Question

For the reaction $A \to B$ the rate law is, ${\text{rate = k}}\left[ {\text{A}} \right]$ . Which of the following statements is incorrect?
A The reaction follows first order kinetics
B The t, of reaction depends upon initial concentration of reactants
C k is constant for the reaction at a constant temperature
D The rate law provides a simple way of predicting the concentration of reactants and
products at any time after the start of the reaction

Answer 1

For a first order reaction, the rate of the reaction is directly proportional to the reactant concentration. The half life period represents the time required for the ${\text{50\% }}$ change in the reactant concentration.

Complete Step by step answer: Consider the reaction $A \to B$
Here, ${\text{A}}$ is the reactant and ${\text{B}}$ is the product.
The rate of the reaction is given by the expression ${\text{rate = }} - \dfrac{{d\left[ {\text{A}} \right]}}{{dt}}$ . It represents the rate of consumption of the reactant ${\text{A}}$ in the unit time.
The rate law of the reaction $A \to B$ is ${\text{rate = k}}\left[ {\text{A}} \right]$ .
Here, $\left[ {\text{A}} \right]$ represents the concentration of the reactant ${\text{A}}$ and ${\text{k}}$ represents the specific reaction rate or the rate constant.
From the rate law expression, you can conclude that the rate of the reaction is directly proportional to the reactant concentration.
${\text{rate }} \propto {\text{ }}\left[ {\text{A}} \right]$
From the above proportionality, you conclude that the reaction follows first order kinetics.
So, the statement (A) is correct.
For the first order reaction the half-life period ${t_{1/2}}$ , is independent of the initial concentration of reactants.
${t_{1/2}} = \dfrac{{0.693}}{k}$
So, the statement (B) is incorrect.
The specific reaction rate or the rate constant $k$ is constant for the reaction at a constant temperature. The rate constant changes either with temperature or with presence of a catalyst.
So, the statement (C) is correct.
The rate law provides a simple way of predicting the concentration of reactants and products at any time after the start of the reaction
$\left[ {\text{A}} \right] = {\left[ {\text{A}} \right]_0}{e^{ - kt}}$
By using the above expression, you can calculate the reactant concentration at any particular instant of the reaction, since you know the initial concentration and the rate constant. From the reactant concentration, you can calculate the change in reactant concentration, the change in product concentration and the reaction stoichiometry.
So, the statement (D) is correct.

Hence, the option (B) represents an incorrect statement.

Note: If you know the half-life period for the first order reaction, you can calculate the rate constant. For this, you can plot a graph of reactant concentrations and different time instances. Then from the graph, you can determine the time needed for the concentration to reduce to one half.