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Category: Fundamental Theory of Chemistry

A part of the theoretical arsenal of modern chemistry: such as, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation.

Algebraic or Bottomley’s method of balancing a chemical equation

What is a chemical equation?

A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and formulae, wherein the reactant entities are given on the left-hand side and the product entities on the right-hand side.

How to balance a chemical equation?

What we are going to demonstrate below is the Algebraic Method or the Bottomley’s Method of balancing a chemical

For example, the following chemical equation can be considered for the purpose of demonstrating how to balance a chemical equation.

PCl5 + H2O –> H3PO4 + HCl

The first step is to assign arbitrary multipliers to each member substance of the equation.

a PCl5 + b H2O –> c H3PO4 + d HCl

Here, the objective is to ascertain the values of the arbitrary multipliers which make the chemical equation, balance. Hence the next step is to come up with linear equations of arbitrary multipliers by balancing the different elements of the two sides of the equation.

By balancing the element Phosphorus (P) –> a = c —-> equation (1)

By balancing the element Chlorine (Cl) –> 5a = d —–> equation (2)

By balancing the element Hydrogen (H) –> 2b = 3 c + d —–> equation (3)

By balancing the element Oxygen (O) –> b = 4c —–> equation (4)

Now we have 4 linear equations with 4 unknowns of a, b, c and d. The next step is to solve these 4 linear equations to find the 4 unknowns.

Since a = c, substituting c with a –>


2b = 3a + d

b = 4a

Since b = 4a, substituting b with 4a —>

5a = d

8a = 3a + d —> 5a = d

Lets assume a = 1

Then d=5, b=4 and c = 1

Finally the balanced chemical equation is as below.

PCl5 + 4 H2O –> H3PO4 + 5 HCl

Atomic Emission Spectroscopy

Atomic emission spectroscopy or AES is a procedure of analyzing chemicals that employs the intensity of light from a plasma, flame, arc or spark at a definite wavelength to calculate the quantitative presence of an element in a particular sample. The atomic spectral line wavelength identifies the element and the intensity of light is proportional to the atom count of the element.

Atomic Emission Spectroscopy Principle

The theory or working principle of Atomic Emission Spectroscopy involves the examination of the wavelengths of photons discharged by atoms and molecules as they transit from a high energy state to a low energy state. A characteristic set of wavelengths is emitted by each element or substance which depends on its electronic structure. A study of these wavelengths can reveal the elemental structure of the sample.

Flame Atomic Emission Spectroscopy

In this method, a sample of the material to be analyzed is brought into flame in the form of a sprayed solution or gas. Free atoms of the material are produced when the flame heat evaporates the solvent and breaks the chemical bonds of the analyte. The heat also changes the atoms into electronically charged particles which emits light when they get back to the ground electronic state. Light is emitted at a wavelength characteristic to each element which is then dispersed by a prism or grating and detected in spectrometer.

Atomic Emission Spectroscopy

Picture 1 – Atomic Emission Spectroscopy

Flame emission spectroscopy is frequently used while studying alkali metals for pharmaceutical research and analysis.

Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES)

Inductively coupled plasma atomic emission spectroscopy (ICP-AES) employs the use of inductively coupled plasma for producing excited ions and atoms that radiate electromagnetically charged particles at wavelengths characteristic to a definite element.

Uses of Inductively Coupled Plasma Atomic Emission Spectroscopy

The various uses of ICP-AES have been discussed below:

  • Inductively coupled plasma atomic emission spectroscopy is used to determine the presence of arsenic in food, metals in wine and to study trace elements that are bound to proteins.
  • ICP-AES is frequently used for analyzing trace elements present in the soil. Forensic experts use this method to study soil samples found at the crime scenes and ascertain their origin. The metal composition of two types of soil samples can be compared to determine the origin of the soil samples taken from crime scene.
  • ICP-AES is also used for analyzing motor oils. The results from such studies help in determining the life of the oil, as well as assist in quality control and help in functional efficiency of automobile engines.

Advantages and disadvantages of ICP Atomic Emission Spectroscopy

There are a few advantages of inductively coupled plasma atomic emission spectroscopy (ICP-AES). These include excellent linear dynamic range and limit of detection, low chemical interference, multi-element capability as well as a stable, reproducible signal.

The disadvantages of this method include a huge cost of infrastructure maintenance and operating expense, the presence of several emission lines or spectral interferences and the necessity of having samples dissolved in solutions.

