The pH of a solution of NH3 and NH4Br is 8.90. What is the molarity of NH4Br if the molarity of NH3 is 0.016 M?

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

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Identify the relevant chemical equilibrium: \(\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-\). This is the equilibrium for ammonia acting as a base.

Use the given pH to find the pOH: \(\text{pOH} = 14 - \text{pH}\). Calculate the hydroxide ion concentration, \([\text{OH}^-]\), using \([\text{OH}^-] = 10^{-\text{pOH}}\).

Write the expression for the base dissociation constant, \(K_b\), for ammonia: \(K_b = \frac{[\text{NH}_4^+][\text{OH}^-]}{[\text{NH}_3]}\). Use the known \(K_b\) value for ammonia.

Assume that the change in concentration of \(\text{NH}_3\) due to dissociation is negligible, so \([\text{NH}_3] \approx 0.016 \text{ M}\). Substitute \([\text{OH}^-]\) and \([\text{NH}_3]\) into the \(K_b\) expression to solve for \([\text{NH}_4^+]\).

Since \([\text{NH}_4^+]\) comes from the dissociation of \(\text{NH}_4\text{Br}\), the molarity of \(\text{NH}_4\text{Br}\) is equal to \([\text{NH}_4^+]\).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, the NH3/NH4Br system acts as a buffer, maintaining a pH of 8.90, which is crucial for understanding the equilibrium between the ammonia and ammonium ions.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acidic and basic components. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base (NH3) and [HA] is the concentration of the acid (NH4+). This equation is essential for calculating the molarity of NH4Br based on the given pH and the concentration of NH3.

Equilibrium and Ka/Kb Values

The equilibrium constant (Ka for acids and Kb for bases) quantifies the strength of an acid or base in solution. For NH3, a weak base, its Kb value can be used to find the pKa of its conjugate acid (NH4+). Understanding these values is important for determining the relationship between the concentrations of NH3 and NH4Br in the buffer solution, which ultimately helps in calculating the molarity of NH4Br.