Question

Define elementary reaction. For a reaction ${\text{A}} \to $ product, rate is $1.25 \times {10^{ - 2}}M/s$ when $[A] = 0.45M$. Determine the rate constant if the reaction is:
A.First order in $A$
B.Second order in $A$

Answer 1

Hint: Rate of reaction: The rate of a reaction is the speed at which a chemical reaction happens.
Order of the reaction: It is defined as the power dependence of the rate of reaction on the concentration of the reactants.

Complete step by step solution:
Let us first define elementary reaction.
Elementary reaction: It is defined as a chemical reaction in which one or more chemical species react directly with each other to form the product in a single step.
Now we will study the rate of reaction and order of reaction.
Order of the reaction: It is defined as the power dependence of the rate of reaction on the concentration of the reactants. For example: if order of reaction is one then rate of reaction depends linearly on the concentration of one reactant. The unit of first order of reaction is ${s^{ - 1}}$. The unit of second order of reaction is $1/Ms$.
Rate of reaction: The rate of a reaction is the speed at which a chemical reaction happens. Rate of reaction is directly proportional to the product of all reactants in the reaction raised to the power of their order. Here the proportionality constant is known as rate constant and is represented by $k$.
For example: if reaction is of first order then rate of reaction will be as $r = k[A]$, where $r$ is rate of reaction, $[A]$ is concentration of the reactant and $k$ is rate constant of the reaction.
Here in the question, for a reaction ${\text{A}} \to $ product, the rate is $1.25 \times {10^{ - 2}}M/s$ when $[A] = 0.45M$.
Now if reaction is of first order then rate of reaction will be as:
$r = k[A]$ and in the question $r = 1.25 \times {10^{ - 2}}$ and $[A] = 0.45M$, so
$
  k = \dfrac{r}{{[A]}} \\
\Rightarrow k = \dfrac{{1.25 \times {{10}^{ - 2}}}}{{0.45}} \\
\Rightarrow k = 2.77 \times {10^{ - 2}}{s^{ - 1}} \\
 $
And if reaction is of second order then rate of reaction will be as:
$r = k{[A]^2}$ and in the question $r = 1.25 \times {10^{ - 2}}$ and $[A] = 0.45M$, so
$
  k = \dfrac{r}{{{{[A]}^2}}} \\
\Rightarrow k = \dfrac{{1.25 \times {{10}^{ - 2}}}}{{{{(0.45)}^2}}} \\
\Rightarrow k = 6.172 \times {10^{ - 2}}Lmo{l^{ - 1}}{s^{ - 1}} \\
 $.
Hence when reaction is first order then rate constant is $2.77 \times {10^{ - 2}}{s^{ - 1}}$ and when reaction is second order type then rate constant is $6.172 \times {10^{ - 2}}Lmo{l^{ - 1}}{s^{ - 1}}$.

Note: Half-time: It is defined as the time duration in which the concentration of a reactant drops to one-half of its initial concentration. It is represented by ${t_{\dfrac{1}{2}}}$.
Half-time of a reaction is inversely proportional to the concentration of the reactant raised to the power of its order of reaction minus one.