Atomic Absorption Spectroscopy

When a ground state atom is collided with light of appropriate wavelength, the atom absorbs the light and enters an excited phase. This process is referred to as atomic absorption. The aim of atomic absorption is to measure the quantity of light at resonant wavelength that is absorbed when it passes through a cluster of atoms. The increase in the amount of absorbed light is proportional to the increase in the number of atoms on the light stream. The quantity of analyte substance present can be calculated by measuring the quantity of absorbed light. The quantitative determination of varied individual elements in presence of other substances is aided by the employment of special light sources as well as the appropriate selection of light wavelength. The atom cloud needed for measuring atomic absorption is produced by exposing the sample to enough thermal energy. This dissociates the structures of chemical compounds and liberates free atoms. This purpose is served by presenting the sample solution into the flame coordinated with the light beam. The majority of atoms will stay in the ground state form when exposed to appropriate flame conditions. These atoms can absorb light emitted from the source lamp at specific analytical wavelength. Atomic Absorption Spectroscopy offers great speed and ease while making comprehensive and accurate calculations and hence it is among the most widely used methods for determining metal samples.

Spark and arc atomic emission spectroscopy

Spark or arc atomic emission spectroscopy is a procedure used for analyzing solid samples for metallic elements. While studying non-conductive substances, conductivity is induced in the solid sample by grinding it with graphite powder. Traditionally, the arc spectroscopy method involved grinding and destroying a solid sample during analysis and passing an electric spark or arc through it. This results in producing a heat of high temperature that excites the atoms into highly charged particles. Light is emitted by the excited atoms at characteristic wavelengths which can then be dispersed and detected using a monochromator. The analysis for metallic elements in solid samples is qualitative as the spark and arc conditions are generally not well monitored. The modern usage of spark sources using controlled discharges under presence of argon is also considered to be quantitative. Both the traditional and modern methods of qualitative and quantitative spark analysis methods are frequently used for quality control in steel mills and foundries.

Atomic Emission Spectroscopy Instrumentation

The sample that needs to be studied should be first converted to highly excited free atoms. The liquid samples are generally nebulized and carried to the source of excitation by flowing gas. Solid samples are introduced into a source by slurry or laser ablation in a stream of gas. Another way of dealing with solid samples would be to directly vaporize the sample and excite it by using a laser pulse or a spark between electrodes. The excitation source should desolvate the sample, atomize and excite the atoms. A number of excitation sources can be used for these purposes, which are listed below:

  • Direct-current plasma (DCP) – This process involves using two electrodes to produce an electrical discharge. A plasma support gas like Argon is necessary.
  • Inductively-coupled plasma (ICP) – This process requires a plasma torch which is made up of concentric quartz tubes. The inner tube contains Argon and the sample and Argon gas flows through the outer tube and acts as a cooling agent. A radiofrequency generator (RF) having a range of 1-5 kW at 27 MHz or 41 MHz creates an oscillating current within an induction coil which surrounds the tubes. An oscillating magnetic field is produced by this induction coil.
  • Flame – A flame is high temperature source that is used to desolvate and vaporize a sample and generate free atoms for spectroscopic study.
  • Laser-induced breakdown (LIBS) – A high energy laser beam is utilized for this method.
  • Microwave-induced plasma (MIP) – In this method, a quartz tube is surrounded by a cavity or a microwave waveguide. A magnetron is required to produce microwaves that will fill the microwave waveguide. A spark is needed to facilitate the plasma state.
  • Laser-induced plasma – A high energy CO2 laser is required to be focused on a support gas such as Argon for maintaining a heated plasma.
  • Spark or arc – Spark and arc excitation sources employ a spark or a current pulse (spark) or an arc of continuous electrical discharge between two electrodes for vaporizing and exciting the atoms of the sample. The electrodes are made of either graphite or metal.

Atomic Emission Spectroscopy Applications

The principal application of atomic emission spectroscopy is to determine the proportional quantity of a particular element in a given sample. The various methods of atomic emission spectroscopy are utilized to examine different substances such as foods and drinks, motor oil and soil samples. Atomic Emission Spectroscopy is predominantly utilized in space research labs by NASA and ESA. It is also used for aiding various military operations.






The enthalpy change for a reaction between a strong acid and a strong alkali

Aim / Objective: 

To determine the enthalpy change for a reaction between a strong acid and a strong alkali.

Introduction:  Enthalpy is defined as the total energy in a system.  The change in energy ∆H can be positive in heat absorbing (endothermic reactions) or negative in heat releasing (exothermic reactions). This experiment focuses on one form of enthalpy change which is enthalpy of neutralization (∆Hn).  Enthalpy of Neutralization is the enthalpy change observed when one mole of water is formed when a base reacts with an acid in a thermodynamic system.

