Problem 21 - General Chemistry

Question

a. For each of the following salts, write the reaction that occurs when it dissociates in water: \(\mathrm{NaCl}(s), \mathrm{NaCN}(s)\) \(\mathrm{KClO}_{2}(s), \mathrm{NH}_{4} \mathrm{NO}_{3}(s), \mathrm{K} \operatorname{Br}(a q),\) and \(\mathrm{NaF}(s)\) b. Consider each of the reactions that you wrote above, and identify the aqueous ions that could be proton donors (acids) or proton acceptors (bases). Briefly explain how you decided which ions to choose. c. For each of the acids and bases that you identified in part \(\mathrm{b}\), write the chemical reaction it can undergo in aqueous solution (its reaction with water). d. Are there any reactions that you have written above that you anticipate will occur to such an extent that the \(\mathrm{pH}\) of the solution will be affected? As part of your answer, be sure to explain how you decided. e. Assume that in each case above, \(0.01 \mathrm{~mol}\) of the salt was dissolved in enough water at \(25^{\circ} \mathrm{C}\) to make \(1.0 \mathrm{~L}\) of solution. In each case, what additional information would you need in order to calculate the pH? If there are cases where no additional information is required, be sure to state that as well. f. Say you take \(0.01 \mathrm{~mol}\) of \(\mathrm{NH}_{4} \mathrm{CN}\) and dissolve it in enough water at \(25^{\circ} \mathrm{C}\) to make \(1.0 \mathrm{~L}\) of solution. Using chemical reactions and words, explain how you would go about determining what effect this salt will have on the \(\mathrm{pH}\) of the solution. Be sure to list any additional information you would need to arrive at an answer.

Step-by-Step Solution

Answer

To determine pH effects, identify ion reactions and compare their dissociation constants. Use \( K_a \) and \( K_b \) values to evaluate acidity or basicity shift.

Step 1: Write Dissociation Reactions

1. When \( \mathrm{NaCl} \) dissolves in water, it dissociates into \( \mathrm{Na^+} \) and \( \mathrm{Cl^-} \): \[ \mathrm{NaCl(s) \rightarrow Na^+(aq) + Cl^-(aq)} \] 2. \( \mathrm{NaCN} \) dissociates into \( \mathrm{Na^+} \) and \( \mathrm{CN^-} \): \[ \mathrm{NaCN(s) \rightarrow Na^+(aq) + CN^-(aq)} \] 3. \( \mathrm{KClO_2} \) dissociates into \( \mathrm{K^+} \) and \( \mathrm{ClO_2^-} \): \[ \mathrm{KClO_2(s) \rightarrow K^+(aq) + ClO_2^-(aq)} \] 4. \( \mathrm{NH_4NO_3} \) dissociates into \( \mathrm{NH_4^+} \) and \( \mathrm{NO_3^-} \): \[ \mathrm{NH_4NO_3(s) \rightarrow NH_4^+(aq) + NO_3^-(aq)} \] 5. \( \mathrm{KBr}(aq) \) is already dissociated into \( \mathrm{K^+} \) and \( \mathrm{Br^-} \): \[ \mathrm{KBr(aq) \rightarrow K^+(aq) + Br^-(aq)} \] 6. \( \mathrm{NaF} \) dissociates into \( \mathrm{Na^+} \) and \( \mathrm{F^-} \): \[ \mathrm{NaF(s) \rightarrow Na^+(aq) + F^-(aq)} \]

Step 2: Identify Potential Acids and Bases

The ions \( \mathrm{NH_4^+} \) and \( \mathrm{CN^-} \) are potential acids and bases respectively. - \( \mathrm{NH_4^+} \) is a weak acid, as it can donate a proton to form \( \mathrm{NH_3} \).- \( \mathrm{F^-} \) and \( \mathrm{CN^-} \) are weak bases, as they can accept protons to form \( \mathrm{HF} \) and \( \mathrm{HCN} \) respectively.

Step 3: Write Reactions with Water

1. The \( \mathrm{NH_4^+} \) ion acts as an acid: \[ \mathrm{NH_4^+(aq) + H_2O(l) \leftrightarrow NH_3(aq) + H_3O^+(aq)} \]2. The \( \mathrm{F^-} \) ion acts as a base: \[ \mathrm{F^-(aq) + H_2O(l) \leftrightarrow HF(aq) + OH^-(aq)} \]3. The \( \mathrm{CN^-} \) ion acts as a base: \[ \mathrm{CN^-(aq) + H_2O(l) \leftrightarrow HCN(aq) + OH^-(aq)} \]

Step 4: Assess pH-affecting Reactions

The \( \mathrm{NH_4^+} \) and \( \mathrm{CN^-} \) ions will affect the pH of the solution as they react with water to produce \( \mathrm{H_3O^+} \) and \( \mathrm{OH^-} \) ions respectively, impacting acidity and basicity. The presence of both can cause a mutual neutralization depending on their respective \( K_a \) and \( K_b \) values.

