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Weak Acid Calculations
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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 itโs HA โ Hโบ + Aโป.
That's correct! Now, what about the expression for the acid dissociation constant, Ka?
Ka = [Hโบ] ร [Aโป] / [HA].
Exactly! Now, hereโs 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 ร 10โปโด, how would we find 'x', which represents the concentration of [Hโบ]?
We can use the approximation: x โ sqrt(Ka ร Cโ) 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 โ sqrt[(1.8 ร 10โปโด) ร (0.020)] which equals about 1.9 ร 10โปยณ M.
Yes, which leads us to calculate the pH. Who can tell us how to calculate that?
pH = -logโโ(x), so pH = -logโโ(1.9 ร 10โปยณ).
Great! And what does that give us?
The pH is approximately 2.72.
Perfect! And then whatโs the percent ionization?
9.5%!
Wonderful! Always remember, the equation for percent ionization is: percent ionization = (x / Cโ) ร 100%. Today we covered how to calculate pH and percent ionization!
Weak Base Calculations
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Now that we've discussed weak acids, let's transition to weak bases. Whatโs the dissociation equation for a weak base?
B + HโO โ BHโบ + OHโป.
Exactly! And how do we find the Kb for this equation?
Kb = [BHโบ] ร [OHโป] / [B].
Right again! Now, letโs take pyridine with a concentration of 0.10 M and Kb of 1.7 ร 10โปโน. What will 'x' be using the same approximation we did for weak acids?
x โ sqrt(Kb ร Cโ) = sqrt[(1.7 ร 10โปโน) ร (0.10)].
Correct! Letโs calculate that.
That equals about 1.30 ร 10โปโต M.
Excellent! Now how would we find the pH from this?
First we need pOH, which is -logโโ(1.30 ร 10โปโต), and that gives us about 4.89. So pH is 14.00 - 4.89.
Exactly! And whatโs the final pH?
The pH is approximately 9.11.
Perfect, team! Donโt forget, the process for weak bases mirrors that of weak acids, solidifying your foundational knowledge. Today, we covered weak base calculations!
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
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:
- Weak Acid Calculations:
- The dissociation of a weak acid (HA) is represented as:
- HA โ Hโบ + Aโป.
- The Ka expression is given by: Ka = [Hโบ] ร [Aโป] / [HA].
- Calculations typically involve approximations when Ka is small relative to the initial concentration, allowing for the use of x โ sqrt(Ka ร Cโ).
- Example Calculation for Formic Acid:
- For 0.020 M formic acid (HCOOH, Ka = 1.8 ร 10โปโด):
- x โ sqrt[(1.8 ร 10โปโด) ร (0.020)] โ 1.9 ร 10โปยณ 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 + HโO โ BHโบ + OHโป.
- The Kb expression is given by: Kb = [BHโบ] ร [OHโป] / [B].
- Similar approximations can apply for Kb when it's small relative to Cโ.
- Example Calculation for Pyridine:
- For 0.10 M pyridine (Cโ Hโ N, Kb = 1.7 ร 10โปโน):
- x โ sqrt[(1.7 ร 10โปโน) ร (0.10)] โ 1.30 ร 10โปโต 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.
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Example 1: Formic Acid (HCOOH)
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Example 1: Formic Acid (HCOOH, Ka = 1.8 ร 10โปโด) at 0.020 M
- Cโ = 0.020 M. Ka = 1.8 ร 10โปโด.
- x โ sqrt(Ka ร Cโ) = sqrt[(1.8 ร 10โปโด) ร 0.020] = sqrt(3.6 ร 10โปโถ) โ 1.9 ร 10โปยณ M.
- [H plus] = 1.9 ร 10โปยณ M โ pH = โ logโโ (1.9 ร 10โปยณ) โ 2.72.
- Percent ionization = (1.9 ร 10โปยณ รท 0.020) ร 100% = 9.5%.
Detailed Explanation
This example illustrates the pH calculation for formic acid, a weak acid. The initial concentration (Cโ) and the acid dissociation constant (Ka) are provided. We find the concentration of hydrogen ions ([H plus]) using the formula x โ sqrt(Ka ร Cโ). This helps us calculate pH using the relation pH = -logโโ([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 tasteโor 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 (Cโ Hโ N)
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Example 2: Pyridine (Cโ Hโ N, Kb = 1.7 ร 10โปโน) at 0.10 M
- Cโ = 0.10 M. Kb = 1.7 ร 10โปโน.
- x โ sqrt(Kb ร Cโ) = sqrt[(1.7 ร 10โปโน) ร 0.10] = sqrt(1.7 ร 10โปยนโฐ) โ 1.30 ร 10โปโต M.
- [OH minus] = 1.30 ร 10โปโต M โ pOH = โ logโโ (1.30 ร 10โปโต) โ 4.89 โ pH = 14.00 โ 4.89 = 9.11.
- Percent protonation (i.e., percent of B converted to BH plus) = (x รท 0.10) ร 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 (Cโ) and the base dissociation constant (Kb). Similar to the weak acid example, we use the approximation x โ sqrt(Kb ร Cโ) 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 slightlyโsimilar to weak bases like pyridine, where the small amount that forms hydroxide ions still impacts pH, but most remains unchanged.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Weak Acid: A substance that only partially dissociates in solution, allowing for an equilibrium between its acid and ions.
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Weak Base: A substance that only partially accepts protons in solution, creating an equilibrium involving hydroxide ions.
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pH Calculation: The process of determining the acidity of a solution using the concentration of hydrogen ions, typically involving logarithmic calculations.
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Percent Ionization: A way to express the strength of a weak acid or base by showing the fraction that dissociates into ions.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example 1: For formic acid (HCOOH) with Ka = 1.8 ร 10โปโด at 0.020 M: x โ sqrt(1.8 ร 10โปโด ร 0.020) = 1.9 ร 10โปยณ M, leading to pH โ 2.72.
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Example 2: For pyridine (Cโ Hโ N) with Kb = 1.7 ร 10โปโน at 0.10 M: x โ sqrt(1.7 ร 10โปโน ร 0.10) = 1.30 ร 10โปโต M, leading to pH โ 9.11.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
๐ต Rhymes Time
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For acids weak, consider Ka, it tells how much Hโบ can sway.
๐ Fascinating Stories
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Imagine youโre at a calm lake; the weak acid is a boat that rocks gently, but doesnโt fall off: thatโs like how it partially ionizes.
๐ง Other Memory Gems
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Remember: HยฒO for acids (H2O helps you recall acidity and its basis).
๐ฏ Super Acronyms
K represents the strength in Ka
- Key Acid gives way!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Acid Dissociation Constant (Ka)
Definition:
A measure of the strength of an acid in solution, representing the equilibrium constant for its dissociation.
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Term: Base Dissociation Constant (Kb)
Definition:
A measure of the strength of a base in solution, representing the equilibrium constant for its dissociation.
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Term: pH
Definition:
A logarithmic scale used to specify the acidity or basicity of an aqueous solution.
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Term: Percent Ionization
Definition:
A measure of the extent of ionization of a weak acid or base, calculated as (concentration of ionized acid/base / initial concentration) ร 100%.