 ## Volumetric Analysis

Subject: Chemistry

#### Overview

Volumetric analysis is a type of quantitative analysis, based on the measurement of the volume of one solution required to react completely with a definite volume of another solution. By comparing the volume of two solutions, we can calculate the concentration of one solution provided that concentration of another solution is known.

### Volumetric Analysis:

It is a type of quantitative analysis based on the measurement of the volume of one solution required to react completely with a definite volume of another solution. By comparing the volume of two solutions, we can calculate the concentration of one solution provided that concentration of another solution is known.

#### EQUIVALENT MASS OF COMPOUNDS

a) Equivalent mass of acid

Equivalent mass of acid = $\frac{Molar\:Mass}{Basicity}$

Basicity = Number of replaceable hydrogen present in 1 molecule of acid

 Acid Molar Mass Basicity Equivalent mass = $\frac{Molar\:Mass}{Basicity}$ 1. Hydrochloric acid (HCl) 36.5 1 36.5 2. Nitric acid (HNO3) 63 1 63 3. Acetic acid (CH3COOH) 60 1 60 4. Sulphuric acid (H2SO4) 98 2 49 5. Oxalic acid (COOH)2.2H2O 126 2 63 6. Phosphoric acid (H3PO4) 98 3 32.66

b) Equivalent mass of base

Equivalent mass = $\frac{Molar\:Mass}{Acidity}$

where Acidity = Number of replacable group for twice the number of oxygen present in 1 molecule of base.

 Base Moalr mass Acidity Equivalent mass = $\frac{Molar\:Mass}{Acidity}$ NaOH 40 1 40 NH4OH 35 1 35 Ca(OH)2 74 2 37 Al(OH)3 78 3 26 CaO 56 2 28 Al2O3 102 6 17

c) Equivalent mass of salt

Equivalent mass = $\frac{Molar\:Mass}{Total\:Positive\:charge\:in\:basic\:radical}$

Example: NH4Cl = $\frac{Molar\:Mass}{1}$ = $\frac {53.5}{1}$ = 53.5

Example: CaCO3 = $\frac{Molar\:Mass}{2}$ = $\frac {100}{2}$ = 50

d) Equivalent mass of oxidizing and reducing agent

Equivalent mass = $\frac{Molar\:Mass}{Change\:in\:Oxidation\:Number\:per\:molecule}$

Example: Equivalent mass of KMnO4

i) Acidic medium

MnO4 -→ Mn2+

+7 +2

Change in oxidation number = 7 - 2 = 5

Equivalent mass = $\frac{Molar\:Mass}{5}$ = $\frac{158}{5}$ = 31.6

ii) Basic medium

MnO4 -→ MnO4 - -

+7 +6

Change in Oxidation Number = 1

Equivalent mass =$\frac{Molar\:Mass}{1}$ = $\frac{158}{1}$ =158

c) Neutral medium

MnO4 -→ MnO2

+7 +4

Change in Oxidation Number = 3

Equivalent mass =$\frac{Molar\:Mass}{3}$ = $\frac{158}{3}$ =52.6

### WAYS OF EXPRESSING CONCENTRATION OF SOLUTION

#### Percentage

%w/v (% by volume): It represents amount of solution (in gram) present in 100 ml of solution

i.e. %w/v = $\frac{Mass\:of\:solute\:in\:gram}{Volume\:of\:solution\:in\:ml}$ x 100

%w/w (% by mass): It represents amount of solution (in gram) present in 100 g of solution

i.e. %w/w = $\frac{Mass\:of\:solute\:in\:gram}{Mass\:of\:solution\:in\:gm}$ x 100

Gram per liter (gL-1): It represents the amount of solute (in gram) present in 1 liter of solution.

gL-1 = $\frac{Mass\:of\:solute\:in\:gram}{Volume\:of\:solution\:in\:liter}$

OR

gL-1 = $\frac{Mass\:of\:solute\:in\:gram}{Volume\:of\:solution\:in\:mililiter}$ x 1000

PPM (Parts per million)

1 PPM = 1mgL-1

Some relations

gL-1 = %w/v x 10

gL-1 = %w/w x specific gravity x 10

#### Normality (N)

Normality of a solution is defined as the number of equivalent of solute present in 1 liter of solution.

i.e. Normality = $\frac{Number\:of\:equivalent\:of\:solute}{Volume\:of\:solution\:in\:liter}$

= $\frac{Number\:of\:equivalent\:of\:solute}{Volume\:of\:solution\:in\:mililiter}$ x 1000

Also,

Normality = $\frac {Mass}{Equivalent\:Mass}$ x $\frac{1000}{Volume\: in \:ml}$

= $\frac{gL^-1}{Equivalent\:Mass}$

Normal solution ( 1 N Normality):The solution containing 1 equivalent of solute in 1 litre of solution is called normal solution.

