Question

What is the rate of reaction for $2A \to B$ ?
A. $ - \dfrac{1}{2}[\dfrac{{d[A]}}{{dt}}]$
B. $ - \dfrac{{d[A]}}{{dt}}$
C. $ - \dfrac{{d[B]}}{{dt}}$
D. $ + \dfrac{{d[A]}}{{dt}}$

Answer 1

Hint: We know that rate of a reaction of a chemical reaction is the speed at which the chemical reaction is taking place. The concentration of reactants always decreases and the concentration of the products always increase in a given chemical reaction.

Complete step-by-step answer:As we already know that rate of reaction is an important concept of chemical kinetics which is used to determine how fast a chemical reaction is taking place. For a chemical reaction $aA + bB \to cC + dD$, the rate of reaction can be written as $R.O.R = - \dfrac{{\dfrac{{d[A]}}{{dt}}}}{a} = - \dfrac{{\dfrac{{d[B]}}{{dt}}}}{b} = + \dfrac{{\dfrac{{d[C]}}{{dt}}}}{c} = + \dfrac{{\dfrac{{d[D]}}{{dt}}}}{d}$. Here, $a,b,c,d$ are the coefficients of $A,B,C,D$ respectively. Here $A,B$ are the reactants and $C,D$ are the products of the reaction $aA + bB \to cC + dD$. For reactants we will write a negative sign because the concentration of the reactants are decreasing. For products we will write a positive sign because the concentration of the products is increasing. $[A],[B],[C],[D]$ are the concentrations of $A,B,C,D$ respectively .
So in the question the reaction given is $2A \to B$, so the rate of reaction of the this chemical equation can be written as
$
  Rate of reaction = - \dfrac{{\dfrac{{d[A]}}{{dt}}}}{2} = + \dfrac{{d[B]}}{{dt}} \\
  Rate of reaction = - \dfrac{1}{2}\dfrac{{d[A]}}{{dt}} = + \dfrac{{d[B]}}{{dt}} \\
 $
We have derived the rate of reaction of the reaction $2A \to B$. So from the above explanation and calculation it is clear to us that the correct answer of the given question is option: A. $ - \dfrac{1}{2}[\dfrac{{d[A]}}{{dt}}]$.

Note: Always remember that for a chemical reaction $aA + bB \to cC + dD$, the rate of reaction can be written as $R.O.R = - \dfrac{{\dfrac{{d[A]}}{{dt}}}}{a} = - \dfrac{{\dfrac{{d[B]}}{{dt}}}}{b} = + \dfrac{{\dfrac{{d[C]}}{{dt}}}}{c} = + \dfrac{{\dfrac{{d[D]}}{{dt}}}}{d}$.We can increase or decrease the rate of reaction by using suitable catalyst and inhibitors. Rate of reaction depends upon the concentration of the reactants and the physical state of the reactant. Always try to solve the question carefully and avoid silly mistakes while solving the numerical.