Calculations used in Analytical Chemistry

Dr. Ashwini WadegaonkarSOE, SPPU

Contents

Some important units of measurements:

SI units

Distinction between mass and weight, mole, millimole and Calculations

Significant figures

Solution and their concentrations-

Molar concentrations, Molar analytical Concentrations, Molar equilibrium

concentration, percent Concentration, part per million, part per billion, part per

thousand,

Solution – Dilatant volume ration, functions, density and specific gravity of

solutions, problems

Chemical Stoichiometry – Empirical and Molecular Formulae, Stoichiometric

Calculations, Problems.

Some important units of Measurement

Generally the metric units of physical quantities

are expressed in SI – System International

(formerly known as MKS unit system)

The SI of units is the modern form of the metric

system and is the most widely used system of

measurement all over the world.

SI units

SI is based on seven fundamental base units.

Common SI Derived units

Prefixes for units

To express small or large measured physical

quantities in terms of a few simple digits,

prefixes are used with these base units and other

derived units. These prefixes multiply the unit by

various powers of 10.

Prefixes for units

Conversion factors

1 A0 = 10 -10 m T = (t0C + 273)K 1 a.m.u. = 1.66 x 10 -27 kg 1 liter = 10 -3 m3 = 1dm3

1 calorie = 4.184 J 1 atm = 101325 Pa (Nm-2) 1 erg =10 -7 Jules 1mm = 133.325 Pa 1cm2 = 10 - 4 m2

1 Kcal mol-1 = 4.18 kJ mol-1

= 6.95 x 10-21 J mol-1

1cm-3 = 10 -6 m-3

1eV = 1.602 x 10 -19 J 1 g cm-3= 10 3 Kg m-3

1 mL = cm3

Distinction between Mass and Weight

https://youtu.be/rFdbY_V7vIo

Distinction between Mass and Volume

Mass Weight

Definition Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.

Weight is a measurement of the gravitational force acting on an object.

Effect of gravity

Mass is always constant at any place and any time

The weight of an object depends on the gravity at that place

Unit of Measureme

nt

Mass is expressed in kilogram (kg), grams (g), and milligram (mg).

Weight is expressed in Newton (N)

Balance used for

measurement

Mass is measured using a pan balance, a triple-beam balance, lever balance or electronic balance.

Weight is measured using a spring balance.

Type of quantity

Scalar and base quantity Vector and derived quantity

Mole

The mole (abbreviation mol) is the SI unit for the amount of a substance.

It is defined as about 6.022 x 1023 atoms or particles or things.

Saying mol is definitely easier than having to say 6.022 x 1023.

If someone says there is 1 mol ofumbrellas outside, that means there are6.022 x 1023 umbrellas.

If someone says there is 1 mol of piecesof dust, that means there are 6.022 x1023 pieces of dust.

It doesn't matter the size or shape of theobject. A mol is a mol.

It's just a number.

Mole

Mole is defined as the amount of the specified

substance that contains the same number of particles

as the number of carbon atoms in exactly 12 grams

of 12C

A mole corresponds to the mass of a substance that

contains 6.023 x 1023 particles of the substance.

6.023 x 1023 is Avogadro’s number

The mole is the SI unit for the amount of a

substance. Its symbol is mol.

1 mole of any element contains the same number of atoms as 1

mole of any other element.

The masses of 1 mole of different elements, however, are

different, since the masses of the individual atoms are drastically

different.

The molar mass of an element (or compound) is the mass in

grams of 1 mole of that substance, expressed in units of grams

per mole (g/mol)

Atomic and Molecular Masses

1 mol of a substance is the quantity identical to the

substance's atomic or molecular mass (atomic or molecular

weight).

The atomic mass of hydrogen is 1.0079, therefore 1 mol of

hydrogen atoms have a mass of 1.0079 grams.

The atomic mass of chlorine is 35.453, therefore 1 mol of

chlorine atoms have a mass of 35.453 grams.

The molecular mass of water is 18.01528, therefore 1 mol

of water molecules have a mass of 18.01528 grams.

