Salts and pH Calculation Notes

Salts

Salts are ionic compounds formed from the reaction between an acid and a base.

• Example:

  NaOH + HCl \rightarrow H_2O + NaCl

  NH_4OH+HCl\rightarrow H_2O+NH_4Cl

Salt Behavior in Water

Salts dissociate into their constituent ions when dissolved in water.

• Examples:

  NaCl \rightarrow Na^+ + Cl^-

  NH_4Cl\rightarrow NH_4^{+}+Cl^{-}

Ions can undergo hydrolysis, reacting with water.

• Example:

  NH_4^{+}+H_2O\rightarrow NH_3+H_3O^{+}

  The extent of hydrolysis depends on the strength of the ion.

Result of Hydrolysis

Hydrolysis can lead to acidic, basic, or neutral salt solutions.

• Examples:

  • Acidic: NH_4^{+}+H_2O\rightarrow NH_3+H_3O^{+} (solution is acidic)

  • Basic: CO_3^{2-}+H_2O\rightarrow HCO_3^{-}+OH- (solution is basic)

  • Neutral: Cl^{-}+H_2O\rightleftharpoons Cl^{-}+H_2O (no significant reaction, solution is neutral)

Determining Hydrolysis Strength

The strength of an ion in hydrolysis depends on the acid or base it originates from:

Rationale:

Consider the equilibrium of a strong acid like HCl:

HCl \rightleftharpoons H^+ + Cl^-

• Strong acids dissociate almost completely, shifting the equilibrium to the right.

• Cl^- is unlikely to react with H_2Oto reform HCl.

Steps to Predict pH of a Salt Solution

1. Identify the Origin: Determine the acid and base from which the salt ions are derived.

2. Assess Hydrolysis: Determine if the ions will hydrolyze based on whether they came from a strong or weak acid/base.

   • Ions from strong acids/bases do not hydrolyze (neutral contribution).

   • Ions from weak acids/bases will hydrolyze (acidic or basic contribution).

3. Determine Hydrolysis Effect: If an ion hydrolyzes, determine if it will form an acidic or basic solution.

4. Determine the Overall Contribution: Determine the combined effect of each ion's contribution to the solution's pH.

   • Acidic + Neutral: Acidic

   • Basic + Neutral: Basic

   • Neutral + Neutral: Neutral

   • Acidic + Basic: Requires comparison of Ka and Kb values.

5. Acidic + Basic Solutions: Compare the Ka and Kb values of the ions.

   • The ion with the higher value will dominate the solution's pH. But you usually only have them for the STARTING acid/base they came from.

   • Ka > Kb: Acidic

   • Ka < Kb: Basic

   • Ka = Kb: Neutral

Finding Ka and Kb

Use the following equation:

Kw = Ka \times K_b

• If you want Ka of an ion, you need Kb of the base it came from

• If you want to find Kb, you need Ka from the acid is came from

Example: Use Kb ofNH^3\left(1.8\times10^{-5}\right) plug in and solve for Ka

(1 \times 10^{-14}) = K_a(ion) \times (1.8 \times 10^{-5})

Ka_{\left(ion\right)}NH_4^{+}=5.56\times10^{-10}

Practice Problems

Problem #1: KBr

Is KBr an acidic, basic, or neutral salt?

• K^+ comes from KOH, a strong base. Therefore, K^+ is a weaker acid and does not hydrolyze (neutral effect).

• Br^- comes from HBr, a strong acid. Therefore, Br^- is a weaker base and does not hydrolyze (neutral effect).

• Conclusion: KBr is a NEUTRAL salt.

Problem #2: K2CO3

Is K_2CO_3 an acidic, basic, or neutral salt?

• K^+ comes from KOH, a strong base. Therefore, K^+ is a weaker acid and does not hydrolyze (neutral effect).

• CO_3^{2-} comes from H_2CO_3 ,a weak acid, therefore,CO_3^{2-} is a stronger base and will hydrolyze (basic effect).

• Conclusion: K_2CO_3is a BASIC salt.

Problem #3: NH_4Br

Is NH_4Br an acidic, basic, or neutral salt?

• NH4^+ comes from NH3, a weak base. Therefore, NH_4^+ is a stronger acid and will hydrolyze (acidic effect).

• Br^- comes from HBr, a strong acid. Therefore, Br^- is a weaker base and does not hydrolyze (neutral effect).

• Conclusion: NH_4Br is an ACIDIC salt.

Problem #4: NH_4CN

Is NH_4CN an acidic, basic, or neutral salt?

• NH4^+ comes from NH3, a weak base. Therefore, NH_4^+ is a stronger acid and will hydrolyze (acidic effect).

• CN^- comes from HCN, a weak acid. Therefore, CN^- is a stronger base and will hydrolyze (basic effect).

• To determine the overall effect, compare Ka and Kb values:

  • Kb(NH3) = 1.8 \times 10^{-5}

  • K_a(HCN) = 4.9 x 10^{-10}

  • Ka(NH4^+) = (1.0 \times 10^{-14}) / (1.8 \times 10^{-5}) = 5.56 \times 10^{-10}

  • K_b(CN^-) = (1.0 \times 10^{-14}) / (4.9 \times 10^{-10}) = 2.04 \times 10^{-5}

  • Since Ka(NH4^+) < Kb(CN^-), NH4CN is a BASIC salt!

Calculating the Actual pH of Salts

To calculate the actual pH value:

1. Determine which ion is the "strong" one (the one being hydrolyzed).

2. Write the hydrolysis reaction for that ion(s).

3. Use an ICE table to determine the equilibrium concentrations.

4. Find \H_3O^+ or OH^- from the ICE table.

5. Calculate the pH using the appropriate formula.

Practice Problem #5: 0.25M NH4NO3

What is the pH of a 0.25M NH4NO3 salt solution?

• NH4^+ comes from NH3, a weak base. Therefore, NH_4^+ is a stronger acid and will hydrolyze (acidic effect).

• NO3^- comes from HNO3, a strong acid. Therefore, NO_3^- is a weaker base and does not hydrolyze (neutral effect).

• Conclusion: NH4NO3 is an ACIDIC salt!

• NH_4^+ is the ion contributing the acidic effect.

  • Hydrolysis: NH4^+ + H2O \rightleftharpoons NH3 + H3O^+

  • We have Kb(NH3) = 1.8 \times 10^{-5}

  • Calculate Ka(NH4^+): Ka(NH4^+) = (1.0 \times 10^{-14}) / (1.8 \times 10^{-5}) = 5.56 \times 10^{-10}

ICE Table

Ka = \frac{[NH3][H3O^+]}{[NH4^+]} = \frac{x^2}{0.25 - x} = 5.56 \times 10^{-10}

Assume x is small (less than 5% of 0.25), so 0.25 - x ≈ 0.25

\frac{x^2}{0.25} = 5.56 \times 10^{-10}

x^2 = 0.25 \times 5.56 \times 10^{-10}

x = \sqrt{0.25 \times 5.56 \times 10^{-10}} = 1.18 \times 10^{-5}

$[H_3O^+] = 1.18 \times 10^{-5}$

pH = -log(1.18 \times 10^{-5}) = 4.93