Chapter 17: Problem 57
Calculate the hydronium ion concentration and \(\mathrm{pH}\) in a \(0.20 \mathrm{M}\) solution of ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl}\).
Short Answer
Expert verified
[H鈧僌鈦篯 for 0.20 M NH鈧凜l is approximately calculated using K鈧 and then pH is found from \(-\log[H鈧僌鈦篯\).
Step by step solution
01
Understand the Problem
We have a 0.20 M solution of ammonium chloride (NH鈧凜l), which is a salt formed from a weak base (NH鈧凮H) and a strong acid (HCl). This solution will act as an acidic solution because NH鈧勨伜 can donate a proton to water, forming hydronium ions, which we need to calculate.
02
Write the Reaction Equation
NH鈧凜l dissociates in water to produce NH鈧勨伜 ions. The ammonium ions then react with water to form hydronium ions:
NH鈧勨伜 + H鈧侽 鈬 NH鈧 + H鈧僌鈦. This equilibrium reaction will help us determine the H鈧僌鈦 concentration.
03
Use the Equilibrium Expression
The equilibrium constant for the reaction is the ionization constant of NH鈧勨伜, represented as K鈧. First, find K鈧 using the relation K鈧 = \( \dfrac{K_w}{K_b} \), where K_w is the ion-product constant for water \(1.0 \times 10^{-14} \) and K_b is the base ionization constant for NH鈧凮H. Use given or standard tables to find these constants.
04
Set Up the Equilibrium Table
Create a table showing initial concentrations (initially, [NH鈧勨伜] = 0.20 M and [H鈧僌鈦篯 = [NH鈧僝 = 0), the change in concentrations, and equilibrium concentrations. Let 'x' be the change in concentration to form H鈧僌鈦 and NH鈧. Therefore, equilibrium concentrations are [NH鈧勨伜] = 0.20 - x, [H鈧僌鈦篯 = x, and [NH鈧僝 = x.
05
Solve the Equilibrium Equation
Using the K鈧 expression for NH鈧勨伜: \( K鈧 = \dfrac{[NH鈧僝[H鈧僌鈦篯}{[NH鈧勨伜]} \) Substitute the equilibrium concentrations into the expression: \( K鈧 = \dfrac{x^2}{0.20-x} \). Assuming 0.20-x 鈮 0.20 (because x is small), solve for x to find [H鈧僌鈦篯.
06
Calculate pH
Once the [H鈧僌鈦篯 is determined, use the formula for pH: \( ext{pH} = -\log[H鈧僌鈦篯 \). Evaluate the logarithm to find the pH of the solution.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Hydronium Ion Concentration
When working with solutions like ammonium chloride, it is crucial to calculate the hydronium ion concentration.
Ammonium chloride, with a concentration of 0.20 M, dissociates fully in water to form ammonium ions (NH鈧勨伜).
These ammonium ions can interact with water molecules to form hydronium ions (H鈧僌鈦).
This reaction can be represented as:
- NH鈧勨伜 + H鈧侽 鈬 NH鈧 + H鈧僌鈦
Equilibrium Expression
An equilibrium expression helps quantify the relationship between the concentrations of reactants and products in a chemical reaction at equilibrium. For the reaction involving NH鈧勨伜 and water:
- NH鈧勨伜 + H鈧侽 鈬 NH鈧 + H鈧僌鈦
- \[ K鈧 = \dfrac{[NH鈧僝[H鈧僌鈦篯}{[NH鈧勨伜]} \]
Ammonium Chloride Solution
Ammonium chloride (NH鈧凜l) is a white crystalline solid that is highly soluble in water.
When dissolved, it dissociates into ammonium ions (NH鈧勨伜) and chloride ions (Cl鈦).
Ammonium chloride solutions tend to be acidic due to the weak base (NH鈧凮H) and strong acid (HCl) from which it originates.
The balanced dissociation equation in water is:
- NH鈧凜l 鈫 NH鈧勨伜 + Cl鈦
Ionization Constant
The ionization constant, or K鈧, is crucial when dealing with weak acids or bases and their salts like ammonium chloride. It represents the strength of the acid or base in a solution, showing how readily it donates protons. For NH鈧勨伜, you can find K鈧 using the formula:
- \[ K鈧 = \dfrac{K_w}{K_b} \]