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Question

What is the pH of 1.5 L of vinegar that is 3% acetic acid by mass ? (Ka=1.8×105)

A
12
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B
4.3
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C
7
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D
2.5
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Solution

The correct option is D 2.5
Assume that the vinegar is really just a solution of acetic acid in water, and that density = 1 g mL1
So if the vinegar is 3% acetic acid by mass and the molar mass of CH3COOH=60.05 g mol1, then
1.5L vinegar×1000 mL1 L×1 g1 mL×3g acetic acid100 g vinegar×1mol acetic acid60.05g acetic acid=0.75 mol CH3COOH
Dividing 0.75 mol by 1.5 L to get an initial concentration of 0.50 M,
considering the ionization of acetic acid in water into acetate ion and hydronium ion. ignoring the concentration of water (a pure liquid).
CH3COOH(aq)+H2O(aq)CH3COO2(aq)+H3O+(aq)
CH3COOHH2OCH3COOH3O+Initial0.5...00Changex...+x+xEquilibrium0.5x...xx
the equilibrium constant expression
Ka=[CH3COO][H3O+][CH3COOH]
1.8×105=[x][x][0.5x]
here x can be neglected because it is very small so, 0.5-x=0.5

x=0.003M=[H3O+]
put up into the formula
pH=log[H3O+]pH=log(0.003)=2.5

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