Question

On the basis of the equilibrium constant values, choose the reactions in which the reactants are favored. (a) \(\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-}\) (aq) \(\quad K=1.0 \times 10^{-14}\) (b) \(\left[\mathrm{AlF}_{6}\right]^{3-}(\mathrm{aq}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq})+6 \mathrm{~F}^{-}\) (aq) \(\quad K=2 \times 10^{-24}\) (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{~s}) \rightleftharpoons 3 \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{PO}_{4}^{3-}(\mathrm{aq})\) \(K=1 \times 10^{-25}\) (d) \(2 \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{~S}^{2-}(\mathrm{aq}) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \quad K=1 \times 10^{88}\)

Short answer

Reactions (a), (b), and (c) favor reactants.

Step-by-step solution

Understanding Equilibrium Constants

The equilibrium constant \( K \) indicates whether the products or reactants are favored at equilibrium. When \( K \) is much less than 1, the reactants are favored, while when \( K \) is much greater than 1, the products are favored.

Analyzing Reaction (a)

For reaction (a) \( \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-} \) (aq), the equilibrium constant is \( K=1.0 \times 10^{-14} \). This value is much less than 1, indicating that the reactants are favored.

Analyzing Reaction (b)

For reaction (b) \( \left[\mathrm{AlF}_{6}\right]^{3-}(\mathrm{aq}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq})+6 \mathrm{~F}^{-} \) (aq), the equilibrium constant is \( K=2 \times 10^{-24} \). This value is much less than 1, indicating that the reactants are favored.

Analyzing Reaction (c)

For reaction (c) \( \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{~s}) \rightleftharpoons 3 \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{PO}_{4}^{3-}(\mathrm{aq}) \), the equilibrium constant is \( K=1 \times 10^{-25} \). This value is much less than 1, indicating that the reactants are favored.

Analyzing Reaction (d)

For reaction (d) \( 2 \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{~S}^{2-}(\mathrm{aq}) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \), the equilibrium constant is \( K=1 \times 10^{88} \). This value is much greater than 1, indicating that the products are favored.

Conclusion

The reactions where the reactants are favored are (a), (b), and (c) because their equilibrium constants are much less than 1.

Key concepts

Chemical Reactions

A chemical reaction involves the transformation of substances, known as reactants, into new substances, called products. These reactions can be categorized based on whether they occur naturally or are induced by external factors, such as temperature, pressure, or a catalyst.
For understanding chemical reactions, we generally observe:

• The breaking of chemical bonds in reactants.
• The formation of new bonds resulting in products.
• Energy changes, as reactions may either release or absorb energy.

In the context of equilibrium, chemical reactions are reversible, meaning the reactants can form products and vice versa, depending on conditions such as concentration and temperature.
Equilibrium is achieved when the forward and reverse reactions occur at the same rate, and the concentrations of reactants and products remain constant. However, this does not necessarily mean they are in equal quantities; it's about the balance between these opposing reactions.

Reactants and Products

In a chemical reaction, reactants are substances that start the reaction, while products are the substances that are formed as a result of the reaction. Understanding this distinction is crucial when analyzing reaction equilibrium.
In terms of equilibrium constants ( K ), a low value indicates a higher concentration of reactants compared to products at equilibrium. This implies that the system favors the reactants, making the reverse reaction more prominent. Conversely, when K is large, greater than 1, the products are favored.
Analyzing the specific chemical reactions from the exercise gives us insight into how equilibrium constants help determine the favorability of reactants over products:

• For example, reaction (a) has a very small K value, indicating reactants are more prevalent at equilibrium compared to products.
• This pattern is seen in reactions (b) and (c) from the exercise, showing similarities in equilibrium behavior.

Being mindful of these distinctions can help you manage and predict which side of a reaction is more dominant under given conditions.

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps predict how different changes affect a system at equilibrium. Essentially, if an external change is applied to a system in equilibrium, the system will adjust itself to counteract that change and re-establish equilibrium.
This principle is applicable in various scenarios like:

• Concentration changes: Adding or removing reactants/products will shift the reaction to restore balance.
• Temperature variations: Increasing temperature favors endothermic reactions, while decreasing favors exothermic.
• Pressure adjustments: Changes in pressure affect reactions involving gases, favoring the side with fewer moles of gas.

Understanding Le Chatelier's Principle allows scientists and chemists to manipulate reactions to favor either the formation of reactants or products, based on the conditions applied externally.
This insight can be used strategically in chemical industries, for instance, to increase the yield of desired products by modifying operational conditions accordingly.