Example Calculations (3.2.4) - Unit 8: Acids and Bases - IB 11 Chemistry
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Example Calculations

Example Calculations

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Practice

Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Weak Acid Calculations

πŸ”’ Unlock Audio Lesson

Sign up and enroll to listen to this audio lesson

0:00
--:--
Teacher
Teacher Instructor

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?

Student 1
Student 1

I think it’s HA β‡Œ H⁺ + A⁻.

Teacher
Teacher Instructor

That's correct! Now, what about the expression for the acid dissociation constant, Ka?

Student 2
Student 2

Ka = [H⁺] Γ— [A⁻] / [HA].

Teacher
Teacher Instructor

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 Γ— 10⁻⁴, how would we find 'x', which represents the concentration of [H⁺]?

Student 3
Student 3

We can use the approximation: x β‰ˆ sqrt(Ka Γ— Cβ‚€) right, since Ka is small?

Teacher
Teacher Instructor

Spot on! Let's calculate it. What do we get when we plug in the numbers?

Student 4
Student 4

It should be x β‰ˆ sqrt[(1.8 Γ— 10⁻⁴) Γ— (0.020)] which equals about 1.9 Γ— 10⁻³ M.

Teacher
Teacher Instructor

Yes, which leads us to calculate the pH. Who can tell us how to calculate that?

Student 1
Student 1

pH = -log₁₀(x), so pH = -log₁₀(1.9 Γ— 10⁻³).

Teacher
Teacher Instructor

Great! And what does that give us?

Student 2
Student 2

The pH is approximately 2.72.

Teacher
Teacher Instructor

Perfect! And then what’s the percent ionization?

Student 3
Student 3

9.5%!

Teacher
Teacher Instructor

Wonderful! Always remember, the equation for percent ionization is: percent ionization = (x / Cβ‚€) Γ— 100%. Today we covered how to calculate pH and percent ionization!

Weak Base Calculations

πŸ”’ Unlock Audio Lesson

Sign up and enroll to listen to this audio lesson

0:00
--:--
Teacher
Teacher Instructor

Now that we've discussed weak acids, let's transition to weak bases. What’s the dissociation equation for a weak base?

Student 4
Student 4

B + Hβ‚‚O β‡Œ BH⁺ + OH⁻.

Teacher
Teacher Instructor

Exactly! And how do we find the Kb for this equation?

Student 1
Student 1

Kb = [BH⁺] Γ— [OH⁻] / [B].

Teacher
Teacher Instructor

Right again! Now, let’s take pyridine with a concentration of 0.10 M and Kb of 1.7 Γ— 10⁻⁹. What will 'x' be using the same approximation we did for weak acids?

Student 2
Student 2

x β‰ˆ sqrt(Kb Γ— Cβ‚€) = sqrt[(1.7 Γ— 10⁻⁹) Γ— (0.10)].

Teacher
Teacher Instructor

Correct! Let’s calculate that.

Student 3
Student 3

That equals about 1.30 Γ— 10⁻⁡ M.

Teacher
Teacher Instructor

Excellent! Now how would we find the pH from this?

Student 4
Student 4

First we need pOH, which is -log₁₀(1.30 Γ— 10⁻⁡), and that gives us about 4.89. So pH is 14.00 - 4.89.

Teacher
Teacher Instructor

Exactly! And what’s the final pH?

Student 1
Student 1

The pH is approximately 9.11.

Teacher
Teacher Instructor

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!

Introduction & Overview

Read summaries of the section's main ideas at different levels of detail.

Quick Overview

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.

Standard

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

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:

  1. Weak Acid Calculations:
  2. The dissociation of a weak acid (HA) is represented as:
  3. HA β‡Œ H⁺ + A⁻.
  4. The Ka expression is given by: Ka = [H⁺] Γ— [A⁻] / [HA].
  5. Calculations typically involve approximations when Ka is small relative to the initial concentration, allowing for the use of x β‰ˆ sqrt(Ka Γ— Cβ‚€).
  6. Example Calculation for Formic Acid:
  7. For 0.020 M formic acid (HCOOH, Ka = 1.8 Γ— 10⁻⁴):
  8. x β‰ˆ sqrt[(1.8 Γ— 10⁻⁴) Γ— (0.020)] β‰ˆ 1.9 Γ— 10⁻³ M, delivering a pH of approximately 2.72 and percent ionization of 9.5%.
  9. Weak Base Calculations:
  10. The dissociation of a weak base (B) is represented as:
  11. B + Hβ‚‚O β‡Œ BH⁺ + OH⁻.
  12. The Kb expression is given by: Kb = [BH⁺] Γ— [OH⁻] / [B].
  13. Similar approximations can apply for Kb when it's small relative to Cβ‚€.
  14. Example Calculation for Pyridine:
  15. For 0.10 M pyridine (Cβ‚…Hβ‚…N, Kb = 1.7 Γ— 10⁻⁹):
  16. x β‰ˆ sqrt[(1.7 Γ— 10⁻⁹) Γ— (0.10)] β‰ˆ 1.30 Γ— 10⁻⁡ 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

Dive deep into the subject with an immersive audiobook experience.

