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What is the order of the reaction whose rate constant has the same unit as the rate of reaction?

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Hint: Rate of reaction depends only on the concentration of reactants and one whose rate of reaction is independent of the concentration of reactants will have the same rate constant as that of the rate of reaction.

Complete answer:
Rate of reaction may be defined as the rate(speed) at which the reactants are completely converted into the products.it is measured as the rate of decrease in the concentration of reactants or the increase in the concentration of products with time. It depends on the initial concentration of the reactants and its units are mol/l/time.
Consider the general reaction as:
             $\text{A+B} \to 2\text {AB}$
     Now, the rate or reaction of this reaction is as:
            Rate=k[A][B]
Where A and B are the reactants and the square brackets represent the molar concentrations of the reactants and k is the constant of proportionality and is known as rate constant.
If the concentration of reactants involved in the reaction is unity i.e., [A]=[B]=1, then the rate of reaction is equal to the rate constant.
             Rate= k ×1×1
             Rate=k
So, thus the rate constant may be defined as the rate of the reaction when the concentration of the reaction is unity.it is independent of the initial concentration of the reactants and depends on the order of the reaction.
Order of the reaction may be defined as the sum of the powers to which the reacting species must be raised in order to express the rate of reaction. The power of the concentration of the particular reactant is called the order of the reaction with respect to that reactant.
Consider the reaction:
$aA+bB\to products$
And the rate of reaction of this reaction is as:
Rate=$k{{[A]} ^{p}} {{[B]} ^{q}} $
Where p, q are the orders with respect to the individual reactants and overall order of the reaction is the sum of these exponents i.e. p+q.
Then, the order of the reaction, n is:
           n= p+q
if the value of n=0, then the reaction is of zero order.
If the value of n=1, then the reaction is of first order.
If the value of n=2, then the reaction is of second order.
If the value of n=3, then the reaction is of third order.
In, zero order reaction, the rate of reaction is independent of the reactants i.e. in such reactions their rate depends on the products. But as we know that the rate of reaction depends on the initial concentration of reactants so, thus, in case of zero order reaction, the rate constant has the same units as that of the rate of reaction.
Considered the following zero order reaction:
                          $2N{{H}_ {3}} \to {{N}_ {2}} +3{{H}_ {2}} $
In this reaction, the rate of reaction is independent of the concentration of ammonia because in this reaction, metal platinum acts as catalysts and at pressure, the surface of the metal is completely covered by the reactant surface and thus, the increase in pressure has no effect on the amount the reactants and thus, the reaction is independent of the concentration of the reactants.
Therefore, Rate=k${{[N{{H}_ {3}}]} ^ {0}} $
                                 Rate=k
 Therefore, order=0
And, thus, in case of zero order reaction, the rate constant k has the same units as that of rate of reaction i.e. mol/l/s.

Note: Always keep in mind that the rate of reaction always depends on the initial concentration of the reactants and not on the concentration of the products and rate constant always depends on the order of the reaction.