Author: J R Reid

Chapter 5Volumetric Analysis

CONCEPT OF VOLUMETRIC ANALYSIS

The reactants will react with the standard solution from burette of a known concentration called titrant.

The analyte in which the concentration to be determined is placed in a conical flask.

The appropriate indicator will add into the conical flaks to determine the end point, showed by the color changing of the indicator

Involves a neutralization reaction in which an acid is reacted with an equivalent amount of base

Titration curve - pH of the solution versus volume of titrant added

Titrant - usually strong standard acid or strong base

Equivalence point - is the point of stoichiometric equivalence between the analyte and the reagent

End point - a point when reaction is completed

ACID BASE TITRATION

CALCULATIONS

Write the balanced chemical equation for the reaction

Extract all the relevant information from the question

Check that data for consistency, for example, concentrations are usually given in M or mol L-1 but volumes are often given in mL. You will need to convert the mL to L for consistency. The easiest way to do this is to multiply the volume in mL x 10-3

Calculate the moles of reactant (n) for which you have both the volume(V) and concentration(M) : n = M x V

From the balanced chemical equation find the mole ratio known reactant : unknown reactant

Use the mole ratio to calculate the moles of the unknown reactant

From the volume(V) of unknown reactant and its previously calculated moles(n), calculate its concentration(M): M = n ÷ V

EXAMPLES

Question: 30 mL of 0.10 M NaOH neutralised 25.0 mL of HCl. Determine the concentration of the acid

Write the balanced chemical equation for the reaction      NaOH(aq) + HCl(aq) -----> NaCl(aq) + H2O(l)

Extract the relevant information from the question:      NaOH      V = 30 mL, M = 0.10M       HCl      V = 25.0 mL, M = ?

Check the data for consistency      NaOH      V = 30 x 10-3 L , M = 0.10 M       HCl      V = 25.0 x 10-3 L, M = ?

Calculate moles NaOH      n(NaOH) = M x V = 0.10 x 30 x 10-3 = 3 x 10-3 moles

From the balanced chemical equation find the mole ratio      NaOH:HCl      1:1

Find moles HCl      NaOH: HCl is 1:1      So n(NaOH) = n(HCl) = 3 x 10-3 moles at the equivalence point

Calculate concentration of HCl: M = n ÷ V      n = 3 x 10-3 mol,       V = 25.0 x 10-3 L      M(HCl) = 3 x 10-3 ÷ 25.0 x 10-3 = 0.12 M or 0.12 mol L-1

SELF-EXERCISE

1. 50mL of 0.2mol L-1 NaOH neutralised 20mL of H2SO4. Determine the concentration of the acid (0.25 M)

2. 25.0mL of 0.05M Ba(OH)2 neutralised 40.0mL of nitric acid. Determine the concentration of the acid. (0.0625 M)

WATER DISSOCIATION

Water is an amphoteric solvent that is having acidic and basic properties.

H2O H+ + OH-

Kw= [H+][OH-]= 1.0 x 10-14

[H+]= [OH-]= 1.0 x 10-7 M

Kw=molar equilibrium constant

pH CALCULATIONS

pH= -log [H+]

pKw=pH + pOH

At 25oC, Kw= 1.0 x 10-14, then

14 = pH + pOH

When [H+]=[OH-]=1.0 x 10-7 M or pH=pOH=7, the solution is neutral.

If [H+]>[OH-] or pH<7, acidic solution. If [H+]<[OH-] or pH>7, basic solution.

EXAMPLE:

Calculate

a) pKw for water ionization constant

b) pH and pOH values for 1.5 x 10-3 M hydrogen ion solution.

Solution:

a)pKw = -log Kw

= -log 1.0 x 10-14 = 14.00

b) [H+] = 1.5 x 10-3 M

pH= -log 1.5 x 10-3 = 2.82 pOH= 14.00 - 2.82 =11.18

WEAK ACID AND WEAK BASE

Weak acid and weak bases will ionize partially The acidity constant (Ka) is used to calculate the total H+ that has

ionized The basicity constant (Kb) is used to calculate the total amount of

OH- ionized. e.g: acetic acid with a concentration of C

CH3COOH H+ + CH3COO-

Initial (M) C 0 0Equilibrium (M) C-x x x

Ka= [H+][CH3COO-] = 1.75 x 10-5

[CH3COOH]

(x)(x) = 1.75 x 10-5

C-x If x at the denominator is neglected, the general formula to determine [H+] for weak acid (HA) with a concentration of CHA:

[H+]= √KaCHA

For weak base, e.g NH3 with basicity constant, Kb will undergo the following reaction in water. NH3 + H2O NH4

++ OH-

The same method can be applied to determine [OH-] for a weak base (B) with a concentration of CB is:[OH-] = √KbCB

EXAMPLE Calculate the pH of 1.0 x 10-2 M acetic acid solution. Ka for acetic

acid is 1.75 x 10-5.