Decinormal solution$( \frac{N}{10}$): The solution containing $\frac{1}{10}$ th equivalent of solute in 1 liter of solution is known as decinormal solution.

Similarly, $\frac{N}{100}$ is called centinormal solution and $\frac{N}{2}$ is called seminormal solution.

Molarity ( mol L -1): Molarity of a solution is defined as the number of moles of solute present in 1 liter of solution.

Molarity = = $\frac{Number\:of\:moles\:of\:solute}{Volume\:of\:solution\:in\:liter}$

= $\frac{Number\:of\:moles\:of\:solute}{Volume\:of\:solution\:in\:mililiter}$ x 1000

Also,

Molarity(M) = $\frac {Mass}{Molecular\:Mass}$ x $\frac{1000}{Volume\: in \:ml}$

= $\frac{gL^-1}{Molecular\:Mass}$

Molar solution ( 1 M Molarity):The solution containing 1 mole of solute in 1 liter of solution is called normal solution.

Decimolar solution$( \frac{M}{10}$): The solution containing $\frac{1}{10}$ th mole of solute in 1 liter of solution is known as decinormal solution.

Similarly, $\frac{M}{100}$ is called centimolar solution and $\frac{N}{2}$ is called semimolar solution.

#### RELATION BETWEEN MOLARITY AND NORMALITY

Normality = $\frac{gL^-1}{Equivalent\:Mass}$

or, gL-1 = Normality x Equivalent mass -----------(i)

Similarly ,

Molarity = $\frac{gL^-1}{Molecular\:Mass}$

or, gL-1 = Molarity x Molecular mass -----------(i)

Combining (i) and (ii)

Normality x Equivalent mass = Molarity x Molecular mass

For acid

Normality x $\frac{Molecular\:Mass}{Basicity}$ = Molarity x Molecular mass

Or, Normality = Molarity x Basicity

For base,

Normality x $\frac{Molecular\:Mass}{Acidity}$ = Molarity x Molecular mass

Or, Normality = Molarity x Acidity

#### Dilution principle

A solution of lower concentration can be prepared from a solution of higher concentration using dilution principle as:

V1 x S1 = V2 x S2

Where, V1 and S1 are volume and concentration of a solution of lower concentration and V2 and S2 are the volume and concentration of a solution of higher concentration.

#### Primary standard substance

A substance of sufficient purity from which standard solution can be prepared by directly weighing the exact quantity of the substance and dissolving indefinite volume of solution is known as primary standard substance. For a substance to be primary standard, it must have the following characteristics

i) The substance should be easily available in the pure state or in the state of known purity.

ii) The substance should not be hygroscopic or reactive in the atmosphere and should be easy to dry.

iii) The composition of substance should not change in solid state or in solution form of sufficiently long time.

iv) The compound should be easily soluble in water under the condition which it is employed.

v) The substance should have comparatively high molar mass or equivalent mass so that error during weighting is minimized.

That substance which does not satisfy the above characteristics is called secondary standard substances. Standard solution of these substances cannot be prepared by directly weighing the exact quantity of the substance and dissolving indefinite volume of solution.

Example: HCl, NaOH, KMnO4, etc.

#### Standard solution

The solution having known concentration is known as a standard solution. It is of two types:

1. Primary Standard Solution
2. Secondary standard solution

A. Primary Standard Solution

A standard solution prepared from the primary standard substance by directly weighing the exact quantity of the substance and dissolving indefinite volume of solution is called primary standard solution. Concentration or composition of this solution does not change during storage for a long time.

B. Secondary standard solution

A standard solution which cannot be prepared by directly weighing the exact quantity of substance or a solution in which exact concentration is determined by titrating it with suitable primary standard substance is known as a secondary standard solution. The concentration or composition of this solution changes during storage.

Factor (f): It is the term which indicates by what factor actual concentration of solution differ from the proposed one.

#### Titration:

The experimental technique used to determine the concentration of the unknown solution by measuring the volume of standard solution required to react completely with a definite volume of unknown solution. The unknown solution is taken in a conical flask and standard solution is added from a long graduated tube called burette till reaction is complete. The completion of the reaction is indicated by some physical change produced by reagent itself or more usually by use of an indicator or some other physical measurement.

#### SOME TERMS USED IN TITRATION

Equivalent point: A stage during titration in which equivalent quantity of the substance is added from burette to the solution in the conical flask is the equivalent point. At this stage, the reaction is usually completed.

End point: The stage during titration at which indicator changes its color to indicate the completion of the reaction is called end point. It is the experimental point.

Titration error: The difference between the end point and the equivalent point is known as titration error.

