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Question: The rate constant of a \({{n}^{th}}\) order has units: A. \(mo{{l}^{1-n}}{{L}^{-1}}{{\sec }^{-1}}\...

The rate constant of a nth{{n}^{th}} order has units:
A. mol1−nL−1sec⁡−1mo{{l}^{1-n}}{{L}^{-1}}{{\sec }^{-1}}
B. mol1−nL1−nsec⁡−1mo{{l}^{1-n}}{{L}^{1-n}}{{\sec }^{-1}}
C. mol1−nLn−1sec⁡−1mo{{l}^{1-n}}{{L}^{n-1}}{{\sec }^{-1}}
D. mol1−n2Ln2sec⁡−1mo{{l}^{1-{{n}^{2}}}}{{L}^{{{n}^{2}}}}{{\sec }^{-1}}

Explanation

Solution

The order of reaction refers to the power dependence of the rate of the reaction on the concentration of each reactant. The order of reaction can be given directly if we know that units of rate constant of the reaction.

Complete step by step answer:
As we know that the rate constant is the proportionality constant in the equation of rate law. This rate constant relates the rate of a given chemical reaction at a given temperature with that of concentration of reactant or to the product of concentration of reactant. It will be much clearer from rate law.
The rate law of a chemical reaction is an equation or expression which given the relation between the rate of the reaction and the concentration of the reactants which are participating in the reaction. Let say for a general equation:
aA+bB→cC+dDaA+bB\to cC+dD
Where a, b, c, d are the stoichiometry coefficients of the reactants and products. Now, the Rate law for above given equation can be given as Rate=k[A]x[B]yRate=k{{[A]}^{x}}{{[B]}^{y}}
Where k = rate constant of the given reaction, [A] is concentration of reactant A; [B] is concentration of reactant B; x+y=nx+y=n will give the order of the given reaction. Here, the units of rate constant (k) can be given as:
∴k=Rate[A]x[B]y\therefore k=\dfrac{Rate}{{{[A]}^{x}}{{[B]}^{y}}}
Thus, (Units)k=[molL−1sec⁡−1][molL−1]n=[molL−1]1−nsec⁡−1(Units)k=\dfrac{[mol{{L}^{-1}}{{\sec }^{-1}}]}{{{[mol{{L}^{-1}}]}^{n}}}={{[mol{{L}^{-1}}]}^{1-n}}{{\sec }^{-1}} ; where, n=n= order of the reaction.
⇒mol1−nLn−1sec⁡−1\Rightarrow mo{{l}^{1-n}}{{L}^{n-1}}{{\sec }^{-1}}
Therefore, the correct answer is option C.

Note: Always remember that the rate law can be determined experimentally only that is the value of order of reaction can only be determined by experimentally only not from the balanced chemical equation.