Question

The unit of rate constant of zero order and first order chemical reactions are respectively: (a) \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}, \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) (b) \(\mathrm{s}^{-1}, \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{~s}^{-1}\) (c) \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}, \mathrm{~s}^{-1}\) (d) None of these

Short answer

The unit of rate constant for a zero order reaction is \text{mol L}^{-1} \text{s}^{-1}, and for a first order reaction, it is s^{-1}.

Step-by-step solution

Understanding Rate Law

The rate of a chemical reaction for zero and first order reactions can be determined using the rate law. For a zero order reaction, the rate is given by rate = k[A]^0, and for a first order reaction, the rate is rate = k[A]^1, where [A] is the concentration of reactant A, and k is the rate constant.

Determine Units for Zero Order Reaction

In a zero order reaction, because [A]^0 = 1 and has no units, the units of the rate (generally mol/L*s) will be the same as the units of the rate constant k. Therefore, k for a zero order reaction will have units of mol/L*s.

Determine Units for First Order Reaction

For a first order reaction, the rate is proportional to the concentration of A. Since the rate has units of mol/L*s, and [A] has units of mol/L, the units of the rate constant k must cancel the units of [A]. Thus, the units for k in a first order reaction will be s^{-1}.

Key concepts

Zero Order Reaction

A zero order reaction is one where the rate of reaction is independent of the concentration of the reactant. In such reactions, the rate at which the reactants are consumed and products are formed remains constant over time. This means that even if you increase the concentration of the reactant, the reaction rate does not change.

The rate law expression for a zero order reaction can be written as: \( rate = k[A]^0 \), where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant. Since any number raised to the power of zero is one, the rate is simply equal to the rate constant: \( rate = k \). Hence, for a zero order reaction, the unit of the rate constant \( k \) aligns with the unit of rate, which is typically measured in \( \text{mol L}^{-1} \text{s}^{-1} \). This unit suggests how much reactant is transformed per unit of time.

First Order Reaction

In contrast to zero order reactions, a first order reaction has a rate that is directly proportional to the concentration of one reactant. Essentially, if the concentration of the reactant is doubled, the rate of the reaction doubles as well.

The rate law for a first order reaction is written as: \( rate = k[A]^1 \), implicating the rate is dependent on the concentration of reactant A. In this case, the rate constant \( k \) is often expressed in \( \text{s}^{-1} \) units, since it needs to cancel out the concentration's unit (\( \text{mol L}^{-1} \)) to give the rate's unit (\( \text{mol L}^{-1} \text{s}^{-1} \)). Therefore, the unit of the rate constant indicates the probability of a reaction occurring per second.

Chemical Reaction Rate Law

Understanding the chemical reaction rate law is fundamental to studying kinetics in chemistry. The rate law is an equation that links the rate of a reaction to the concentration of its reactants. It takes on the general form: \( rate = k[A]^{m}[B]^{n}... \), where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to reactants A and B.

The rate law is determined empirically; it cannot be deduced solely from the balanced chemical equation. It gives insight into the mechanism of the reaction by indicating which reactants affect the rate and how sensitive the rate is to changes in reactant concentrations. The determination of the rate law is a key step in solving kinetics problems and understanding how reactions proceed over time.

Reaction Rate Constant

The reaction rate constant, represented by the symbol \( k \), is a crucial parameter in the rate law that provides the relationship between the concentration of reactants and the reaction rate. Its value is determined experimentally and it reflects the intrinsic speed of a given chemical reaction. Importantly, the rate constant is influenced by factors such as temperature, the presence of a catalyst, and the physical state of the reactants.

The units of the rate constant vary depending on the overall order of the reaction. For zero order reactions, as aforementioned, they are \( \text{mol L}^{-1} \text{s}^{-1} \) while for first order reactions, the units are \( \text{s}^{-1} \). Understanding and calculating the correct units for the rate constant is vital in chemistry because it ensures proper use of the rate law in predicting reaction rates and in designing experiments to explore reaction kinetics.