Question

In the following reaction:
\[{\text{xA}} \to {\text{yB}}\]
\[{\text{log [}}\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}}{\text{] = log[}}\dfrac{{{\text{d[B]}}}}{{{\text{dt}}}}{\text{] + log2}}\]
Where –ve sign indicates rate of disappearance of the reactant. Thus x:y is :
\[1)1:2\]
\[2)2:1\]
\[3)3:1\]
\[4)3:10\;\]

Answer 1

Hint: We have to know that chemical kinetics is one of the topics used to study the kinetics nature of the chemical reaction. It is used to optimize the chemical reaction for industrial purposes. The reactant to the product so many parameters are required. All are optimised by using this chemical kinetics. Chemical kinetics is used as a mechanism of reactant to product in the chemical reaction.
Formula used:
In logarithm, some addition formula are there,
\[{\text{log m + logn = logmn}}\]
Complete step by step answer:
Given data,
In the following reaction:
\[{\text{xA}} \to {\text{yB}}\]
Here, A is the reactant in the reaction and B is the product of the reaction. x is the number of moles of A reactant and y is the number of moles of product will form in his reaction.
\[{\text{log [}}\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}}{\text{] = log[}}\dfrac{{{\text{d[B]}}}}{{{\text{dt}}}}{\text{] + log2}}\]
Where –ve sign indicates rate of disappearance of the reactant.
We calculate x:y in the given reaction.
\[{\text{log [}}\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}}{\text{] = log[}}\dfrac{{{\text{d[B]}}}}{{{\text{dt}}}}{\text{] + log2}}\]
We applying logarithm formula,
 Some addition formula is,
\[{\text{log m + logn = logmn}}\]
\[{\text{log [}}\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}}{\text{] = log[}}\dfrac{{{\text{2d[B]}}}}{{{\text{dt}}}}{\text{]}}\]
We cancel logarithm on both side in the above equation,
\[\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}}{\text{ = }}\dfrac{{{\text{2d[B]}}}}{{{\text{dt}}}}\]
We compare the coefficient of the equation with coefficient of the reaction,
\[\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}} = {\text{xA}}\]
Here –ve sign indicates rate of disappearance of the reactant.
The value of\[{\text{x = 1}}\].
\[\dfrac{{{\text{2d[B]}}}}{{{\text{dt}}}} = {\text{yB}}\]
The value of\[{\text{y = 2}}\].
From the above calculation we conclude the value x and y is \[{\text{1and2}}\] respectively.
In the following reaction:
\[{\text{xA}} \to {\text{yB}}\]
\[{\text{log [}}\dfrac{{{\text{ - d[A]}}}}{{{\text{dt}}}}{\text{] = log[}}\dfrac{{{\text{d[B]}}}}{{{\text{dt}}}}{\text{] + log2}}\]
Where –ve sign indicates rate of disappearance of the reactant. Thus x:y is \[{\text{1:2}}\].

Hence, option A is correct.

Note:
We also know that the rate of the reaction is an important factor for the study of reaction. The rate of reaction is an important concept for chemical kinetics. Rate of the reaction depends on the concentration of the reactant. The rate of reaction is also calculated by using the concentration of the product in the chemical reaction. Depending on the concentration, the sign of the rate will change.