Problem 53 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The correct order of increasing \(\left[\mathrm{OH}^{-}\right]\) in the following aqueous solution is (a) \(0.01 \mathrm{M}-\mathrm{NaHCO}_{3}<0.01 \mathrm{M}-\mathrm{NaCN}\) \(<0.01 \mathrm{M}-\mathrm{KCl}\) (b) \(0.01 \mathrm{M}-\mathrm{KCl}<0.01 \mathrm{M}-\mathrm{NaCN}\) \(<0.01 \mathrm{M}-\mathrm{NaHCO}_{3}\) (c) \(0.01 \mathrm{M}-\mathrm{KCl}<0.01 \mathrm{M}-\mathrm{NaHCO}_{3}\) \(<0.01 \mathrm{M}-\mathrm{NaCN}\) (d) \(0.01 \mathrm{M}-\mathrm{NaCN}<0.01 \mathrm{M}-\mathrm{KCl}\) \(<0.01 \mathrm{M}-\mathrm{NaHCO}_{3}\)

Step-by-Step Solution

Answer

The correct order is (c) 0.01 M-KCl < 0.01 M-NaHCO3 < 0.01 M-NaCN.

Step 1: Identify the Nature of Compounds

Analyze each compound to determine if it is acidic, basic, or neutral in water. Sodium bicarbonate (NaHCO3) is a weak base since HCO3- can accept H+. Sodium cyanide (NaCN) is a weak base since CN- is a strong nucleophile and can remove H+ from water to form HCN and OH-. Potassium chloride (KCl) is neutral, as it completely dissociates into K+ and Cl-, neither of which react with water to change the OH- concentration.

Step 2: Compare Basic Strength

Since KCl is neutral, it doesn't affect the OH- concentration. Comparing NaHCO3 and NaCN, under the same conditions, species with stronger base (or weaker conjugate acid) will produce more OH-. HCN is a weaker acid than H2CO3, hence CN- is a stronger base than HCO3-.

Step 3: Arrange in Increasing order of [OH-]

Since NaCN will produce more OH- than NaHCO3, and KCl does not affect OH- levels, the order should go from the neutral compound KCl to the weaker base NaHCO3, and then to the stronger base NaCN.

Key Concepts

Acid-Base Equilibrium

Understanding acid-base equilibrium is essential for grasping the behavior of solutions in water. It's a condition where the rate of the forward reaction (acid dissociating into its ions) equals the rate of the backward reaction (ions recombining into the acid), leading to a steady-state concentration of products and reactants. In aqueous solutions, acids and bases can be strong or weak, determining their tendency to donate or accept protons (H+). The pH of the solution is indicative of its acidity or basicity, which is derived from the concentration of hydrogen ions () or hydroxide ions (). The stronger the acid or base, the further the equilibrium lies to the side of ions, meaning more H+ or OH- will be present in the solution.

Chemical Solution Ranking

The chemical solution ranking involves ordering solutions based on a particular property, like the hydroxide ion concentration (). This process is crucial for chemists to anticipate how solutions will behave in reactions. Regarding the hydroxide ion concentration, we typically arrange solutions to show an increase in basicity. To accurately rank solutions, we must consider both the concentration of the solute and the nature of the solute, i.e., whether it’s acidic, basic, or neutral. Solutions with higher concentrations of OH- are more basic and are ranked higher in the context of basicity. In the given exercise, ranking is based on the assumption that each solution has the same molarity, thereby highlighting the importance of the chemical nature of the compounds involved.

Weak Bases and Conjugate Acids

When discussing weak bases and their conjugate acids, one must remember that a weak base does not fully dissociate in water, and thus, equilibrium is established between the base and its conjugate acid. The conjugate acid forms when the base accepts a proton (H+). Its strength is inversely related to the strength of the base: the weaker the base, the stronger its conjugate acid, and vice versa. In solutions, this relationship affects the pH and indirectly influences the concentration of OH-. For example, in the exercise, NaCN is a weak base with a conjugate acid HCN; NaHCO3's conjugate acid is H2CO3. By analyzing the acidity of their conjugate acids, we determined that CN- is a stronger base than HCO3-, which then dictates the order of the solutions in terms of increasing OH- concentration.