Question

In a zero-order reaction:-
A. The rate constant has the unit ${\text{mol }}{{\text{L}}^{{\text{ - 1}}}}{{\text{s}}^{{\text{ - 1}}}}$
B. The rate is independent of the concentration of the reactants.
C. The half-life depends on the concentration of the reactants.
D. The rate is independent of the temperature of the reaction.

Answer 1

Hint: -The rate of reaction is the speed at which a reaction takes place. The reaction rate is expressed in terms of concentration. We know the rate law expression. It states that the rate of a reaction can be expressed in terms of the reactant concentration raised to a power that is determined experimentally. The power can be 0, 1, 2, or 3, etc. If the power of the reactant concentration is zero, it is called a zero-order reaction. For a reaction ${\text{A + B}} \to {\text{C + D}}$ , according to rate law expression, ${\text{Rate = k[A}}{{\text{]}}^{\text{x}}}{{\text{[B]}}^{\text{y}}}$ , where ${\text{x + y}}$ gives the order of the reaction. (Anything raised to the power zero is 1)

Complete step by step answer:
From the above-mentioned explanation, we can conclude that for a zero-order reaction, the order is zero. This means that the rate does not depend on the concentration of the reactants in a zero-order reaction. Thus, option B is correct.
These reactions are independent of reactant concentration.
$A \to P$ , for a reaction in which reactant A gives product P, the rate can be written as${\text{Rate = - }}\dfrac{{{\text{d[A]}}}}{{{\text{dt}}}}$ , and now let us consider it as a zero-order reaction.
We know that at a time $t = 0$ , the concentration of A is ${A_0}$ whereas, at a time t, the concentration of A is ${A_t}$.
Since this is a zero-order reaction, the rate law expression can be written as
$Rate = - \dfrac{{d[{A_t}]}}{{dt}} = k{[{A_t}]^0}$ , k is the rate constant for this reaction. {since rate is independent of reactant concentration in a zero-order reaction}
$ - \dfrac{{d[{A_t}]}}{{dt}} = k$ Because anything raised to zero is 1 and applying this to the above equation.
$ - d{[{A_t}]_t} = kdt$ (rearranging)
So now let us integrate both sides, we get
$ - \int {d{A_t} = k\int {dt} } $ (Since k is a constant it can be taken out from the integration)
$ - {[A]_t} = kt + c$
As we already discussed above when time is zero sec $t = 0$s, the concentration of A is ${[A]_0}$. So we can find the integration constant, $ - {[A]_0} = k(0) + c$
 So we can write it as $ - {[A]_0} = c$
$ - {[A]_t} = kt - {[A]_0}$
On rearranging, the rate constant ,$k = \dfrac{{{{[A]}_0} - {{[A]}_t}}}{t}$
So from the above equation, we can find the unit of the rate constant, $k = \dfrac{{concentration}}{{time}}$
$k = \dfrac{{mol/L}}{s}$ as we know the unit of concentration is mol per litre and that of time is sec.
Unit of the rate constant, k for a zero-order reaction is $mol{L^{ - 1}}{s^{ - 1}}$
Thus, we could say that option A is correct.
Half-life is the time when the concentration of the reactant is reduced to half its initial concentration.
So, for a zero-order reaction, at half-life ${t_{1/2}}$ , $[A] = \dfrac{{{{[A]}_0}}}{2}$
Thus, we can write the rate equation for zero-order at half-life.
$k = \dfrac{{{{[A]}_0} - \dfrac{{{{[A]}_0}}}{2}}}{{{t_{1/2}}}}$
\[ \Rightarrow k = \dfrac{{{{[A]}_0}}}{{2{t_{1/2}}}}\]
\[ \Rightarrow {t_{1/2}} = \dfrac{{{{[A]}_0}}}{{2k}}\]
Therefore half-life depends on the concentration of the reactant in zero-order reaction. Therefore option C is correct.
We know that the rate of a reaction depends on its temperature. Thus, option D is incorrect.

So, the correct answer is Option A,B,C.

Note: If the power of the concentration of the reactant is 1, it is a first-order reaction and 2 for second-order reaction and goes on. The unit of the rate constant of ${{\text{n}}^{{\text{th}}}}$ order reaction can be found out easily using the formula ${\text{mo}}{{\text{l}}^{{\text{1 - n}}}}{\text{ }}{{\text{L}}^{{\text{n - 1}}}}{\text{ }}{{\text{s}}^{{\text{ - 1}}}}$ . The rate of reaction depends on the temperature, concentration, pressure, presence of catalyst except in zero-order which is independent of concentration.