Enrol to start learning
Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.
3.2.4. Example Calculations
Interactive Audio Lesson
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free account
Today, we're going to discuss how to calculate pH for weak acids. Let's start with the general dissociation equation for a weak acid. Who can remind me what that looks like?
I think it’s HA ⇌ H⁺ + A⁻.
That's correct! Now, what about the expression for the acid dissociation constant, Ka?
Ka = [H⁺] × [A⁻] / [HA].
Exactly! Now, here’s a memory aid: think of Ka as the Key Acid that unlocks the 'H' from 'HA'. Now, if we have a weak acid called formic acid with a concentration of 0.020 M and a Ka of 1.8 × 10⁻⁴, how would we find 'x', which represents the concentration of [H⁺]?
We can use the approximation: x ≈ sqrt(Ka × C₀) right, since Ka is small?
Spot on! Let's calculate it. What do we get when we plug in the numbers?
It should be x ≈ sqrt[(1.8 × 10⁻⁴) × (0.020)] which equals about 1.9 × 10⁻³ M.
Yes, which leads us to calculate the pH. Who can tell us how to calculate that?
pH = -log₁₀(x), so pH = -log₁₀(1.9 × 10⁻³).
Great! And what does that give us?
The pH is approximately 2.72.
Perfect! And then what’s the percent ionization?
9.5%!
Wonderful! Always remember, the equation for percent ionization is: percent ionization = (x / C₀) × 100%. Today we covered how to calculate pH and percent ionization!
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free account
Now that we've discussed weak acids, let's transition to weak bases. What’s the dissociation equation for a weak base?
B + H₂O ⇌ BH⁺ + OH⁻.
Exactly! And how do we find the Kb for this equation?
Kb = [BH⁺] × [OH⁻] / [B].
Right again! Now, let’s take pyridine with a concentration of 0.10 M and Kb of 1.7 × 10⁻⁹. What will 'x' be using the same approximation we did for weak acids?
x ≈ sqrt(Kb × C₀) = sqrt[(1.7 × 10⁻⁹) × (0.10)].
Correct! Let’s calculate that.
That equals about 1.30 × 10⁻⁵ M.
Excellent! Now how would we find the pH from this?
First we need pOH, which is -log₁₀(1.30 × 10⁻⁵), and that gives us about 4.89. So pH is 14.00 - 4.89.
Exactly! And what’s the final pH?
The pH is approximately 9.11.
Perfect, team! Don’t forget, the process for weak bases mirrors that of weak acids, solidifying your foundational knowledge. Today, we covered weak base calculations!
Overview
Short Summary
This section covers example calculations related to acid-base dissociation constants, showcasing how to compute pH, percent ionization, and the relationships among weak acids and bases.
Medium Summary
In this section, various example calculations are discussed, focusing on the calculations of pH for weak acids and bases using their dissociation constants. It elaborates on how to determine the concentration of hydronium ions, percent ionization, and demonstrates using specific examples like formic acid and pyridine to illustrate these principles.
Detailed Summary
Example Calculations
This section provides detailed example calculations for weak acids and bases in relation to their dissociation constants. Key concepts include the acid dissociation constant (Ka) for weak acids and the base dissociation constant (Kb) for weak bases.
Key Points Covered:
-
Weak Acid Calculations:
- The dissociation of a weak acid (HA) is represented as:
- HA ⇌ H⁺ + A⁻.
- The Ka expression is given by: Ka = [H⁺] × [A⁻] / [HA].
- Calculations typically involve approximations when Ka is small relative to the initial concentration, allowing for the use of x ≈ sqrt(Ka × C₀).
-
Example Calculation for Formic Acid:
- For 0.020 M formic acid (HCOOH, Ka = 1.8 × 10⁻⁴):
- x ≈ sqrt[(1.8 × 10⁻⁴) × (0.020)] ≈ 1.9 × 10⁻³ M, delivering a pH of approximately 2.72 and percent ionization of 9.5%.
-
Weak Base Calculations:
- The dissociation of a weak base (B) is represented as:
- B + H₂O ⇌ BH⁺ + OH⁻.
- The Kb expression is given by: Kb = [BH⁺] × [OH⁻] / [B].
- Similar approximations can apply for Kb when it's small relative to C₀.
-
Example Calculation for Pyridine:
- For 0.10 M pyridine (C₅H₅N, Kb = 1.7 × 10⁻⁹):
- x ≈ sqrt[(1.7 × 10⁻⁹) × (0.10)] ≈ 1.30 × 10⁻⁵ M, leading to pH calculation resulting in approximately 9.11 with a very small percent protonation.
These calculations are essential for understanding acid-base behavior in solutions and have practical applications in various chemical contexts.
