Chapter 17: Problem 35
A
Short Answer
Expert verified
(a) 2.87, (b) 4.56, (c) 5.34, (d) 8.72, (e) 12.10
Step by step solution
01
Initial Setup
First, identify the initial moles of acetic acid ( ) before any is added. The moles of is given by . Hence, .
02
Determine pH Before Addition of KOH (0.0 mL)
Since no base is added, the solution contains only , a weak acid with . Set up the equilibrium . Create the ICE table, solve for using the approximation . Solving for , , gives . Therefore, .
03
After Addition of 5.0 mL KOH
Calculate moles of added: . Compute remaining : . Form at same moiety of . Use the Henderson-Hasselbalch equation: . With , .
04
After Addition of 10.0 mL KOH
Calculate moles of added: . Compute remaining : . Form at with excess.Use Henderson-Hasselbalch equation: . With , .
05
After Addition of 12.5 mL KOH (Equivalence Point)
Calculate moles of added: . This is equal to initial moles of , resulting in complete titration. At the equivalence point, concentration of in 37.5 mL total solution is . Calculate using : , and find concentration. Finally, find .
06
After Addition of 15.0 mL KOH
Calculate moles of added: . Excess = . Calculate as . Calculate pOH = , giving .
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Acid-Base Equilibrium
Acid-base equilibrium is crucial for understanding reactions between acids and bases in solutions. When a weak acid like acetic acid ( ) is in water, it partly dissociates into its ions: (a proton) and (acetate ion). This dissociation can be expressed by an equilibrium expression reflecting the balance between the reactants and products.
The equilibrium constant for a weak acid is defined as: Here, provides insight into the position of the equilibrium and the strength of the acid. A higher value means a stronger acid which dissociates more. In acetic acid titration, knowing the allows calculation of the changes in concentration as the base is added.
- The more the acid dissociates, the stronger it is.
- Equilibrium concepts help us understand this dissociation in quantitative terms.
The equilibrium constant
Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation is a simplified method for pH calculations in buffer solutions, turning the complex equilibrium dynamics into more manageable arithmetic. It assists in determining the pH during titrations involving weak acids or bases and their salts.
When a weak acid ( ) and its conjugate base ( ) are present, you use the equation:
This equation presumes that the concentrations of acid and conjugate base are similar, a condition often met in buffer solutions or pre-equivalence stages of titration. It's a powerful tool for pH prediction as it accounts for shifts in concentration due to added base or acid.
When a weak acid (
is the negative logarithm of the acid dissociation constant.- The fraction
is the ratio of the concentration of the conjugate base to the acid.
This equation presumes that the concentrations of acid and conjugate base are similar, a condition often met in buffer solutions or pre-equivalence stages of titration. It's a powerful tool for pH prediction as it accounts for shifts in concentration due to added base or acid.
pH Calculation
Calculating pH is about determining the acidity or basicity of a solution quantitatively, using the concentration of hydrogen ions . During titration of acetic acid with , the pH changes at each step: initial, any point before and after equivalence, and finally when excess base is present.
Each addition of changes the pH as it consumes and increases . To compute the resulting pH, conversion from to and accordingly to pH, via , is necessary once excess is present. Consistently track these changes to accurately predict solution acidity or basicity.
- Before adding any
, the pH depends on undissociated acetic acid, calculated using its . - The titration equivalence point is when equal moles of acid and base react, often resulting in a different pH due to the nature of the resulting solution.
- Beyond the equivalence point, pH depends on excess base.
Each addition of