Question

Which of these reactions are having homogeneous equilibrium: (a) \(\mathrm{N}_{2} \mathrm{O}_{4} \rightleftharpoons 2 \mathrm{NO}_{2}\) \(' \mathrm{~g}^{\prime} \quad{ }^{6} \mathrm{~g}^{\prime}\) (b) \(\mathrm{H}_{2}+\mathrm{Cl}_{2} \rightleftharpoons 2 \mathrm{HCl}\) \(' \mathrm{~g}^{\prime} \quad{ }^{2} \mathrm{~g}^{\prime} \quad{ }^{\mathrm{s}} \mathrm{g}^{\prime}\) (c) \(\mathrm{CaCO}_{3} \rightleftharpoons \mathrm{CaO}+\mathrm{CO}_{2}\) 's' \(\quad{ }^{\prime} \mathrm{s}^{\prime} \quad{ }^{\prime} \mathrm{g}\) ' (d) Both (a) and (b)

Short answer

Reaction (a) has homogeneous equilibrium, assuming (b) typo suggests gas.

Step-by-step solution

Understanding Homogeneous Equilibrium

A homogeneous equilibrium occurs when all the reactants and products are in the same phase. Common phases include gas (g), liquid (l), and aqueous (aq). In this problem, we are looking for reactions where all substances are gases.

Analyze Reaction (a)

The reaction for (a) is: \(\text{N}_2\text{O}_4 \rightleftharpoons 2 \text{NO}_2\). Both the reactants and products are in the gaseous phase ('g'). Therefore, this reaction is a homogeneous equilibrium.

Analyze Reaction (b)

The reaction for (b) is: \(\text{H}_2 + \text{Cl}_2 \rightleftharpoons 2 \text{HCl}\). The reactants \(\text{H}_2\) and \(\text{Cl}_2\) are gases, but it is stated that the product \(\text{HCl}\) is in the solid phase ('s') in the question. This makes it heterogeneous, but normally, \(\text{HCl}\) is considered a gas, so there might be a typo. Nevertheless, based on the information given, this would be a heterogeneous equilibrium.

Analyze Reaction (c)

The reaction for (c) is: \(\text{CaCO}_3 \rightleftharpoons \text{CaO} + \text{CO}_2\). Here, \(\text{CaCO}_3\) and \(\text{CaO}\) are in the solid phase ('s'), and \(\text{CO}_2\) is in the gaseous phase ('g'). This means the phases are mixed, resulting in a heterogeneous equilibrium.

Draw Conclusion

Reactions (a) and considered (b) if \(\text{HCl}\) is a gas (note potential typo), indicates the same phase but evaluate logically: \(\text{CaCO}_3\) equilibrium is different. Consistency checks confirm reaction (a) is definitely homogeneous; caution around reaction (b) label's typo.

Key concepts

Gas Phase Reactions

Gas phase reactions involve reactants and products that are all in the gaseous state. This is important because, in such reactions, molecules without physical barriers can freely interact and exchange. This dynamic allows the reactants to reach equilibrium more swiftly, as opposed to reactions where different phases such as solids or liquids are present.
Reactions that involve all gaseous substances are classified under homogeneous equilibria. Here, you do not have to worry about solubility or phase transitions interfering with the reaction. Instead, focus is on pressures and concentrations of the gases. For example, the reaction of dinitrogen tetroxide (\( ext{N}_2 ext{O}_4\)) and nitrogen dioxide (\(2 ext{NO}_2\)) is a typical gas phase reaction, where both sides are gases.
In gas phase reactions, factors such as pressure and temperature heavily influence the reaction rate and equilibrium position. According to Le Chatelier's principle, increasing pressure will favor the reaction side with fewer moles of gas.

Chemical Equilibrium

Chemical equilibrium is a state where the rate of the forward reaction equals the rate of the reverse reaction. In other words, the concentrations of reactants and products remain constant over time. Equilibrium does not mean that the reactants and products are equal in concentration but that their ratios remain steady.
To determine whether a reaction has reached equilibrium, you can use the equilibrium constant (\(K_c\) for concentration or \(K_p\) for pressure). These constants provide a ratio of the concentrations of products to reactants at equilibrium. If the value of \(K\) is much greater than one, products dominate at equilibrium; if it is much less than one, reactants dominate.
In homogeneous equilibria, like the gaseous reaction \( ext{N}_2 ext{O}_4 ightleftharpoons 2 ext{NO}_2\), the \(K_p\) will only involve gaseous products and reactants. Understanding the balance of reactions helps chemists manipulate conditions to favor the formation of desired products.

Phase Difference in Reactions

When reactions involve more than one phase, they are known as heterogeneous equilibria. Understanding the phase difference in reactions is crucial in determining the type of equilibrium present. In examples of heterogeneous equilibria, like the decomposition of calcium carbonate (\( ext{CaCO}_3\)), the reaction involves solids and gases, resulting in a two-phase system.
Here, equilibrium is approached differently because solids and liquids have constant concentration terms in the equilibrium expression. Their concentrations are not included in the \(K\) calculations unless they participate in the gas phase or ion formation. This means in reactions like: \( ext{CaCO}_3 ightleftharpoons ext{CaO} + ext{CO}_2\),
only the gaseous component (e.g., \( ext{CO}_2\)) is considered in the equilibrium equation.
Phase differences thus play a vital role in how reactions are balanced and calculated, informing how you can shift equilibriums via changes in pressure, temperature, or concentration.