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# If the reaction $A+B\to C+D$ is known to be zero order, what is the expression for its rate law?A.Rate = $k\left[ A \right]{{\left[ B \right]}^{2}}$B.Rate = $k{{\left[ A \right]}^{x}}{{\left[ B \right]}^{y}}$C.Rate = $k\left[ A \right]\left[ B \right]$D.Rate = $k$

Last updated date: 20th Jun 2024
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Hint: A zero order reaction is the one that has a rate that is independent of the concentration of the reactant(s) i.e. increasing or decreasing the concentration of the reacting species will not speed up or slow down the reaction rate.

A reaction is zero-order if concentration data is plotted versus time and the result is a straight line. In the above given options, the one in which rate law is independent of reactant concentrations is option- (D). The square bracket term represents the concentration of the term written inside it. So, in all the other options, the rate is dependent on concentrations of A and B which are the reactants according to the given equation- $A+B\to C+D$. Therefore, the rate law for a zero order reaction is Rate=$k$. The rate constant k will have units of concentration/time, such as M/s.

So, option D is correct.

Important points regarding zero-order reactions:
For a zero-order reaction, increasing the concentration of the reacting species will not speed up the rate of the reaction.
Zero-order reactions are found when a material that is required for the reaction to proceed, such as a surface is saturated by the reactants.
A reaction is zero-order if concentration data is plotted versus time and the result is a straight line.
The integral form of zero order reaction is written as- $\left [A \right]=-k t +\left [{{A} {0}} \right]$
So when we compare this equation to straight line equation, $y=mx+ c$ so we get a graph of $\left [A \right]$against t as straight line with slope equal to (-k) and intercept equal to\ [\ left [ {{A}_{0}} \right]\].
The rate constant is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.
Half Life Time: The half- life of a reaction is the time required for the reactant concentration to decrease to one-half of its initial value. The half -life of a zero order reaction decreases as the initial concentration of the reactant in the reaction decreases. It is given by- ${{t}_{{}^{1}/{}_{2}}}=\dfrac {\left [{{A}_ {0}} \right]}{2k}$
Where the expression $\left [{{A}_ {0}} \right]$is initial concentration.

Note:
Rate law for First order reaction is: A first-order reaction is a reaction—that precedes at a rate that depends linearly on only one reactant concentration.
Rate law for Second order reaction is: Second order reactions can be defined as chemical reactions wherein the sum of the exponents in the corresponding rate law of the chemical reaction is equal to two.