The literature standard enthalpy for a strong acid-base reaction is -57.1kJ/mol. For weak acids and bases the heat of neutralization is different as they are not fully dissociated and hence some heat will be absorbed.

Materials/ Apparatus:

1.0M HCl solution, 1.0M NaOH solution, 2 measuring cylinders, 2 Styrofoam cups, 2 beakers, 1 thermometer, 1 glass stirring rod.

Method / Procedure:

  1. Use a measuring cylinder to measure 50cm3 of sodium hydroxide (NaOH) and pour into a Styrofoam cup.
  2. Use a thermometer to measure the temperature of the NaOH. Record the reading.
  3. Use a measuring cylinder to measure 50cm3 of hydrochloric acid (HCl) and pour into a Styrofoam cup.
  4. Use a thermometer to measure the temperature of the HCl. Record the reading.
  5. Mix the contents of both cups in a beaker and stir the contents using the glass stirring rod.
  6. Take the temperature after stirring the mixture then record the reading.
  7. Repeat steps 1 to 6 TWO times and then tabulate the results.

Suggested Results:

Experiment numberInitial temperature / °CFinal temperature / °C

Discussion / Calculations:

Heat released = mcΔT

  1. Calculate mass

1000g = 1kg

1000g ÷1000

x = 1kg

50cm3 of acid and 50cm3 alkali = 100cm3 = 1kg

  1. Average temperature = (32+30+30+33.5+30.5+30.5) / 6

= 186.5/6

= 31.08°C

  1. Change in temperature (ΔT) = final temperature – initial temperature

= (46 – 31.08) °C

= 14.92°C

Change °C to K = 14.92 + 273 =287.92

  1. Specific heat capacity = 4.187JK-1kg-1
  2. Heat energy released = mcΔT

= 1kg x 4.187JK-1kg-1 x 287.92K

= 1205.52104J

  1. Enthalpy change = mcΔT / number of moles

50cm3 of acid & base contains (2/1000) x 50

=0.1 moles

0.1 moles H20 = 727.92J

1.0 moles H2O = 727.92J / 0.1 moles

= 7279.2J

Change from J to kJ

7279.2J / 1000 = 7.279kJ

Write the molecular and ionic equation for the reaction

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

H+(aq)   +    OH(aq)                 H2O(l)

Explain whether the reaction was exothermic or endothermic?

Heat was lost from the mixture to the environment can be said to be exothermic.

What was the use of the Styrofoam cups?

They were used to minimize heat loss of the mixture to the environment.

Chromatographic Methods of separation of substances of a mixture

Chromatography is used to analyze small quantities of a mixture of substances which are chemically similar to each other. It involves the partition of the components of the mixture between a stationary phase and a mobile phase. The mixture to be separated is introduced on the stationary phase which stays still. The mobile phase is then allowed to move over the stationary phase for separation. Partition depends on the different solubilities of the components in the mobile phase and the different adsorption forces of the components with the stationary phase. Adsorption is the temporary attraction of molecules of a gas or liquid to a solid surface. Components with greater solubilities will dissolve into the mobile phase and move along with it readily. Components with stronger adsorption forces will be held on the stationary phase and not move along readily with the mobile phase. The differences in solubilities and adsorption bring about separation.

Paper Chromatography

In paper chromatography, a piece of filter paper or chromatography paper is used which consists of stationary water molecules embedded in a cellulose matrix. The water molecules act as the stationary phase. The mobile phase consists of a suitable solvent that travels up the stationary phase. The mixture to be separated is spotted a short distance from one end of the paper (the base line). The end below the spot is placed in the solvent. As the solvent moves along the paper it carries the mixture with it. The distance the solvent moves from the baseline is called the solvent front. Components of the mixture will separate readily according to how strongly they adsorb on the stationary phase and how readily they dissolve in the mobile phase. If the separated components are colorless, then a visualizing agent can be used to convert them into colored spots. The positions of certain substances can also be determined by fluorescing under a UV lamp. The ratio of the distance moved by a component of the mixture to the distance moved by the solvent is called retention factor. Rf = distance moved by a component distance moved by solvent Each component has a characteristic Rf value for a given solvent under controlled conditions. Thus Rf values of known substances can be used to identify components of a mixture. Paper chromatography is used to analyze mixtures such as dyes in ink, coloring in food additives and amino acids from protein hydrolysis. A visualizing agent such as ninhydrin is used to detect amino acids and amines.

