Chapter 17, Problem 72A

Interpretation Introduction

Interpretation:

The illustration that represents an equilibrium mixture have to be shown. The number of molecules of A₂B reacted initially have to be stated.

Concept Introduction:

Chemical equilibrium: Chemical equilibrium is a state of a chemical reaction when the rate of forward reaction is equal to the rate of backward reaction. The chemical reaction follows the law of mass action. The law of mass action states that the rate of a chemical reaction is directly proportional to the product of active masses of the reactants.

  $aA+bB\rightleftharpoons cC+dD$

  $Rateoftheforwardreaction{r}_f=k_f{[A]}^a{[B]}^b$

  $Rateofthebackwardreaction{r}_b=k_b{[C]}^c{[D]}^d$

  $k_{f}and{k}_{b}aretherateconstantsofforwardandbackwardreactionrespectively$

  $Atequilibriumtherateoftheforwardreaction=therateofthebackwardreaction$

  $k_f{[A]}^a{[B]}^b=k_b{[C]}^c{[D]}^d$

  $\frac{k_f}{k_b}=K_{eq}=\frac{{[C]}^c{[D]}^d}{{[A]}^a{[B]}^b}$

  $K_{eq}istheequilibriumconstantofthereaction.$

Answer to Problem 72A

The first snapshot illustrates that the container contains 4 molecules of A₂B, 2 molecules of A₂ and 1 molecule of B₂. The second snapshot represents that the container contains 2 molecules of A₂B, 4 molecules of A₂ and 2 molecules of B₂ and the third snapshot represents that the container contains 2 molecules of A₂B, 4 molecules of A₂ and 2 molecules of B₂. Therefore the number of molecules remain constant in the third snapshot. That means the system is in equilibrium and the number of molecules are not changing.

So the second snapshot represents the equilibrium mixture.

From the equation we see that 2 molecules of A₂B give 2 molecules of A₂ and 1 molecule of B₂. The first snapshot illustrates that the container contains 2 molecules of A₂ and 1 molecule of B₂. That means 2 molecules of A₂B reacted initially.

Explanation of Solution

The given chemical equation is-

  $\begin{array}{l}2A_{2}B(g)\rightleftharpoons 2A_2(g)+B_2(g)\\ K_{eq}=\frac{{[A_2]}^2[B_2]}{{[A_{2}B]}^2}\end{array}$

The first snapshot illustrates that the container contains 4 molecules of A₂B, 2 molecules of A₂ and 1 molecule of B₂. The second snapshot represents that the container contains 2 molecules of A₂B, 4 molecules of A₂ and 2 molecules of B₂ and the third snapshot represents that the container contains 2 molecules of A₂B, 4 molecules of A₂ and 2 molecules of B₂. Therefore the number of molecules remain constant in the third snapshot. That means the system is in equilibrium and the number of molecules are not changing.

So the second snapshot represents the equilibrium mixture.

From the equation we see that 2 molecules of A₂B give 2 molecules of A₂ and 1 molecule of B₂. The first snapshot illustrates that the container contains 2 molecules of A₂ and 1 molecule of B₂. That means 2 molecules of A₂B reacted initially.