Question

When the following reactions come to equilibrium, does the equilibrium mixture contain mostly reactants or mostly products? $$\begin{array}{ll}{\text { (a) } \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)} & {K_{c}=1.5 \times 10^{-10}} \\ {\text { (b) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)} & {K_{p}=2.5 \times 10^{9}}\end{array}$$

Short answer

In conclusion, the equilibrium mixtures for the given reactions will contain mostly reactants for reaction (a) \( (\mathrm{N}_{2} \text{ and } \mathrm{O}_{2})\) due to the small Kc value and mostly products for reaction (b) \( (\mathrm{SO}_{3})\) due to the large Kp value.

Step-by-step solution

(a) N2(g) + O2(g) ⇌ 2 NO(g), Kc = 1.5 × 10^(-10)

: The equilibrium constant Kc for this reaction is very small \( (K_c = 1.5 \times 10^{-10}) \). Since the value of Kc is much less than 1, the equilibrium favors the reactants over the products. Therefore, the equilibrium mixture for this reaction will contain mostly reactants (N2 and O2).

(b) 2 SO2(g) + O2(g) ⇌ 2 SO3(g), Kp = 2.5 × 10^9

: For this reaction, the equilibrium constant Kp is very large \( (K_p = 2.5 \times 10^9) \). Since the value of Kp is much greater than 1, the equilibrium favors the products over the reactants. So, the equilibrium mixture will mainly consist of the product (SO3). In conclusion, for reaction (a) the equilibrium mixture will contain mostly reactants, whereas for reaction (b) the equilibrium mixture will contain mostly products.

Key concepts

Equilibrium Constant

When understanding chemical equilibrium, the role of the **equilibrium constant** is crucial. It quantifies the balance between the concentrations of reactants and products at equilibrium.
The equilibrium constant, represented as either \(K_c\) for concentrations or \(K_p\) for partial pressures, provides insight into which direction the reaction favors once equilibrium is reached.
For reaction (a), \(K_c = 1.5 \times 10^{-10}\) indicates a very small value. This tells us the reaction forms very little product compared to the reactants, leaning the equilibrium towards reactants. On the other hand, reaction (b), with \(K_p = 2.5 \times 10^9\), shows a large equilibrium constant, pointing towards being product-favored, meaning more products are present at equilibrium. This information is pivotal in predicting the composition of the equilibrium mixture in chemical reactions.

Favorable Reactions

**Favorable reactions** refer to those that are more inclined to proceed in a particular direction when reaching equilibrium. The equilibrium constant helps determine the direction in which a reaction is favorable.
- If \(K\) is large (greater than 1), the products at equilibrium are favored, as seen in reaction (b). This indicates a **product-favored** reaction, where more products are generated than reactants at equilibrium.
- Conversely, if \(K\) is small (less than 1), such as in reaction (a), the reactants are favored. This means the reaction will not yield much product, maintaining a higher concentration of reactants.Understanding which reactions are product- or reactant-favored guides the expectations around reaction yields and the feasibility of a process under certain conditions.

Reactants vs Products

In a chemical reaction, the presence of **reactants and products** at equilibrium is a balancing act. Whether the mixture contains more reactants or products can be deduced using the equilibrium constant.
- For reaction (a), with a small \(K_c\), **mostly reactants** (\(N_2\) and \(O_2\)) remain. This occurs because the formation of products (\(NO\)) is minimal when equilibrium is reached.
- For reaction (b), a large \(K_p\) value suggests the presence of **mostly products** (\(SO_3\)). The system adjusts to ensure a high production of the product to reach equilibrium.Analyzing the ratio of products to reactants offers a clear picture of how reactions behave in equilibrium. This balance is essential in determining reaction conditions, efficiency, and potential yield in practical applications.