifies to Rate = k. Therefore, the units for the rate constant (k) in a zero-order rate law will be the same as the units for the rate of a chemical reaction, which is M/s.

Identifying the required units for a first-order rate law

A first-order reaction has a rate law in the form of: Rate = k[A], where Rate is the rate of the reaction, k is the rate constant, and [A] is the concentration of a reactant. To determine the units for k, we can rearrange the rate law: k = Rate / [A]. Since Rate has the units M/s and [A] has the units M, the units for k in a first-order rate law will be (M/s)/(M), which simplifies to 1/s or s^{-1}.

Identifying the required units for a second-order rate law

A second-order reaction has a rate law in the form of: Rate = k[A]^2, where Rate is the rate of the reaction, k is the rate constant, and [A] is the concentration of a reactant. To determine the units for k, we can rearrange the rate law: k = Rate / ([A]^2). Since Rate has the units M/s and [A]^2 has the units M^2, the units for k in a second-order rate law will be (M/s)/(M^2), which simplifies to L/mol*s or M^{-1}s^{-1}.

Identifying the required units for a third-order rate law

A third-order reaction has a rate law in the form of: Rate = k[A]^3, where Rate is the rate of the reaction, k is the rate constant, and [A] is the concentration of a reactant. To determine the units for k, we can rearrange the rate law: k = Rate / ([A]^3). Since Rate has the units M/s and [A]^3 has the units M^3, the units for k in a third-order rate law will be (M/s)/(M^3), which simplifies to L^2/mol^2*s or M^{-2}s^{-1}. In conclusion, the units for each parameter are as follows: a. rate of a chemical reaction: M/s b. rate constant for a zero-order rate law: M/s c. rate constant for a first-order rate law: s^{-1} d. rate constant for a second-order rate law: M^{-1}s^{-1} e. rate constant for a third-order rate law: M^{-2}s^{-1}