Problem 262 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{pH}\) of \(0.005 \mathrm{M}\) calcium acetate (pKa of \(\mathrm{CH}_{3} \mathrm{COOH}\) \(=4.74\) ) is (a) \(7.37\) (b) \(9.37\) (c) \(9.26\) (d) \(8.37\)

Step-by-Step Solution

Answer

The pH of 0.005 M calcium acetate is 9.26, corresponding to option (c).

Step 1: Determine the Source of Acidity or Basicity

Calcium acetate dissociates into calcium ions and acetate ions in solution. The acetate ion ( ext{CH}_3 ext{COO}^- ) is the conjugate base of acetic acid ( ext{CH}_3 ext{COOH}), which has a given ext{pKa} of 4.74. Therefore, acetate can accept protons from water, making the solution basic.

Step 2: Calculate the Concentration of Acetate Ion

Since calcium acetate ext{Ca(CH}_3 ext{COO})_2 dissociates completely, its initial concentration of 0.005 M will result in 0.01 M of acetate ion ( ext{CH}_3 ext{COO}^- ). This is because each formula unit provides two acetate ions.

Step 3: Apply Henderson-Hasselbalch Equation

Use the Henderson-Hasselbalch equation for bases: \[ pH = 14 - (pK_a + ext{log} rac{[ ext{HA}]}{[ ext{A}^-]}) \]Since the solution contains only ext{A}^- (acetate ion), \[ pH = 14 - (4.74 + ext{log} rac{0}{0.01}) \]Simplifying, we have:\[ pH = 14 - (4.74 - ext{log}(0.01)) \]Since the log of zero is undefined, we actually directly use the solution's concentration.\[ pH = 14 - (4.74 - (-2)) = 9.26 \]

Step 4: Choose the Correct pH from Given Options

Compare the calculated ext{pH} of 9.26 with the given options. The closest match is option (c) 9.26, which is correctly calculated.

Key Concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a powerful tool used in chemistry to estimate the pH of a solution containing a weak acid or base and its conjugate pair. This equation relates the pH, the pK\(_a\) (which is the negative logarithm of the acid dissociation constant), and the concentrations of an acid-base conjugate system.

For a basic solution, the formula is given by:

• \( pH = 14 - (pK_a + \log \frac{[HA]}{[A^-]}) \)

Here, \([HA]\) stands for the concentration of the weak acid, and \([A^-]\) indicates the concentration of its conjugate base. In cases where the concentration of the acid (\([HA]\)) is zero, the equation simplifies to rely solely on the base concentration.

This equation gives you insight into how acidity and basicity fluctuate in a solution when you tweak the concentrations of the components. It is an essential part of calculating pH when dealing with weak acids and bases.

weak acids and bases

Weak acids and bases do not completely dissociate in solution, which means not all molecules break apart into their ionic forms. This partial dissociation is what gives these substances their characteristic behaviors.

When you have a weak acid, it dissociates into its conjugate base and protons. Similarly, a weak base picks up protons to form its conjugate acid.

• Weak acids, like acetic acid \((\text{CH}_3\text{COOH})\), have a specific \(pK_a\) value, which indicates their propensity to donate protons.
• Weak bases, or their conjugate forms like the acetate ion \((\text{CH}_3\text{COO}^-)\), accept protons and have known counterparts in acidic forms.

The extent to which these compounds dissociate is not absolute, allowing for equilibrium balance and pH control in various solutions. The weaker the acid or base, the less likely it is to fully dissociate in water, affecting the solution's pH.

dissociation in solution

Dissociation in solution refers to the process where molecules split into smaller particles, usually ions, when dissolved in a solvent like water. This process is critically important in understanding how weak acids and bases react in solutions.

For compounds like calcium acetate \((\text{Ca(CH}_3\text{COO})_2)\), dissociation involves the separation into calcium ions \((\text{Ca}^{2+})\) and acetate ions \((\text{CH}_3\text{COO}^-)\). Each formula unit of calcium acetate releases two acetate ions into the solution.

• This dissociation is essential because the free ions in solution determine the overall chemical behavior, such as the balance of acidity or basicity.
• The degree of dissociation influences the calculated pH using formulas like the Henderson-Hasselbalch equation, particularly under conditions where one ion form is predominant.
• Complete dissociation is assumed for strong acids and bases, whereas partial dissociation characterizes weak acids and bases, affecting calculations of solution concentrations.

Recognizing how substances dissociate in solution is vital when predicting and controlling the pH of the substance in the aqueous environment.