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Consider the titration of 100.0 mL of 0.200 M acetic acid () by 0.100 M . Calculate the pH of the resulting solution after the following volumes of have been added.

User Jjwchoy
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1 Answer

4 votes

Answer:

A) 2.7218

B) 4.2676

C) 4.7447

D) 5.6990

E) 8.7843

F) 11.5086

Step-by-step explanation:

A)

When 0.0 mL of KOH is added ,

CH3COOH dissociates as:

CH3COOH ⇒ H⁺ + CH3COO⁻

0.2 0 0

0.2-x x x

Kₐ = [H⁺][CH3COO⁻] / [CH3COOH]

Kₐ = x*x / (c-x)

Assuming x can be ignored as compared to c, the above expression becomes

Kₐ = x*x / c

so, x = √Kₐ.c

x = √((1.8*10⁻⁵)*0.2) = 1.897*10⁻³

since c is much greater than x, then our assumption is correct

so, x = 1.897*10⁻³ M

use:

pH = -log [H⁺]

= -log (1.897*10⁻³)

= 2.7218

B)

When 50.0 mL of KOH is added

Given:

M(CH3COOH) = 0.2 M

V(CH3COOH) = 100 mL

M(KOH) = 0.1 M

V(KOH) = 50 mL

mol(CH3COOH) = M(CH3COOH) * V(CH3COOH)

mol(CH3COOH) = 0.2 M * 100 mL

= 20 mmol

mol(KOH) = M(KOH) * V(KOH)

mol(KOH) = 0.1 M * 50 mL = 5 mmol

We have:

mol(CH3COOH) = 20 mmol

mol(KOH) = 5 mmol

5 mmol of both will react

excess CH3COOH remaining = 15 mmol

Volume of Solution = 100 + 50 = 150 mL

[CH3COOH] = 15 mmol / 150 mL = 0.1M

[CH3COO⁻] = 5 / 150 = 0.0333M

They form acidic buffer

acid is CH3COOH

conjugate base is CH3COO⁻

Kₐ = 1.8*10⁻⁵

pKₐ = -log (Kₐ)

= -log(1.8*10⁻⁵)

= 4.745

use:

pH = pKₐ + log (conjugate base / acid)

= 4.745 + log {3.333*10⁻² / 0.1}

= 4.268

C)

When 100.0 mL of KOH is added

Given:

M(CH3COOH) = 0.2 M

V(CH3COOH) = 100 mL

M(KOH) = 0.1 M

V(KOH) = 100 mL

mol(CH3COOH) = M(CH3COOH) * V(CH3COOH)

mol(CH3COOH) = 0.2 M * 100 mL = 20 mmol

mol(KOH) = M(KOH) * V(KOH)

mol(KOH) = 0.1 M * 100 mL = 10 mmol

We have:

mol(CH3COOH) = 20 mmol

mol(KOH) = 10 mmol

10 mmol of both will react

excess CH3COOH remaining = 10 mmol

Volume of Solution = 100 + 100 = 200 mL

[CH3COOH] = 10 mmol / 200 mL = 0.05M

[CH3COO-] = 10/200 = 0.05M

They form acidic buffer

acid is CH3COOH

conjugate base is CH3COO⁻

Kₐ = 1.8*10⁻⁵

pKₐ = -log (Kₐ)

= -log(1.8*10⁻⁵)

= 4.745

use:

pH = pKₐ + log (conjugate base / acid)

= 4.745 + log (5*10⁻² / 5*10⁻²)

= 4.745

D)

When 180.0 mL of KOH is added

Given:

M(CH3COOH) = 0.2 M

V(CH3COOH) = 100 mL

M(KOH) = 0.1 M

V(KOH) = 180 mL

mol(CH3COOH) = M(CH3COOH) * V(CH3COOH)

mol(CH3COOH) = 0.2 M * 100 mL = 20 mmol

mol(KOH) = M(KOH) * V(KOH)

mol(KOH) = 0.1 M * 180 mL = 18 mmol

We have:

mol(CH3COOH) = 20 mmol

mol(KOH) = 18 mmol

18 mmol of both will react

excess CH3COOH remaining = 2 mmol

Volume of Solution = 100 + 180 = 280 mL

[CH3COOH] = 2 mmol / 280 mL = 0.0071M

[CH3COO-] = 18/280 = 0.0643M

They form acidic buffer

acid is CH3COOH

conjugate base is CH3COO⁻

Kₐ = 1.8*10⁻⁵

pKₐ = -log (Kₐ)

= -log(1.8*10⁻⁵)

= 4.745

use:

pH = pKₐ + log (conjugate base / acid)

= 4.745 + log (6.429*10⁻² / 7.143*10⁻³)

= 5.699

E)

When 200.0 mL of KOH is added

Given:

M(CH3COOH) = 0.2 M

V(CH3COOH) = 100 mL

M(KOH) = 0.1 M

V(KOH) = 200 mL

mol(CH3COOH) = M(CH3COOH) * V(CH3COOH)

mol(CH3COOH) = 0.2 M * 100 mL = 20 mmol

mol(KOH) = M(KOH) * V(KOH)

mol(KOH) = 0.1 M * 200 mL = 20 mmol

We have:

mol(CH3COOH) = 20 mmol

mol(KOH) = 20 mmol

20 mmol of both will react to form CH3COO⁻ and H₂O

CH3COO⁻ here is strong base

CH3COO⁻ formed = 20 mmol

Volume of Solution = 100 + 200 = 300 mL

Kb of CH3COO- = Kw / Ka = 1*10⁻¹⁴ / 1.8*10⁻⁵ = 5.556*10⁻¹⁰

concentration of CH3COO⁻, c = 20 mmol / 300 mL = 0.0667M

CH3COO⁻ dissociates as

CH3COO⁻ + H₂O ⇒ CH3COOH + OH⁻

0.0667 0 0

0.0667-x x x

Kb = [CH3COOH][OH-] / [CH3COO-]

Kb = x*x / (c-x)

Assuming x can be ignored as compared to c

So, above expression becomes

Kb = x*x / c

so, x = √Kb.c

x = √((5.556*10⁻¹⁰) * 6.667*10⁻²) = 6.086*10⁻⁶

since c is much greater than x, our assumption is correct

so, x = 6.086*10⁻⁶ M

[OH⁻] = x = 6.086*10⁻⁶ M

use:

pOH = -log [OH⁻]

= -log (6.086*10⁻⁶)

= 5.2157

use:

PH = 14 - pOH

= 14 - 5.2157

= 8.7843

F)

When 210.0 mL of KOH is added

Given:

M(CH3COOH) = 0.2 M

V(CH3COOH) = 100 mL

M(KOH) = 0.1 M

V(KOH) = 210 mL

mol(CH3COOH) = M(CH3COOH) * V(CH3COOH)

mol(CH3COOH) = 0.2 M * 100 mL = 20 mmol

mol(KOH) = M(KOH) * V(KOH)

mol(KOH) = 0.1 M * 210 mL = 21 mmol

We have:

mol(CH3COOH) = 20 mmol

mol(KOH) = 21 mmol

20 mmol of both will react

excess KOH remaining = 1 mmol

Volume of Solution = 100 + 210 = 310 mL

[OH⁻] = 1 mmol / 310 mL = 0.0032 M

use:

pOH = -log [OH⁻]

= -log (3.226*10⁻³)

= 2.4914

use:

PH = 14 - pOH

= 14 - 2.4914

= 11.5086

User Phenwoods
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