Post on 18-Dec-2021
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.