Question

How is the attainment of equilibrium recognized in case of following equilibria? (i) dissociation of magnesium carbonate in a closed vessel (ii) dissociation of \(\mathrm{N}_{2} \mathrm{O}_{5}\) in a closed vessel

Short answer

Answer: For the dissociation of magnesium carbonate, the attainment of equilibrium can be recognized by monitoring the pressure of CO₂. Equilibrium is reached when the pressure of CO₂ no longer changes over time. For the dissociation of N₂O₅, equilibrium can be recognized by monitoring the concentrations of N₂O₅, NO₂, and O₂. The system is at equilibrium when the concentrations of these gases no longer change over time.

Step-by-step solution

(i) Dissociation of magnesium carbonate

: 1. Write the expression for the equilibrium constant In order to recognize the attainment of equilibrium, we need to write the expression for the equilibrium constant. For the dissociation of magnesium carbonate: \(K_c = \frac{[\mathrm{CO}_{2}]^{1}}{[\mathrm{MgCO}_{3}]^{1}}\) Please note that since \(\mathrm{MgO}\) is a solid its concentration remains constant, so it is excluded from the \(K_c\) expression. 2. Observe the changes in concentration over time As the reaction proceeds, the pressure of \(\mathrm{CO}_{2}\) increases and remains constant once equilibrium is reached. Graphically, we can observe an increase in pressure until it levels out. 3. Determine equilibrium from pressure of \(\mathrm{CO}_{2}\) When the pressure of \(\mathrm{CO}_{2}\) no longer changes over time, the system is at equilibrium. The attainment of equilibrium can be recognized by monitoring the pressure of \(\mathrm{CO}_{2}\).

(ii) Dissociation of \(\mathrm{N}_{2}\mathrm{O}_{5}\)

: 1. Write the expression for the equilibrium constant In order to recognize the attainment of equilibrium, we need to write the expression for the equilibrium constant. For the dissociation of \(\mathrm{N}_{2}\mathrm{O}_{5}\): \(K_c = \frac{[\mathrm{NO}_{2}]^{4}[\mathrm{O}_{2}]^{1}}{[\mathrm{N}_{2}\mathrm{O}_{5}]^{2}}\) 2. Observe the changes in concentration over time As the reaction proceeds, the concentration of \(\mathrm{O}_{2}\) and \(\mathrm{NO}_{2}\) increase, while the concentration of \(\mathrm{N}_{2}\mathrm{O}_{5}\) decreases. At equilibrium, the concentrations of \(\mathrm{O}_{2}\) and \(\mathrm{NO}_{2}\) stop increasing, while the concentration of \(\mathrm{N}_{2}\mathrm{O}_{5}\) stops decreasing. 3. Determine equilibrium from concentrations of \(\mathrm{N}_{2}\mathrm{O}_{5}\), \(\mathrm{NO}_{2}\), and \(\mathrm{O}_{2}\) When the concentrations of \(\mathrm{N}_{2}\mathrm{O}_{5}\), \(\mathrm{NO}_{2}\), and \(\mathrm{O}_{2}\) no longer change over time, the system is at equilibrium. The attainment of equilibrium can be recognized by monitoring the concentrations of these gases.

Key concepts

Equilibrium Constant Expression

When we think about chemical reactions reaching a state where the forward and reverse reaction rates are equal, we're delving into the world of chemical equilibrium. To quantify this state, we use the equilibrium constant expression, denoted as \( K_c \) for concentrations or \( K_p \) for partial pressures.

For a hypothetical reaction \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant expression is written as \(K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\), where the brackets [ ] represent the concentration of each substance in moles per liter. It's important to remember to only include gases and aqueous solutions in this expression, as pure solids and liquids have constant concentrations that do not affect the equilibrium constant.

Dissociation of Magnesium Carbonate

Chemical equilibrium gets even more interesting when we take a look at specific reactions such as the dissociation of magnesium carbonate. This process can be summarized by the reaction equation \(MgCO_3(s) \rightleftharpoons MgO(s) + CO_2(g)\). The equilibrium constant for this reaction, ignoring the solid magnesium oxide, is \(K_c = \frac{[CO_2]}{[MgCO_3]}\).

Here's an interesting fact: even though we write magnesium carbonate in the denominator of the equilibrium expression, in reality, because it's a solid, its concentration remains unchanged and does not appear in the actual expression. The key to understanding equilibrium in such a scenario is to monitor the concentration of \(CO_2\) over time until it stabilizes, indicating that the system has achieved equilibrium.

Dissociation of N2O5

Consider the reaction where dinitrogen pentoxide, \(N_2O_5\), dissociates in a closed vessel: \(2N_2O_5(g) \rightleftharpoons 4NO_2(g) + O_2(g)\). The equilibrium constant expression can be daunting at first, but it's expressed as \(K_c = \frac{[NO_2]^4 [O_2]}{[N_2O_5]^2}\).

This tells us that the concentration of \(N_2O_5\) tends to decrease over time, while the concentrations of \(NO_2\) and \(O_2\) increase until they reach a point where they no longer change. That's our cue that equilibrium has been achieved. This punctuation mark in the reaction is crucial to understand, as it reflects a perfect balance between formation and dissociation of reactants and products.

Concentration Changes Over Time

Every reaction takes its own time to reach equilibrium, and during this journey, the concentrations of substances involved change. In our magnesium carbonate example, we observe that the concentration of \(CO_2\) in the gas phase increases until it levels off, which is when equilibrium is attained.

In contrast, for the dissociation of \(N_2O_5\), both products' concentrations, \(NO_2\) and \(O_2\), increase and that of \(N_2O_5\) decreases until they all stabilize. By plotting these concentration changes over time on a graph, we can visually pinpoint the moment equilibrium is established—it’s when the line flattens out.

Equilibrium in Closed Systems

The concept of a closed system is pivotal in chemical equilibrium. Closed systems allow no matter to enter or leave, and under these conditions, chemical reactions reach equilibrium. For both the dissociation of magnesium carbonate and \(N_2O_5\), these reactions occur in closed vessels to prevent any escape or addition of substances which would otherwise disturb the process reaching equilibrium.

Such isolated environments help us better observe and measure the equilibrium constant, as the variable we're monitoring, be it pressure or concentration, can only be influenced by the reaction at hand and not by external changes. Understanding how closed systems work gives us clarity on how a state of equilibrium is both reached and maintained.