Computation of number of moles

The molar mass of acetic acid is 60.05⋅g⋅mol−1

Explanation:

And how did we get this quantity? Take the molar mass of each element in the formula

of acetic acid, weighted according to its frequency, i.e.

CH3COOH Molar mass =

{2×12.011(C)+4×1.00794(H)+2×15.999(O)}⋅g⋅mol−1

= 60.05⋅g⋅mol−1.

Therefore 1 mole of acetic acid has a mass of 60.0 g.

Millimole

Sometimes amount of chemical substance in

mole is very small quantity, it is more convenient

to express the same quantity in millimole and to

make calculations with millimoles rather than

moles.

Milli is a prefix use in SI units and it is the

number 1/1000 or 103 of a mole.

Calculate the number of moles and millimoles of

benzoic acid contained in 5.00g of the pure

benzoic acid.

(given – molar mass of benzoic acid is 122.1 g

mol-1)

Formula –

The number of moles of benzoic acid =

given mass of benzoic acid / molar mass of benzoic

acid mol-1

Significant figures

The accuracy of a physical measurementis properly indicated by the number offigures used to express the numericalmeasure.

Conventionally only those figures that arereasonably trustworthy are retained andthese are called significant figures.

RULES FOR SIGNIFICANT FIGURES

1. All non-zero numbers ARE significant. The number 33.2 has THREE significant

figures because all of the digits present are non-zero.

2. Zeros between two non-zero digits ARE significant. 2051 has FOUR significant

figures. The zero is between a 2 and a 5.

3. Leading zeros are NOT significant. They're nothing more than "place holders." The

number 0.54 has only TWO significant figures. 0.0032 also has TWO significant figures. All

of the zeros are leading.

4. Trailing zeros to the right of the decimal ARE significant. There are FOUR

significant figures in 92.00.

92.00 is different from 92: a scientist who measures 92.00 milliliters knows his value to

the nearest 1/100th milliliter; meanwhile his colleague who measured 92 milliliters only

knows his value to the nearest 1 milliliter. It's important to understand that "zero" does not

mean "nothing." Zero denotes actual information, just like any other number. You cannot

tag on zeros that aren't certain to belong there.

Trailing zeros in a whole number with the decimal shown ARE

significant. Placing a decimal at the end of a number is usually not done. By

convention, however, this decimal indicates a significant zero. For example,

"540." indicates that the trailing zero IS significant; there are THREE significant

figures in this value.

6. Trailing zeros in a whole number with no decimal shown are NOT

significant. Writing just "540" indicates that the zero is NOT significant, and

there are only TWO significant figures in this value.

7. Exact numbers have an INFINITE number of significant figures. This

rule applies to numbers that are definitions.

For example, 1 meter = 1.00 meters = 1.0000 meters =

1.0000000000000000000 meters, etc.

Solutions and their concentrations

1. Molar Concentration or Molarity

Molar concentration = Number of moles of solute (n)

-----------------------------------

Volume of solution in Litres (L)

Percent concentration

2. Percent or parts per hundred

weight of solute in g

Weight percent (w/w) = ------------------------ x 100

weight of solution in g

volume of solute in mL

Volume percent (v/v) = --------------------------- x 100

volume of solution in mL

weight of solute in g

Weight to Volume percent (v/v) = --------------------------- x 100

volume of solution in mL

Solutions and their concentrations

1. Parts per million

mass of solute (g)

Concentration in ppm (C ppm) = ---------------------- x 106 ppm

mass of solution (g)

P-Function

Scientists frequently express the concentration of a solute

species in terms of its p-function/p-value

It is convenient to express the concentration as a p-value,

when working concentrations that span many orders of

magnitude.

The p-value is the negative logarithm to the base 10 of the

molar concentration of that solute species. Thus, for the

solute species X,

pX = -log [X]

Density and Specific Gravity of solutions

In Analytical chemistry two physical quantities – density and

specific gravity are commonly used and they are inter-related

with each other.

