Question

Which of the following statement is not correct for the reaction:
${\text{4A + B}} \to {\text{2C + 2D}}$
a.) The rate of appearance of ${\text{C}}$is one-half of the rate of disappearance of ${\text{B}}$.
b.) The rate of disappearance of ${\text{B}}$is one-fourth of the rate of disappearance of ${\text{A}}$.
c.) The rate of formation of ${\text{D}}$ is one-half of the rate of consumption of ${\text{A}}$.
d.) The rates of formation of \[{\text{C}}\] and ${\text{D}}$ are equal.

Answer 1

Hint: Rate of reaction-speed at which a chemical reaction proceeds. It is expressed in two ways, either in the concentration (amount per unit volume) of a product that is formed in a unit of time or the concentration of the reactants that is consumed in the unit time. In other words, the rate of reaction can be defined as the reactant consumed or the product formed in a unit time.

Complete step by step solution: For reactants \[{\text{A}}\] and ${\text{B}}$ ,there will be rate of disappearance(consumption) and for the products ${\text{C}}$ and ${\text{D}}$ there will be the rate of appearance(formation).
Now if we write the equation for the rate of reaction for the given equation-
${\text{4A + B}} \to {\text{2C + 2D}}$
Rate equation for the Rate of reaction =
$\dfrac{{{\text{ - 1}}}}{{\text{4}}}\dfrac{{{\text{d}}\left[ {\text{A}} \right]}}{{{\text{dt}}}}{\text{ = }}\dfrac{{{\text{ - d}}\left[ {\text{B}} \right]}}{{{\text{dt}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{\text{d}}\left[ {\text{C}} \right]}}{{{\text{dx}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{\text{d}}\left[ {\text{D}} \right]}}{{{\text{dx}}}}$
Here the concentration of the reactants and products are written in brackets and the stoichiometric coefficients are written in fractional value with the sign. The reactants are written with negative signs since they are disappearing and products are written in the positive sign since they are getting appeared.
Let us check for each option-
For the option (A)
From the rate equation we see the following relation between ${\text{C}}$ and ${\text{B}}$,
$\dfrac{{{\text{ - d}}\left[ {\text{B}} \right]}}{{{\text{dt}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{\text{d}}\left[ {\text{C}} \right]}}{{{\text{dx}}}}$
So, from here we see that the rate of disappearance of ${\text{B}}$ is one-half of the rate of appearance of ${\text{C}}$ but the statement in the option is saying otherwise, hence the statement given is not correct.
Similarly, for option(B)
$\dfrac{{{\text{ - 1}}}}{{\text{4}}}\dfrac{{{\text{d}}\left[ {\text{A}} \right]}}{{{\text{dt}}}}{\text{ = }}\dfrac{{{\text{ - d}}\left[ {\text{B}} \right]}}{{{\text{dt}}}}$
So, here we know that the rate of disappearance of ${\text{ B}}$ is one-fourth of the rate of disappearance of ${\text{A}}$ Hence the statement given in the option is correct.
Similarly, for option (C)
$\dfrac{{{\text{ - 1}}}}{{\text{4}}}\dfrac{{{\text{d}}\left[ {\text{A}} \right]}}{{{\text{dt}}}} = \dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{\text{d}}\left[ {\text{D}} \right]}}{{{\text{dx}}}}$
On simplifying,
$\dfrac{{{\text{ - 1}}}}{2}\dfrac{{{\text{d}}\left[ {\text{A}} \right]}}{{{\text{dt}}}} = \dfrac{{{\text{d}}\left[ {\text{D}} \right]}}{{{\text{dx}}}}$
Here also we see that, the rate of formation of ${\text{ D}}$ is one-half of the rate of consumption of ${\text{A}}$. Hence the statement given in the option is correct.

Now for the option (D)
$\dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{\text{d}}\left[ {\text{C}} \right]}}{{{\text{dx}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{\text{d}}\left[ {\text{D}} \right]}}{{{\text{dx}}}}$
$\dfrac{{{\text{d}}\left[ {\text{C}} \right]}}{{{\text{dx}}}}{\text{ = }}\dfrac{{{\text{d}}\left[ {\text{D}} \right]}}{{{\text{dx}}}}$ So, the appearance of both products are equal. So, the statement in the option is correct.
So, from the above explanation we see that only the statement of option (A) is not correct.

Hence the option (A) is the correct option for the given problem.

Note: There are some factors which will affect the rate of reaction of any chemical reaction. Such factors are as follows-
1. Surface area of the solid reactants.
2. Concentration or the Pressure of the reactants.
3. Temperature of the reactants.
4. Nature of the reactants.
5. Presence of the catalyst.