Solution CH3COOH H+ + CH3COO-

Initial(M) 1.00 x 10-2 0 0 Equilibrium (M) 1.00 x 10-2-x x xKa = [H+] [CH3COO-]= 1.75 x 10-5

[CH3COOH] (x)(x) = 1.75 x 10-5

1.00 x 10-2-xX at the denominator can be neglected since C > 100 Ka

(x)(x) = 1.75 X 10-5

1.00 x 10-2

x = 4.18 x 10-4 M = [H+] pH= -log 4.18 x 10-4 = 3.38

SELF-EXERCISE

Calculate the pH and pOH of a 1.00 x 10-3 M solution of acetic acid.

(answer: pH=3.88;pOH=10.12)

TITRATION OF STRONG ACID WITH STRONG BASE

The titrant and the analyte ionize completely since strong acid and strong base dissociate completely

e.g: titration between HCl and NaOH

HCl + NaOH H2O + NaCl

NaOH (aq) + HCl (aq) H2O (l) + NaCl (aq)

TITRATION CURVE STRONG ACID WITH STRONG BASE

• Before addition of NaOH

- pH = 1.00

• When the NaOH added

- pH increase slowly at first

• Near the equivalence point (the point which equimolar amounts of acid and base have reacted)

- the curve rises almost vertically

• Beyond the equivalence point

- pH increases slowly

CALCULATION OF pH AT EVERY STAGE OF TITRATION

1) After addition of 10.0 mL of 0.100 M NaOH to 25.0 mL of 0.100 M HCl

Total volume = 35.0 mL

i) Moles of NaOH in 10.0 mL

ii) Moles of HCl in 25.0 mL

M = mol L = 0.1 x (10 mL/1000 mL)= 1.00 x 10-3 mol

M = mol L = 0.1 x (25 mL/1000 mL)= 2.50 x 10-3 mol

Amount of HCl left after partial neutralization

= (2.50 x 10-3) - (1.00 x 10-3)

= 1.50 x 10-3 mol

Concentration of H+ ions in 35.0 mL

[H+] = 0.0429 M,

pH = -log 0.0429 = 1.37

2) After addition of 25.0 mL of 0.100 M NaOH to 25.0 mL of 0.100 M HCl

[H+] = [OH-] = 1.00 x 10-7pH = 7.00

M = mol L = 1.50 x 10-3 mol (35/1000)= 0.0429 M

3) After addition of 35.0 mL of 0.100 M NaOH to 25.0 mL of 0.100 mL of HCl

Total volume = 60.0 mLMoles of NaOH added

Moles of HCl in 25.0 mL solution = 2.50 x 10-3 mol

After complete neutralization of HCl, no of moles of NaOH left = (3.50 x 10-3) - (2.50x10-3)= 1.00 x 10-3 mol

M = mol L = 0.1 x (35 mL/1000 mL)= 3.50 x 10-3 mol

Concentration of NaOH in 60.0 mL solution

[OH-] = 0.0167 M

pOH = -log 0.0167 = 1.78

pH = 14.00 – 1.78 = 12.22

M = mol L = 1.00 x 10-3 mol (60/1000)= 0.0167 M

WEAK ACID versus STRONG BASE WITH BUFFER REGION

The titration between acetic acid and NaOH.

CH3COOH + NaOH H2O + CH3COONa

The acetic acid which is only a few percent ionized is neutralized to water and equivalent amount of CH3COONa salt

•For the first part of the graph, we have an excess of sodium hydroxide. The curve will be exactly the same as when we add hydrochloric acid to sodium hydroxide.

•Once the acid is in excess, there will be a difference.

•Past the equivalence point - a buffer solution containing sodium acetate and acetic acid.

As soon as the titration is started, some of the acetic acid is converted to sodium acetate

As the titration proceeds, the pH slowly increased as the ratio [Acetate]/[Acetic acid] changes.

At the midpoint of the titration, [Acetate]/[Acetic acid] and the pH is equal to pKa.

At the equivalence point, we have a solution of sodium acetate

Since this is a Bronsted base, the pH at the equivalence point will be alkaline.

The pH will depend on the concentration of sodium acetate

The greater the concentration, the higher the pH.

WEAK BASE versus STRONG ACID WITH BUFFER REGION

The titration between hydrochloric acid and ammonia

NH3 + HCl NH4+ + Cl-

•At the very beginning of the curve, the pH starts by falling quite quickly as the acid is added, but the curve very soon gets less steep (some of the NH3 is converted to NH4

+). This is because a buffer solution is being set up - composed of the excess ammonia and the ammonium chloride being formed

•At the midpoint of the titration, [NH4+] equals [NH3]

•The equivalence point (solution of NH4Cl form) is somewhat acidic (less than pH 5), because pure ammonium chloride isn't neutral. However, the equivalence point still falls on the steepest bit of the curve.

•Beyond the equivalence point, the pH is determined by the concentration of H+ added in excess.