Example 1: Formic Acid (HCOOH)

Chapter 1 of 2

πŸ”’ Unlock Audio Chapter

Sign up and enroll to access the full audio experience

0:00
--:--

Chapter Content

Example 1: Formic Acid (HCOOH, Ka = 1.8 Γ— 10⁻⁴) at 0.020 M

  • Cβ‚€ = 0.020 M. Ka = 1.8 Γ— 10⁻⁴.
  • x β‰ˆ sqrt(Ka Γ— Cβ‚€) = sqrt[(1.8 Γ— 10⁻⁴) Γ— 0.020] = sqrt(3.6 Γ— 10⁻⁢) β‰ˆ 1.9 Γ— 10⁻³ M.
  • [H plus] = 1.9 Γ— 10⁻³ M β†’ pH = – log₁₀ (1.9 Γ— 10⁻³) β‰ˆ 2.72.
  • Percent ionization = (1.9 Γ— 10⁻³ Γ· 0.020) Γ— 100% = 9.5%.

Detailed Explanation

This example illustrates the pH calculation for formic acid, a weak acid. The initial concentration (Cβ‚€) and the acid dissociation constant (Ka) are provided. We find the concentration of hydrogen ions ([H plus]) using the formula x β‰ˆ sqrt(Ka Γ— Cβ‚€). 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 tasteβ€”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.

Example 2: Pyridine (Cβ‚…Hβ‚…N)

Chapter 2 of 2

πŸ”’ Unlock Audio Chapter

Sign up and enroll to access the full audio experience

0:00
--:--

Chapter Content

Example 2: Pyridine (Cβ‚…Hβ‚…N, Kb = 1.7 Γ— 10⁻⁹) at 0.10 M

  • Cβ‚€ = 0.10 M. Kb = 1.7 Γ— 10⁻⁹.
  • x β‰ˆ sqrt(Kb Γ— Cβ‚€) = sqrt[(1.7 Γ— 10⁻⁹) Γ— 0.10] = sqrt(1.7 Γ— 10⁻¹⁰) β‰ˆ 1.30 Γ— 10⁻⁡ M.
  • [OH minus] = 1.30 Γ— 10⁻⁡ M β†’ pOH = – log₁₀ (1.30 Γ— 10⁻⁡) β‰ˆ 4.89 β†’ pH = 14.00 – 4.89 = 9.11.
  • Percent protonation (i.e., percent of B converted to BH plus) = (x Γ· 0.10) Γ— 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 (Cβ‚€) and the base dissociation constant (Kb). Similar to the weak acid example, we use the approximation x β‰ˆ sqrt(Kb Γ— Cβ‚€) 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 slightlyβ€”similar to weak bases like pyridine, where the small amount that forms hydroxide ions still impacts pH, but most remains unchanged.

Key Concepts

  • 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 & Applications

Example 1: For formic acid (HCOOH) with Ka = 1.8 Γ— 10⁻⁴ at 0.020 M: x β‰ˆ sqrt(1.8 Γ— 10⁻⁴ Γ— 0.020) = 1.9 Γ— 10⁻³ M, leading to pH β‰ˆ 2.72.

Example 2: For pyridine (Cβ‚…Hβ‚…N) with Kb = 1.7 Γ— 10⁻⁹ at 0.10 M: x β‰ˆ sqrt(1.7 Γ— 10⁻⁹ Γ— 0.10) = 1.30 Γ— 10⁻⁡ M, leading to pH β‰ˆ 9.11.

Memory Aids

Interactive tools to help you remember key concepts

🎡

Rhymes

For acids weak, consider Ka, it tells how much H⁺ can sway.

πŸ“–

Stories

Imagine you’re at a calm lake; the weak acid is a boat that rocks gently, but doesn’t fall off: that’s like how it partially ionizes.

🧠

Memory Tools

Remember: HΒ²O for acids (H2O helps you recall acidity and its basis).

🎯

Acronyms

K represents the strength in Ka

Key Acid gives way!

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) Γ— 100%.

Reference links

Supplementary resources to enhance your learning experience.

Next Activity

Practice Section

Apply what you’ve learned with hands-on practice.