Problem 21 - Chemistry and Chemical Reactivity

Question

If each of the salts listed here were dissolved in water to give a \(0.10 \mathrm{M}\) solution, which solution would have the highest pH? Which would have the lowest pH? (a) \(\mathrm{Na}_{2} \mathrm{S}\) (d) NaF (b) \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) (e) \(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\) (c) \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) (f) \(\mathrm{AlCl}_{3}\)

Step-by-Step Solution

Answer

Highest pH: Na2S; Lowest pH: AlCl3.

Step 1: Understand the Problem

We are given various salts and need to determine which solution has the highest and lowest pH when each salt is dissolved in a 0.10 M solution.

Step 2: Analyze Anionic Components

Identify the conjugate base of the acid associated with each salt. Strong conjugate bases will increase the pH (more basic), while weak conjugate bases or conjugate acids will decrease the pH (more acidic).

Step 3: Sodium Sulfide Analysis ( \(\mathrm{Na}_{2} \mathrm{S}\) )

Sulfide ion (\(\mathrm{S}^{2-}\)) is a strong base, as it is the conjugate base of the weak acid \(\mathrm{HS}^{-}\). Therefore, \(\mathrm{Na}_2\mathrm{S}\) will yield a basic solution.

Step 4: Sodium Phosphate Analysis ( \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) )

Phosphate ion (\(\mathrm{PO}_{4}^{3-}\)) is the conjugate base of a weak acid (\(\mathrm{HPO}_{4}^{2-}\)). This makes \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) solution basic.

Step 5: Sodium Dihydrogen Phosphate Analysis ( \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) )

Dihydrogen phosphate ion (\(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)) is an intermediate form of phosphoric acid, making this solution slightly acidic.

Step 6: Sodium Fluoride Analysis ( \(\mathrm{NaF}\) )

Fluoride ion (\(\mathrm{F}^{-}\)) is the conjugate base of a weak acid (\(\mathrm{HF}\)), producing a basic solution.

Step 7: Sodium Acetate Analysis ( \(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\) )

Acetate ion (\(\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}\)) is the conjugate base of a weak acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2}\mathrm{H}\), making the solution basic.

Step 8: Aluminum Chloride Analysis ( \(\mathrm{AlCl}_{3}\) )

\(\mathrm{AlCl}_{3}\) is acidic. The \(\mathrm{Al}^{3+}\) ion can hydrolyze in water to form acidic solutions. Therefore, \(\mathrm{AlCl}_{3}\) will yield the lowest pH.

Step 9: Determine Highest and Lowest pH

The most basic solution is \(\mathrm{Na}_{2} \mathrm{S}\) due to the strong \(\mathrm{S}^{2-}\) base, and the most acidic solution is \(\mathrm{AlCl}_{3}\) due to \(\mathrm{Al}^{3+}\).

Key Concepts

Salt Solutions

When salts dissolve in water, they can affect the solution's pH based on the nature of their ions. Whether a solution is acidic, basic, or neutral depends on the ions derived from the salt once dissolved.

• Salts of strong acids and strong bases, such as \( ext{NaCl}\), usually produce a neutral pH.
• Salts containing the conjugate base of a weak acid, like \( ext{NaF}\) with the fluoride ion, typically form basic solutions.
• Conversely, salts containing metal cations of weak bases, such as \( ext{AlCl}_3\), can make acidic solutions.

To predict the pH of a salt solution, identify the parent acid and base of the salt's ionic components. Strong acids and bases dissociate completely in water, influencing whether the resulting solution is neutral, acidic, or basic.

Conjugate Base

The conjugate base of a substance is formed when an acid donates a proton during a chemical reaction. In the presence of water, this conjugate base affects the solution's pH.

• The stronger the base, the higher the pH or the more basic the solution becomes.
• In reverse, a weak conjugate base from a strong acid has little effect on the pH, keeping the solution neutral.

For example, \( ext{Na}_2 ext{S}\) forms a basic solution because the sulfide ion \( ext{S}^{2-}\) is the conjugate base of the weak acid \( ext{HS}^-\). Similarly, the acetate ion \( ext{CH}_3 ext{CO}_2^-\) from \( ext{NaCH}_3 ext{CO}_2\) is the conjugate base of acetic acid, which is also weak, resulting in a basic solution. On the other hand, \( ext{AlCl}_3\) contains the \( ext{Al}^{3+}\) ion, not a traditional conjugate base, leading to an acidic solution due to its effect on water.

Acidic and Basic Solutions

Acidic and basic solutions form based on the interaction between water and dissolved salt ions. A solution's pH is determined by the balance of hydronium ions (H extsubscript{3}O extsuperscript{+}) and hydroxide ions (OH extsuperscript{-}).

• An acidic solution means excess hydronium ions, often resulting from metal cations like \( ext{Al}^{3+}\), which can hydrolyze water to release \( ext{H}^{+}\) ions.
• Basic solutions have more hydroxide ions, attributable to the presence of strong conjugate bases like \( ext{S}^{2-}\) or \( ext{CH}_3 ext{CO}_2^-\), which accept protons from water, increasing OH extsuperscript{-} concentration.

In our examples, \( ext{Na}_2 ext{S}\) and \( ext{Na}_3 ext{PO}_4\) are alkaline because of their strong conjugate base ions. \( ext{AlCl}_3\) produces \( ext{H}_3 ext{O}^+\) ions, making its solution acidic.

Hydrolysis of Metal Ions

Hydrolysis of metal ions is a process where metal cations interact with water, altering the solution's pH by either producing additional hydronium or hydroxide ions. This process is prevalent in salts where the metal cation is a high charge density ion, like \( ext{Al}^{3+}\).

• The \( ext{Al}^{3+}\) ion is capable of hydrolyzing water because of its strong positive charge, pulling electrons towards it, facilitating the release of \( ext{H}^{+}\).
• This increases the concentration of \( ext{H}_3 ext{O}^+\), lowering the pH, hence, making it more acidic.

When \( ext{AlCl}_3\) dissolves, \( ext{Al}^{3+}\) ions produce an acidic solution due to their interaction with water molecules. This is a pivotal concept when predicting the acidic nature of solutions formed from metal salt hydrolysis.