Problem 68 - Chemistry

Question

Compare the \(\mathrm{pH}\) values for \(0.10-\mathrm{M}\) solutions of \(\mathrm{NaOH}\) and of \(\mathrm{NH}_{3}\) to illustrate the difference between a strong base and a weak base.

Step-by-Step Solution

Answer

NaOH has a pH of 13 (strong base), while NH₃ has a pH of 11.13 (weak base).

Step 1: Determine the pH of NaOH Solution

NaOH is a strong base, meaning it fully dissociates in water. For a \(0.10\,\text{M}\) NaOH solution, the hydroxide ion concentration \([ ext{OH}^-]\) is \(0.10\,\text{M}\). To find the \(\text{pH}\), first calculate the \(\text{pOH}\): \(\text{pOH} = -\log [\text{OH}^-] = -\log(0.10) = 1\). Then use the relation \(\text{pH} + \text{pOH} = 14\) to find \(\text{pH} = 14 - 1 = 13\).

Step 2: Determine the pH of NH₃ Solution

NH₃ is a weak base, it partially dissociates in water. Use the equilibrium equation: \(\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-\). \(K_b\) for NH₃ is \(1.8 \times 10^{-5}\). Use the expression \(K_b = \frac{[\text{NH}_4^+][\text{OH}^-]}{[\text{NH}_3]}\) and assume \(x = [\text{OH}^-]\), \(K_b = \frac{x^2}{0.10 - x} \approx \frac{x^2}{0.10}\), solving the quadratic gives \(x \approx 1.34 \times 10^{-3}\,\text{M}\). Now, \(\text{pOH} = -\log (1.34 \times 10^{-3}) \approx 2.87\), and \(\text{pH} = 14 - 2.87 = 11.13\).

Step 3: Compare the pH Values

The \(\text{pH}\) of \(0.10\,\text{M}\) NaOH is 13, indicating a strong base with complete dissociation. The \(\text{pH}\) of \(0.10\,\text{M}\) NH₃ is 11.13, showing a weaker base with incomplete dissociation. This illustrates the difference in pH levels between strong and weak bases at the same concentration.

Key Concepts

Strong Base

A strong base is a substance that completely dissociates into its ions in water. This means that every molecule of a strong base that dissolves in water splits into its respective ions. As a result, strong bases drastically increase the [OH^-] concentration in a solution. One of the most common examples of a strong base is sodium hydroxide (NaOH).

• Complete Dissociation: In an aqueous solution, NaOH will fully dissociate to form Na⁺ and OH^- ions. Therefore, the concentration of OH^- ions in the solution is equal to the concentration of the NaOH solution you start with.
• Effect on pH: Because of this complete dissociation, strong bases will have high pH values. In our example, a 0.10 M NaOH solution has a pH of 13, indicating a very basic (or alkaline) solution.

Weak Base

Contrary to strong bases, weak bases only partially dissociate in water. This means that only a small fraction of the base molecules release ions into the solution. Ammonia (NH₃) is a classic example of a weak base.

• Partial Dissociation: NH₃ does not entirely dissociate into ions in aqueous solutions. Instead, it establishes an equilibrium between the ammonia molecules and the ions (NH₃ + H₂O ⇌ NH₄⁺ + OH⁻).
• Effect on pH: Due to partial dissociation, the concentration of OH⁻ ions in a weak base solution is lower compared to strong bases with the same concentration. For example, a 0.10 M solution of NH₃ results in a pH of 11.13, signifying a less basic solution compared to a strong base.

NaOH

Sodium hydroxide (NaOH) is not just any base; it is one of the most common strong bases used in laboratory and industrial processes. It is important to understand its properties to handle it safely and effectively.

• Powers of NaOH: In water, NaOH completely dissociates into sodium (Na⁺) and hydroxide (OH⁻) ions. Because of this property, NaOH is highly effective at raising the pH of a solution.
• Handling NaOH: Due to its strong basic nature, NaOH solutions are corrosive and can cause severe burns. It's crucial to use protective gear when handling NaOH solutions.
• Applications: NaOH is used in the manufacturing of soap, paper, and as a cleaning agent to dissolve grease and oils.

NH₃

Ammonia (NH₃) is a weak base that finds a range of applications due to its properties in solution. Unlike strong bases, it only partially dissociates in water, which affects its behavior in chemical reactions.

• Properties: Ammonia interacts with water to form ammonium (NH₄⁺) and hydroxide (OH⁻) ions, establishing an equilibrium in the solution. Its base nature allows it to be used in household cleaning products and fertilizer production.
• Role in pH: As a weak base, NH₃ will increase the pH of a solution, though not as significantly as a strong base like NaOH. This makes it suitable for applications where moderate pH adjustment is needed.
• Application: It is widely used as a refrigerant, in the production of fertilizers, and in water purification processes due to its effectiveness to neutralize acids and its balance between reactivity and safety.