Audio Book
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountExample 1: Formic Acid (HCOOH, Ka = 1.8 × 10⁻⁴) at 0.020 M
- C₀ = 0.020 M. Ka = 1.8 × 10⁻⁴.
- x ≈ sqrt(Ka × C₀) = sqrt[(1.8 × 10⁻⁴) × 0.020] = sqrt(3.6 × 10⁻⁶) ≈ 1.9 × 10⁻³ M.
- [H plus] = 1.9 × 10⁻³ M → pH = – log₁₀ (1.9 × 10⁻³) ≈ 2.72.
- Percent ionization = (1.9 × 10⁻³ ÷ 0.020) × 100% = 9.5%.
Detailed Explanation
This example illustrates the pH calculation for formic acid, a weak acid. The initial concentration (C₀) and the acid dissociation constant (Ka) are provided. We find the concentration of hydrogen ions ([H plus]) using the formula x ≈ sqrt(Ka × C₀). This helps us calculate pH using the relation pH = -log₁₀([H plus]). Additionally, we determine how much of the acid ionizes by calculating the percent ionization.
Examples & Analogies
Think of mixing lemonade. The amount of lemon juice you add represents the weak acid. Even if you don't see the lemon juice fully mixing in, some of it will dissolve and provide the sour taste—or in our case, generate hydrogen ions that affect the pH. Just like determining how much lemon juice you need for the right sourness, we calculate percent ionization to understand how much of the acid is effectively contributing to the pH.
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountExample 2: Pyridine (C₅H₅N, Kb = 1.7 × 10⁻⁹) at 0.10 M
- C₀ = 0.10 M. Kb = 1.7 × 10⁻⁹.
- x ≈ sqrt(Kb × C₀) = sqrt[(1.7 × 10⁻⁹) × 0.10] = sqrt(1.7 × 10⁻¹⁰) ≈ 1.30 × 10⁻⁵ M.
- [OH minus] = 1.30 × 10⁻⁵ M → pOH = – log₁₀ (1.30 × 10⁻⁵) ≈ 4.89 → pH = 14.00 – 4.89 = 9.11.
- Percent protonation (i.e., percent of B converted to BH plus) = (x ÷ 0.10) × 100% = 0.013%. Very small.
Detailed Explanation
In this example, we calculate the pH of pyridine, a weak base. We start with the initial concentration (C₀) and the base dissociation constant (Kb). Similar to the weak acid example, we use the approximation x ≈ sqrt(Kb × C₀) to find the concentration of hydroxide ions ([OH minus]). pOH is derived from that, and we convert it to pH using the equation pH = 14.00 - pOH. The very low percent protonation indicates that only a tiny fraction of pyridine reacts to form its conjugate acid.
Examples & Analogies
Imagine trying to dissolve a tiny amount of salt in water. Even if you add just a pinch, it can still change the taste of the water, but only slightly—similar to weak bases like pyridine, where the small amount that forms hydroxide ions still impacts pH, but most remains unchanged.
--
Key Concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
Weak Acid: A substance that only partially dissociates in solution, allowing for an equilibrium between its acid and ions.
Weak Base: A substance that only partially accepts protons in solution, creating an equilibrium involving hydroxide ions.
pH Calculation: The process of determining the acidity of a solution using the concentration of hydrogen ions, typically involving logarithmic calculations.
Percent Ionization: A way to express the strength of a weak acid or base by showing the fraction that dissociates into ions.
Examples
Step-by-step examples to apply the section's ideas and test your understanding.
Example 1: For formic acid (HCOOH) with Ka = 1.8 × 10⁻⁴ at 0.020 M: x ≈ sqrt(1.8 × 10⁻⁴ × 0.020) = 1.9 × 10⁻³ M, leading to pH ≈ 2.72.
Example 2: For pyridine (C₅H₅N) with Kb = 1.7 × 10⁻⁹ at 0.10 M: x ≈ sqrt(1.7 × 10⁻⁹ × 0.10) = 1.30 × 10⁻⁵ M, leading to pH ≈ 9.11.
Memory Aids
Interactive tools to help you remember key concepts
Stories
Flash Cards
Glossary
Acid Dissociation Constant (Ka)
A measure of the strength of an acid in solution, representing the equilibrium constant for its dissociation.
Base Dissociation Constant (Kb)
A measure of the strength of a base in solution, representing the equilibrium constant for its dissociation.
pH
A logarithmic scale used to specify the acidity or basicity of an aqueous solution.
Percent Ionization
A measure of the extent of ionization of a weak acid or base, calculated as (concentration of ionized acid/base / initial concentration) × 100%.