Calculate The Ph of A 0.20 M Solution of Nh4br

Introduction

The pH of a solution is a logarithmic measure of the concentration of hydrogen ions (H⁺) in the solution. It is calculated using the formula:

For a solution of NH4Br, which is a salt of a weak base (NH3) and a strong acid (HBr), the pH can be determined using the following steps:

1. Calculate the concentration of NH3 (the conjugate base of NH4⁺).
2. Use the Ka value of NH3 to find the equilibrium concentration of NH3.
3. Calculate the pH from the equilibrium concentration of NH3.

How to Calculate the pH

Step 1: Understand the Dissociation

NH4Br dissociates in water according to the following reaction:

NH3 is a weak base with a dissociation constant (Ka) of 1.8 × 10⁻⁵. The HBr is a strong acid that completely dissociates in water.

Step 2: Set Up the Equilibrium Equation

The equilibrium equation for NH3 is:

The Ka expression for this reaction is:

Step 3: Calculate the Equilibrium Concentrations

For a 0.20 M solution of NH4Br, the initial concentration of NH3 is 0.20 M (since NH4Br dissociates completely into NH3 and HBr).

Let x be the equilibrium concentration of NH3 that dissociates. At equilibrium:

Substituting into the Ka expression:

Solving this quadratic equation gives the value of x.

Step 4: Calculate the pH

Once x is known, the pH can be calculated using the concentration of OH⁻:

Example Calculation

Let's calculate the pH of a 0.20 M solution of NH4Br step by step.

Step 1: Assume Initial Concentrations

Initial [NH3] = 0.20 M

Step 2: Solve the Ka Equation

Solving this equation gives x ≈ 0.00134 M.

Step 3: Calculate [OH⁻]

[OH⁻] = x ≈ 0.00134 M

Step 4: Calculate pOH and pH

The calculated pH of a 0.20 M solution of NH4Br is approximately 11.13.

Interpreting the Results

A pH of 11.13 indicates that the solution is basic. This is expected because NH4Br dissociates to form NH3, which is a weak base.

The pH increases as the concentration of NH4Br increases because more NH3 is available to dissociate and form OH⁻ ions.