Titrant: A standard solution or solution taken in burette is called titrant.

Titrand: An unknown solution or solution taken in the conical flask is called titrand.

Standardization: The process of finding the actual concentration of the secondary standard solution by titrating it with a suitable primary standard solution is known as standardization.

Indicator: An auxiliary substance used during titration to indicate completion by a sharp change in color is called indicator. Example: Phenolphthalein, Methyl Orange, Methyl red, etc

#### TYPES OF TITRATION

a) Acid-Base Titration (Acidimetry/Alkalimetry)

The titration between acid and base is called acid-base titration. In this titration, neutralization reaction takes place.

Acidimetry:The process of finding a concentration of unknown acid by titrating it with a standard solution of base is called acidimetry.

Alkalimetry:The process of finding a concentration of a base by titrating it with a standard solution of acid is called alkalimetry.

b) Redox Titration

The titration between the oxidizing agent and reducing a reducing agent is known as redox titration. In this titration, redox reaction (oxidation and reduction) takes place.

KMnO4 + H2SO4→ K2SO4 + MnSO4 + CO2 + H2O

Indicator used: KMnO4 (as self-indicator)

c) Precipitation Titration

In this titration, the reaction involved is precipitation reaction. Example: Titration between Halide solution and AgNO3 solution.

d) Complexometric titration

Reaction involved: Complex compound formation reaction

Example: Titration between metal ion with EDTA
EDTA = Ethylene Diamine Tetra Acetic Acid

### ACID-BASE INDICATORS AND THEIR SELECTION

#### Action of acid-base indicator

Those indicators which are used in acid-base titration like phenolphthalein, methyl orange, methyl red, etc. are called acid-base indicators. These indicators are weak acid or base themselves. Each indicator has two different forms and each form has its own color. The color given by indicator in particular solution depends on the relative concentration of the two forms.

Consider phenolphthalein indicator which is represented by HPH .

Here, phenolphthalein has two different form (HPH) or unionized form is a colorless and ionized form (PH-) is pink. When this indicator is added to the acidic solution, due to the common ion effect of H+ ion, equilibrium is largely shifted to the backward. This means unionized form is dominant hence, is colorless in acidic solution. Similarly, when the indicator is added to the alkaline solution, H+ ion of indicator combines with OH- ion of a base to produce unionized water molecule and equilibrium is largely shifted to forward. This means indicator is dominantly found in ionized form and gives pink color in ionized form.

Selection of Acid-Base Indicator

Each indicator has its own pH range for a color change. Some indicators have a pH range in a slightly acidic side. For example; Methyl orange (3.1 to 4.5). Some indicators have a pH range in the slightly basic side such as Phenolphthalein (8.3 – 10).

During the acid-base titration, pH of the resulting solution changes by adding acid or base. When we plot pH of titrating solution against the volume of acid or base added, we get a curve called titration curve. The curve shows that there is a sharp change in pH near the equivalent point.

i) Titration between strong acid and strong base

During this titration, pH of the resulting solution changes from 3 to 11 (approximately) near equivalent point and equivalent point lies at pH = 7. Any indicators which have a pH range between 3 to 11 can be used in this titration and suitable indicators are phenolphthalein, methyl orange or methyl red.

ii) Titration between strong acid and weak base

During this titration, pH of the resulting solution changes from 3 to 8 (approximately) and its equivalent point lies at pH less than 7 i.e. acidic side due to the hydrolysis of salt. Any indicators which have a pH range in the slightly acidic side can be used in the titration and the suitable indicators are methyl orange or methyl red.

iii) Titration between weak acid and strong base

During this titration, pH of the resulting solution changes from 6 to 11 (approximately) and equivalent point lies at pH more than 7 i.e. at alkaline side due to the hydrolysis of salt. Any indicators which have a pH range in the slightly alkaline side can be used in this titration and a suitable indicator is a phenolphthalein.

iv) Titration between weak acid and weak base

During this titration, there is no sharp change in pH near equivalent point and there is no suitable indicator.

References: -

Sthapit, Moti Kaji, and Dr.Raja Ram Pradhananga. Foundations Of Chemistry. 5th. Vol. 1. Kathmandu: Supravaha Press, 2010. 3 vols.

##### Things to remember
• Equivalent mass = $\frac{Molar\:Mass}{Change\:in\:Oxidation\:Number\:per\:molecule}$
• gL-1 = $\frac{Mass\:of\:solute\:in\:gram}{Volume\:of\:solution\:in\:mililiter}$ x 1000
•  The solution containing $\frac{1}{10}$ th mole of solute in 1 liter of solution is known as decinormal solution.
• The composition of substance should not change in solid state or in solution form of sufficiently long time.
• It includes every relationship which established among the people.
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