Chapter 4

Calculations in Analytical Chemistry

SI and other Units,

Amount

Concentration

Density

Stoichiometry

SI UNITS

In science generally use SI units are used but in Analytical

Chemistry, due to the very wide range of quantities (from

very small to very large) we sue derived SI orr sometimes

non SI units.

For example visible radiation is given in terms of nm; eg

the wavelenght of the yellow light of sodium flame is 590

nm

Volumes can vary from micro liters to liters.

Mass can be anywhere from micrograms to kilograms.

You must learn the units, the prefixes and unit conversions

using conversion factors!

The Mole (mol)

This is the amount of chemical matter. I mol contains

Avagadro’s number of particles.

Millimol and micromol are derived units of mol and are

10-3 and 10-6 mol respectively.

Relationship between mass (m), molar mass (MM) and

amount in mols (n) is given by the following eqn:

Amount in mols = ����

���������

n = �

��

Example

How many grams of C is present in a 72.8 g sample of

Iron(III) carbonate.

Solution Concentrations - MOLARITY

Molar concentration cX of a solution of a chemical species X

is the number of moles of that species contained in 1 liter of

the solution (not one liter of the solvent).

The unit of molar concentration is molarity, M. It has the

dimensions of mol/L or mol·L-1

cX = ����� ���� �����

����� �� �������

�.���������

���������

Example

Calculate the molar concentration of ethanol in an aqueous

solution that contains 5.80g ethanol in 2.50 L solution

At times it is necessary to distinguish between two types of

concentrations.

Analytical Molarity is the total number of moles of a solute,

irrespective of its chemical state, in 1 L of solution. It

describes how a solution of a given molarity can be prepared.

Equilibrium Molarity is the molar concentration of a particular

species in a solution. This can either be calculated if the

relevant equilibrium constants are known or measured

experimentally.

Example

Calculate the analytical and equilibrium molar concentrations

of the solute species in an aqueous solution that contains 285

mg of trichloroacetic acid in 10.0 mL(the acid is 73% ionized

in water).

Other concentration units Other concentration units

Try and avoid the use of these units. Only w/w is temperature

independent

Eg Nitric acid is sold as a 70% w/w solution. What mass

should you take to prepare a 1 L 2 M HNO3(aq) solution

Other concentration units

APPROXIMATION

For dilute aqueous solutions whose densities are approximately

1.00 g/mL.

1ppm= 1.00 mg/L

1ppb= 1.00 µg/L

Other concentration units

p-functions

Frequently in chemistry the p-function or p-value is used to

express the concentration of certain species. This is the

negative logarithm (to the base 10) of the molar concentration

of that species. Thus for species X:

pX=-log10[X]

Useful for expressing concentrations that are small and vary

over ten or more orders of magnitude.

Example

Calculate the molar concentration of Ag+ in a solution that has

a pAg+ of 6.372.

DENSITY AND SPECIFIC GRAVITY OF SOLUTIONS

Example

STOICHIOMETRY

Quantitative relationship between reacting chemicals.

Empirical and Molecular Formula

1. A 25.00-g sample of an orange compound contains 6.64 g

of potassium, 8.84 g of chromium, and 9.52 g of oxygen.

Find the empirical formula.

2. From the elemental analysis of 5.00-g acetic acid, we get

7.33 g CO2 and 3.00 g H2O. The compound is known to

contain C, H and O only. Find the empirical formula.

3. Analysis by a mass spectrometer gives the molar mass of

acetic acid as 60 g/mol. Determine its molecular formula.

Stoichiometric calculations

1. Write a balanced chemical equation

2. Establish stoichiometric factors between the reactant and

product species

3. Use these factors to calculate unknown quantities from

known quantities.

Example