Step 5: Additional Information for pH Calculation

To calculate the pH, we need the acid dissociation constant \( K_a \) for \( \mathrm{NH_4^+} \) and the base dissociation constants \( K_b \) for \( \mathrm{F^-} \) and \( \mathrm{CN^-} \). If no further information is needed, we use water's autoionization constant if neutral.

Step 6: Determine Effect of \(\mathrm{NH_4CN}\) on pH

Dissociation of \( \mathrm{NH_4CN} \) results in \( \mathrm{NH_4^+} \) and \( \mathrm{CN^-} \) reactions with water, producing \( \mathrm{H_3O^+} \) and \( \mathrm{OH^-} \). To determine pH, compare \( K_a(NH_4^+) \) and \( K_b(CN^-) \) to identify if the solution becomes acidic, basic or remains neutral. Additional data on these constants would be required.

Key Concepts

Salt Dissociation

When salts dissolve in water, they break apart into positive and negative ions. This process is known as dissociation. For example, table salt, or \( \mathrm{NaCl} \), dissociates into \( \mathrm{Na^+} \) and \( \mathrm{Cl^-} \) ions.
This dissociation is crucial because it determines the available ions that can interact in the solution. Each salt will break into specific ions:

• \( \mathrm{NaCN} \) forms \( \mathrm{Na^+} \) and \( \mathrm{CN^-} \).
• \( \mathrm{KClO_2} \) forms \( \mathrm{K^+} \) and \( \mathrm{ClO_2^-} \).
• \( \mathrm{NH_4NO_3} \) splits into \( \mathrm{NH_4^+} \) and \( \mathrm{NO_3^-} \).
• \( \mathrm{KBr} \) results in \( \mathrm{K^+} \) and \( \mathrm{Br^-} \).
• \( \mathrm{NaF} \) yields \( \mathrm{Na^+} \) and \( \mathrm{F^-} \).

These ions play important roles in further reactions within the solution.

pH Calculation

The pH of a solution tells us how acidic or basic it is. The scale ranges from 0 to 14, with 7 being neutral. Below 7 indicates acidity, and above 7 indicates basicity. When we calculate pH, we're determining the concentration of hydrogen ions, \( \mathrm{H^+} \), in a solution.
For solutions of salts that affect pH, we need additional information:

• The acid dissociation constant, \( K_a \), which tells how easily an acid donates protons.
• The base dissociation constant, \( K_b \), indicating how readily a base accepts protons.

By understanding these constants, we can accurately predict the pH based on the interactions of different ions in the solution. For example, if \( \mathrm{NH_4^+} \) and \( \mathrm{CN^-} \) are present, their respective \( K_a \) and \( K_b \) will indicate the dominant ion affecting pH.

Weak Acids and Bases

Not all acids and bases are strong, meaning they don't completely dissociate in solution. Weak acids and bases partially dissociate, affecting the balance of protons and hydroxide ions in the solution.
For instance:

• \( \mathrm{NH_4^+} \) is a weak acid that can donate a proton to form \( \mathrm{NH_3} \).
• \( \mathrm{F^-} \) and \( \mathrm{CN^-} \) are weak bases that can accept protons, forming \( \mathrm{HF} \) and \( \mathrm{HCN} \) respectively.

The weak nature of these ions means they do not completely alter the pH unless in higher concentrations or under specific conditions. Understanding their partial dissociation is key to predicting the behavior of solutions.

Hydrolysis Reactions

Hydrolysis involves water breaking down compounds, often altering pH in the process. It occurs when an ion reacts with water to produce \( \mathrm{H^+} \) or \( \mathrm{OH^-} \) ions.
For the salt \( \mathrm{NH_4CN} \), hydrolysis reactions include:

• \( \mathrm{NH_4^+} \) ion acts with water to generate \( \mathrm{H_3O^+} \), potentially lowering the pH by increasing acidity.
• \( \mathrm{CN^-} \) ion reacts with water to form \( \mathrm{OH^-} \), which can raise the pH by increasing basicity.

These reactions highlight how salts derived from weak acids or bases can significantly impact the pH of a solution, either increasing or decreasing it based on the dominant hydrolysis reaction.

Acid-Base Reactions

Acid-base reactions are central to understanding chemistry and pH balance. In these reactions, acids donate protons, and bases accept them, forming new substances. The behavior of ions like \( \mathrm{NH_4^+} \) and \( \mathrm{CN^-} \) represents typical acid and base reactions in water.
When \( \mathrm{NH_4^+} \) reacts with water:

• Results in \( \mathrm{NH_3} \) and \( \mathrm{H_3O^+} \), an acidic reaction affecting pH.

Conversely, when \( \mathrm{CN^-} \) reacts with water:

• Forms \( \mathrm{HCN} \) and \( \mathrm{OH^-} \), a basic reaction influencing pH.

These reactions do not just determine pH but also hint at the dominance of either acidic or basic character in the solution, leading to a balanced or imbalanced pH.