Question

Write the equilibrium expression for each of the following reactions. a. \(\mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) b. \(\mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g)\) c. \(2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g)\)

Short answer

The equilibrium expressions for the given reactions are: a. \(K_c = \frac{[\mathrm{NO}_{2}][\mathrm{O}_{2}]}{[\mathrm{NO}][\mathrm{O}_{3}]}\) b. \(K_c = \frac{[\mathrm{SO}_{3}][\mathrm{NO}]}{[\mathrm{SO}_{2}][\mathrm{NO}_{2}]}\) c. \(K_c = \frac{[\mathrm{HCl}]^4[\mathrm{O}_{2}]}{[\mathrm{Cl}_{2}]^2[\mathrm{H}_{2}\mathrm{O}]^2}\)

Step-by-step solution

Write the general form of the equilibrium expression

For a given reaction: \(aA + bB \rightleftharpoons cC + dD\), the equilibrium expression will be given by: \[ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]

Write the equilibrium expression for reaction (a)

For reaction (a): \[ \mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \] The equilibrium expression will be: \[ K_c = \frac{[\mathrm{NO}_{2}][\mathrm{O}_{2}]}{[\mathrm{NO}][\mathrm{O}_{3}]} \]

Write the equilibrium expression for reaction (b)

For reaction (b): \[ \mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g) \] The equilibrium expression will be: \[ K_c = \frac{[\mathrm{SO}_{3}][\mathrm{NO}]}{[\mathrm{SO}_{2}][\mathrm{NO}_{2}]} \]

Write the equilibrium expression for reaction (c)

For reaction (c): \[ 2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g) \] The equilibrium expression will be: \[ K_c = \frac{[\mathrm{HCl}]^4[\mathrm{O}_{2}]}{[\mathrm{Cl}_{2}]^2[\mathrm{H}_{2}\mathrm{O}]^2} \]

Key concepts

Chemical Equilibrium

In chemistry, chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical process are equal, resulting in no net change in the concentrations of the reactants and products over time. At this point, the reaction has reached a state of balance, but it is important to understand that the reactions are still occurring; they are just happening at the same rate in both directions.

For example, when nitrogen monoxide gas reacts with ozone, the forward reaction where these gases react to form nitrogen dioxide and oxygen gas happens at the same rate as the reverse reaction, where nitrogen dioxide and oxygen revert back to nitrogen monoxide and ozone. The equilibrium expression, which is derived from the law of mass action, quantifies this equilibrium state by relating the concentrations of reactants and products in a balanced equation. This expression is crucial for predicting the position of equilibrium and understanding how different factors can affect it.

Reaction Quotient

The reaction quotient (Q) is a measure that tells us the direction in which a reaction will shift to reach equilibrium. It is calculated using the same formula as the equilibrium constant (Kc), but with the initial concentrations of the reactants and products instead of the equilibrium concentrations.

When comparing Q to Kc, there are three main possibilities:

• If Q < Kc, the system will shift towards the products to reach equilibrium.
• If Q > Kc, the system will shift towards the reactants to reach equilibrium.
• If Q = Kc, the system is already at equilibrium.

This concept allows chemists to predict which way a reaction will proceed under certain conditions by calculating the reaction quotient using initial concentrations and comparing it to the known equilibrium constant.

Le Chatelier's Principle

Le Chatelier's Principle is an essential concept in chemical equilibrium that helps predict how a system at equilibrium will respond to external changes. According to this principle, if an external stress, such as a change in concentration, pressure, or temperature, is applied to a system at equilibrium, the system will adjust itself in such a way as to counteract the effect of the stress and re-establish equilibrium.

For instance, if more reactants are added to the system, the equilibrium will shift to favor the formation of products to reduce the concentration of the added reactants. And conversely, if a product is removed, the equilibrium shifts to make more of that product. The same applies to changes in pressure and temperature, where the system will adjust to minimize the change induced by these external factors. Understanding Le Chatelier's Principle aids in controlling chemical reactions and can be applied to a range of practical situations in industrial chemistry and environmental engineering.