Chapter U6, Problem 11STP

Interpretation Introduction

Interpretation:

The instantaneous concentrations of the reactant(s) and the product(s) of a particular chemical reaction need to be determined at a particular time during the course of the reaction.

Concept introduction:

During a chemical reaction, the concentrations of the starting materials or reactants decrease with time while the concentrations of the products increases. This process continues until a chemical equilibrium is reached when the concentrations of the reactants and the products attain a steady value and do not change further with time. At chemical equilibrium, the conversion of the reactants to the products (forward reaction) and the re-combination of the products to the reactants (reverse reaction) proceed at equal rates so that their concentrations do not change with time.

The concentration of a chemical species in a system is defined as the amount of the species (in units of moles or millimoles) divided by the volume of the system. Therefore, the concentrations of the reactants and the products in this reaction are given as follows:

$\text{Concentration, c =}\frac{\text{mols}}{\text{volume}}$

Answer to Problem 11STP

The second option, option (B) is the correct answer.

Explanation of Solution

Reason for Correct Option:

The volume of the rigid container is not mentioned in the question; however, for the purpose, assume the volume of the container as V (in liters).

The concentrations of A and B at 240 s are given as follows:

$\begin{array}{l}\left[\text{A}\right]=\frac{15\text{ mol}}{\text{V L}}\\ \left[\text{B}\right]=\frac{\text{15 mol}}{\text{V L}}\end{array}$

Since 15 mol of A and B are formed, hence, as per the concept of chemical equilibrium, 15 mol of AB must have been consumed in the reaction and the amount of AB retained in the container at 240 s is

$\begin{array}{l}\left(25-15\right)\text{ mol}\\ \text{=10 mol}\end{array}$

The concentration of AB at 240 s is given as

$\left[\text{AB}\right]=\frac{\text{10 mol}}{\text{V L}}$

Without knowing the exact value of V, it can be seen from the above arguments that [A] is higher [AB] since the numerator of [A] is greater than the numerator of [AB]. Also, for same volume, number of moles can be compared which are less in case of AB. Thus, the second option is the correct answer.

Conclusion

Reasons for Incorrect Options:

Since the concentration of A is higher than that of AB, hence, options (A) and (C) are definitely incorrect.

The system is already at chemical equilibrium at 240 s, since the concentrations of A and B do not change with time since 180 s. It can be easily seen from the question that the concentrations of A and B do not change with time post 180 s and thus, the reaction is at equilibrium.