The density of a substance is its mass per unit volume, and its

specific gravity is the ratio of its mass to the mass of an equal

volume of water at 40C.

Density has units – kilograms per liter or g /ml

Specific gravity is a dimensionless quantity and so is not

commonly used to any particular system of units.

The specific gravity is widely used in describing analytical

reagent grade or laboratory grade chemicals purchased

commercially.

Chemical Stoichiometry

Stoichiometry of the reaction is the relationship among

the number of moles of reactants and products as

represented by a balanced chemical equation.

The quantitative aspects dealing with mass and volume

relationship between the reactants and products called

stoichiometry.

Empirical and Molecualr formulae

Empirical formula –

An empirical formula gives the simplest whole number ratio

of atoms of each element present in a molecule or chemical

compound.

Eg CH is empirical formula of benzene.

It indicates that benzene is composed of carbon and

hydrogen in the ratio of 12:1 by weight.

Two or more compounds have the same empirical formula.

Eg the empirical formula of compound C6H12O6 and

CH3COOH is the same as CH2O

Empirical and Molecualr formulae

Molecular formula –

Molecular formula of a compound is one which indicates the

actual number of atoms of each element present in one

molecule.

The molecular formula specifies the number of atoms in a

molecule.

Eg CH2O is both the empirical and the molecualr

formula of formaldehyde. It is also empirical formula

for diverse substances like acetic acid, C2H4O2,

glyceraldehyde, C3H6O3 and Glucose, C6H12O

Molecular formula

Molecular formula = n x empirical formula

Molecular formula weight

n = -----------------------------

Molecular formula weight

Molecular formula indicates the various elements present in

the molecule and number of atoms of each element.

Determination of Empirical and Molecularformula - STEPS

1. The percentage composition of the compound is determined by

quantitative analysis

2. The percentage of each element is divided by its atomic weight

giving atomic ratio of the elements present in the compound.

3. The atomic ratio of each element is divided by minimum value

of atomic ratio as to get simplest ratio of atoms of elements.

4. If the simplest ratio is fractional then the values of simplest

ratio of each element are multiplied by a smallest integer to get

a simplest whole number for each element.

Determination of Empirical and Molecularformula - STEPS

5. To get empirical formula, symbols of various elements are written

side by side with their respective whole number ratio as a

subscript to the lower right hand corner of the symbol.

6. The molecular formula may be determined from the empirical

formula if the molar mass of the substance is known.

7. The molecular formula is always a simple multiple of

empirical formula and the value of simple multiple is

obtained by dividing molar mass with empirical formula

mass.

Determination of Empirical and Molecularformula

A compound contains 34.8% Oxygen, 52.2% carbon and 13.0%

hydrogen. Calculate the empirical formula mass of the

compound.

Given – Molar mass of C=12 g mol-1 , O=16 g mol-1 , H=1 g mol-1

Element %Weight

Molar mass of atom

Relative number of atom

Simplest ratio

Oxygen 34.8 16 34.8/ 16 = 2.175

2.175/2.175 = 1

Carbon 52.2 12 52.2/ 12 = 4.35

4.35 / 2.175 = 2

Hydrogen 13.0 1 13.0/ 1 = 13.0 13.0/ 2.175 = 6

Determination of Empirical and Molecularformula

Therefore empirical formula is C2H6O

Empirical formula mass =

[2 x 12g mol-1] + [6x1 g mol-1] + [1x16 g mol-1] = 46 g mol-1

Stoichiometric calculations

A balanced chemical reaction indicates the quantitative

relationship between the moles of reactants and

products.

These stoichiometric relationships provide the basis for

many analytical calculations.

Stoichiometric calculations - steps

1. When the mass of a reactant or product is given the mass is

first converted to the number of moles, using molar mass

2. The stoichiometric ratio given by the chemical equation for the

reaction is then used to find the number of moles of another

reactant that combines with the original substance or the

number of moles of product that forms.

3. Finally, the mass of the other reactant or the product is

computed from its molar mass.