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A 25.0mL solution of 0.100MCH3COOH is titrated with a 0.200MKOH solution. Calculate the pH after the following additions of the KOH solution: (a) 0.0 mL, (b) 5.0 mL (c) 10.0 mL (d) 12.5 mL (e) 15.0 mL

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 (CH3COOH) before any KOH is added. The moles of CH3COOH is given by moles=volume×molarity. Hence, 0.025 L×0.100 M=0.0025 moles.
02

Determine pH Before Addition of KOH (0.0 mL)

Since no base is added, the solution contains only CH3COOH, a weak acid with Ka=1.8×105. Set up the equilibrium CH3COOHH++CH3COO. Create the ICE table, solve for x using the approximation Ka=x20.100xx20.100. Solving for x, x=1.8×106, gives x=1.34×103. Therefore, pH=log(1.34×103)2.87.
03

After Addition of 5.0 mL KOH

Calculate moles of KOH added: 0.005 L×0.200 M=0.001 moles. Compute remaining CH3COOH: 0.00250.001=0.0015 moles. Form CH3COO at same moiety of 0.001 moles. Use the Henderson-Hasselbalch equation: pH=pKa+log(0.0010.0015). With pKa=4.74, pH=4.74+log(0.667)4.56.
04

After Addition of 10.0 mL KOH

Calculate moles of KOH added: 0.01 L×0.200 M=0.002 moles. Compute remaining CH3COOH: 0.00250.002=0.0005 moles. Form CH3COO at 0.002 moles with excess.Use Henderson-Hasselbalch equation: pH=pKa+log(0.0020.0005). With pKa=4.74, pH=4.74+log(4)5.34.
05

After Addition of 12.5 mL KOH (Equivalence Point)

Calculate moles of KOH added: 0.0125 L×0.200 M=0.0025 moles. This is equal to initial moles of CH3COOH, resulting in complete titration. At the equivalence point, concentration of [CH3COO] in 37.5 mL total solution is 0.00250.0375=0.0667 M. Calculate [OH] using Kw/Ka: Kb=1.0×10141.8×105, and find OH concentration. Finally, find pH = 8.72.
06

After Addition of 15.0 mL KOH

Calculate moles of KOH added: 0.015 L×0.200 M=0.003 moles. Excess OH = 0.0030.0025=0.0005 moles. Calculate [OH] as 0.00050.040=0.0125 M. Calculate pOH = log(0.0125)1.90, giving pH=141.90=12.10.

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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 (CH3COOH) is in water, it partly dissociates into its ions: H+ (a proton) and CH3COO (acetate ion). This dissociation can be expressed by an equilibrium expression reflecting the balance between the reactants and products.
  • The more the acid dissociates, the stronger it is.
  • Equilibrium concepts help us understand this dissociation in quantitative terms.

The equilibrium constant Ka for a weak acid is defined as:Ka=[H+][CH3COO][CH3COOH]Here, Ka provides insight into the position of the equilibrium and the strength of the acid. A higher Ka value means a stronger acid which dissociates more. In acetic acid titration, knowing the Ka allows calculation of the changes in H+ concentration as the base is added.
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 (CH3COOH) and its conjugate base (CH3COO) are present, you use the equation:pH=pKa+log([A][HA])
  • pKa is the negative logarithm of the acid dissociation constant.
  • The fraction [A][HA] 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 [H+]. During titration of acetic acid with KOH, the pH changes at each step: initial, any point before and after equivalence, and finally when excess base is present.
  • Before adding any KOH, the pH depends on undissociated acetic acid, calculated using its Ka.
  • 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 KOH changes the pH as it consumes H+ and increases [OH]. To compute the resulting pH, conversion from [OH] to pOH and accordingly to pH, via pH=14pOH, is necessary once excess OH is present. Consistently track these changes to accurately predict solution acidity or basicity.

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