Problem 36 - Chemistry and Chemical Reactivity

Question

For each of the following reactions, predict whether the equilibrium lies predominantly to the left or to the right. Explain your prediction briefly. (a) \(\mathrm{H}_{2} \mathrm{S}(\mathrm{aq})+\mathrm{CO}_{3}^{2-}(\mathrm{aq}) \rightleftarrows \mathrm{HS}^{-}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq})\).(b) \(\mathrm{HCN}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq}) \rightleftarrows \mathrm{CN}^{-}(\mathrm{aq})+\mathrm{HSO}_{4}^{-}(\mathrm{aq})\).(c) \(\mathrm{SO}_{4}^{2-}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq}) \rightleftarrows\) \(\mathrm{HSO}_{4}^{-}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq})\)

Step-by-Step Solution

Answer

(a) Left, (b) Right, (c) Right.

Step 1: Analyze Reaction (a)

The reaction is \( \mathrm{H}_{2}\mathrm{S} + \mathrm{CO}_{3}^{2-} \rightleftarrows \mathrm{HS}^{-} + \mathrm{HCO}_{3}^{-} \). We need to compare the acidities and basicities of the reactants and products. \( \mathrm{H}_{2}\mathrm{S} \) is a weak acid and \( \mathrm{HS}^{-} \) is its conjugate base, while \( \mathrm{CO}_{3}^{2-} \) is a weak base and \( \mathrm{HCO}_{3}^{-} \) its conjugate acid. In this case, a stronger acid-base pair generally favors products. However, because both acids and bases involved are weak, equilibrium lies more to the left, favoring the formation of \( \mathrm{H}_{2}\mathrm{S} \) over \( \mathrm{HS}^{-} \).

Step 2: Analyze Reaction (b)

The reaction is \( \mathrm{HCN} + \mathrm{SO}_{4}^{2-} \rightleftarrows \mathrm{CN}^{-} + \mathrm{HSO}_{4}^{-} \). \( \mathrm{HCN} \) is a weak acid and \( \mathrm{CN}^{-} \) its conjugate base, while \( \mathrm{SO}_{4}^{2-} \) is a weak base and \( \mathrm{HSO}_{4}^{-} \) the conjugate acid. \( \mathrm{HSO}_{4}^{-} \) is stronger as an acid compared to \( \mathrm{HCN} \), thus this makes \( \mathrm{SO}_{4}^{2-} \) a weaker base compared to \( \mathrm{CN}^{-} \). Therefore, equilibrium tends to lie to the right, favoring \( \mathrm{CN}^{-} + \mathrm{HSO}_{4}^{-} \).

Step 3: Analyze Reaction (c)

The reaction is \( \mathrm{SO}_{4}^{2-} + \mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H} \rightleftarrows \mathrm{HSO}_{4}^{-} + \mathrm{CH}_{3}\mathrm{CO}_{2}^{-} \). \( \mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H} \) (acetic acid) is a weak acid and \( \mathrm{CH}_{3}\mathrm{CO}_{2}^{-} \) is its conjugate base, whereas \( \mathrm{SO}_{4}^{2-} \) is a weak base with \( \mathrm{HSO}_{4}^{-} \) as the conjugate acid. \( \mathrm{HSO}_{4}^{-} \) is a stronger acid than \( \mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H} \), and because \( \mathrm{CH}_{3}\mathrm{CO}_{2}^{-} \) is stronger than \( \mathrm{SO}_{4}^{2-} \) as a base, the equilibrium tends to lie to the right favoring \( \mathrm{HSO}_{4}^{-} + \mathrm{CH}_{3}\mathrm{CO}_{2}^{-} \).

Key Concepts

Acid-Base Reactions

Acid-base reactions are a fundamental aspect of chemical equilibrium. These reactions involve the transfer of protons ( H^+ ) from acids to bases. An acid is a proton donor, while a base is a proton acceptor. Understanding the points of equilibrium in these reactions is crucial, because it helps predict the extent to which products or reactants will form.
In the context of the reactions given, knowing whether a solution consists of strong or weak acids and bases helps predict the equilibrium position. Strong acids dissociate completely, while weak acids only partially dissociate. The same concept applies to bases. In these reactions, equilibrium tends to favor the side with the weaker acid and base if there is a considerable difference between their strengths. This is because weaker acids and bases are less likely to donate and accept protons and hence remain intact in the solution.
Understanding the basic principles of acid-base reactions is a stepping stone to grasping more complex chemical equilibria. Whether dealing with weak or strong acids and bases, knowing their behavior allows for better prediction of products and reactants in a given chemical scenario.

Conjugate Acid-Base Pairs

In acid-base reactions, conjugate acid-base pairs play a pivotal role in determining the equilibrium position. A conjugate acid-base pair is formed when an acid donates a proton to become a conjugate base, and a base accepts a proton to become a conjugate acid.
For instance, in the given reaction examples:

• For the reaction involving H_2S and CO_3^{2-} , HS^- is the conjugate base of H_2S , and HCO_3^- is the conjugate acid of CO_3^{2-} .
• Similarly, for the reaction between HCN and SO_4^{2-} , CN^- forms the conjugate base of HCN , and HSO_4^- serves as the conjugate acid of SO_4^{2-} .

The strength of each conjugate acid or base can profoundly impact the direction of the equilibrium. Stronger conjugate acids and bases tend to have a more significant influence on reaction direction. Recognizing these pairs and their relative strengths allows chemists to predict which direction a given reaction will likely favor.

Equilibrium Position Prediction

Predicting the equilibrium position in acid-base reactions involves comparing the strengths of the acids and bases on each side of the equation. In essence, the equilibrium position tends to favor the formation of the weaker acids and bases, as these are less likely to react further.
Let's consider some equilibrium projection guidelines:

• For weaker acid and base pairings like H_2S and CO_3^{2-} , the equilibrium is generally to the left, favoring the reactants.
• When there is a stronger pairing like HCN and SO_4^{2-} , where HSO_4^- is a stronger acid than HCN , the equilibrium shifts to the right, favoring products.

Understanding how to predict equilibrium positions helps in designing chemical reactions and in applications like buffer solutions. By knowing the relative acid and base strengths, it becomes easier to predict the direction of the equilibrium. This understanding is crucial in various fields, including pharmaceuticals, environmental science, and industrial chemistry, as it ensures that desired reaction outcomes are achieved efficiently and accurately.