Question

For a general chemical change
$1A + 3B \to products$,
The rate of disappearance of $A$ is ${r_1}$ and of $B$ is ${r_2}$. The rate ${r_1}$ and ${r_2}$ are related as:
A.) $3{r_1} = {r_2}$
B.) ${r_1} = {r_2}$
C.) ${r_1} = 3{r_2}$
D.) ${r_1} = r_2^3$

Answer 1

Hint: In a chemical reaction, the rate of disappearance of reactants can be given as the negative of the rate of change of the reactant because the concentration of reactants is decreasing with the time and the rate of product or rate of appearance of product can be given as positive of rate of change of product because here the concentration of the product is increasing with the time.

Complete step by step answer:
As we know that the rate of reaction or reaction rate can be defined as the change in concentration of a reactant or a product with respect to the time. In a reaction, like:
Reactants $ \to $ Products
We know that during the reaction process, the reactants molecules are used up and product molecules are formed. That is, we can say that during the reaction, the reactants are disappearing and the products are forming with the time.
For a general chemical reaction:
$aA + bB \to cC + dD$
The rate of reaction \[ = - \dfrac{1}{a}\dfrac{{\Delta [A]}}{{\Delta t}} = - \dfrac{1}{b}\dfrac{{\Delta [B]}}{{\Delta t}} = \dfrac{1}{c}\dfrac{{\Delta [C]}}{{\Delta t}} = \dfrac{1}{d}\dfrac{{\Delta [D]}}{{\Delta t}}\]
Here as we can see that the rate of disappearance of reactant is given as negative this is because the concentration of reactant is decreasing with time and rate of formation of product is positive because the concentration of reactant is increasing with time.
So for the given reaction,
$1A + 3B \to products$
Rate of disappearance of $A = {r_1} = - \dfrac{{\Delta [A]}}{{dt}}$
Rate of disappearance of $B = {r_2} = - \dfrac{1}{3}\dfrac{{\Delta [B]}}{{dt}}$
As we know that rate remains same for any reactant or product thus we can write,
$
  \dfrac{{\Delta [A]}}{{dt}} = \dfrac{{\Delta [B]}}{{dt}} \\
\Rightarrow - {r_1} = - 3{r_2} \\
\Rightarrow {r_1} = 3{r_2} \\
 $

Hence, option C.) is the correct answer.

Note: Always remember that the rate of any chemical reaction remains the same for a given reaction whether we expressed it in terms of concentration of reactants or in concentration of products.