Thin Layer Chromatography (TLC)

This method is similar to paper chromatography. The stationary phase is a thin layer of powered alumna or silica gel which s fixed on to a glass or plastic plate. Plates can be coated with a slurry of the powered adsorbent and then oven – dried. The mixture to be analyzed is spotted near the bottom of the plate. The end below the spot s placed in a suitable solvent. This solvent is the mobile phase and moves up the plate causing the components of the moving solvent. The separated components may be recovered for further analysis by scraping spots off the plate. Thin layer chromatography has the advantage that a variety of adsorbents can be used for separation. It is commonly used to separate amino acids in blood samples and for analysis of food dyes.

Column Chromatography

This method is similar to thin layer chromatography however the stationary phase is packed into a vertical glass column (diameter 1- 2cm) instead of being coated on a plate. A slurry of silica gel or alumina is commonly used for column chromatography. The mobile phase is a suitable solvent which is added to the top of the loaded column. The solvent flows down the column under gravity causing the components of the mixture to partition between the adsorbent and solvent. Each component emerges from the column at different times and can be collected separately. The time between addition of the sample at the top of the column and the emergence of a component at the bottom of the column is called the retention time of that component. Identical substances will have the same retention time under the same conditions thus retention times can be used to identify substances. Column chromatography has the advantage that larger quantities can be separated and therefore can be used to prepare compounds in addition to analyzing them. This method is used in biochemical research and in hospitals to identify amino acids, peptides and nucleotides.

High Performance Liquid Chromatography (HPLC)

This technique is similar to column chromatography however instead of gravity feed, high pressure is used to force the solvent through the column. Columns are smaller than those used in column chromatography, some being 10cm to 30cm long and 4mm in diameter. Retention times are shorter thus rapid analysis of substances can be made. HPLC s used n the industry and hospitals. It is also used to identify suspected stimulants, doping and drugs that may be present in athletes and racehorses.

Gas – Liquid Chromatography (GLC)

GLC uses a longer column than HPLC. It is usually packed with the stationary phase which is an inert powder coated with an non-volatile oil. The column is maintained at a constant, preset temperature in an oven. The mobile phase is an un-reactive gas. The sample to be analyzed has to be in the vapor state at the temperature at which the column is operated. The vaporized sample is carried through the column by the mobile phase. The sample is partitioned between the oil and the carrier gas A detector records each component as it leaves the column at different times. Emerging components can also be fed directly into a mass spectrometer for identification. GLC method of analysis is very sensitive and can be used in forensic testing, to monitor air and water pollution, to detect and identify traces of pesticides or agricultural chemicals in foodstuff and to check dosage of drugs in blood or urine samples.

Periodic Table Trends

Atomic Radius

The atomic radius of an element is half of the distance between the centers of two atoms of that element that are touching each other. Generally, the atomic radius decreases across a period from left to right and increases down a given group. The atoms with the largest atomic radii are located in group 1 and at the bottom of groups.

Moving from left to right across a period, electrons are added one at a time to the outer energy shell. Electrons within a shell cannot shield each other from the attraction of protons. Since the number of protons is also increasing, the effective nuclear charge increases across the period. This causes the atomic radius to decrease. Moving down a group in the periodic table, the number of electrons and filed electron shells increases, but the number of valence electrons remains the same. The outermost electrons in a group are exposed to the same effective nuclear charge, but electrons are found farther from the nucleus as the number of filled energy shells increases. Therefore, the atomic radius increases.

Ionization energy

The ionization energy or ionization potential is the energy required to completely remove an electron from a gaseous atom or ion. The closer and more tightly bound an electron is to the nucleus, the more difficult it will be to remove, and thus the higher its ionization energy will be. The first ionization energy is the energy required to remove one electron from its parent atom. The second ionization energy is the energy required to remove a second valence electron. The second ionization energy is always greater than the first ionization energy.

Ionization energies increase moving from left to right across a period (deceasing atomic radius). Ionization energy decreases moving down a group (increasing atomic radius). Group 1 elements have low ionization energies because the loss of an electron forms a stable octet.

Electron Affinity

Electron affinity reflects the ability of an atom to accept an electron. It is the energy change that occurs when an electrons is added to a gaseous atom. Atoms with stronger effective nuclear charge have greater electron affinity. Group IIA elements and alkaline earth metals have low electron affinity values. These elements are relatively stable because they have filled “s” sub shells. Group VIIA elements, the halogens have high electron affinities because the addition of an electron to an atom results in a completely filled shell. Group VIII elements, noble gases, have electron affinities near zero, since each atom possesses a stable octet and will not accept an electron readily. Elements of other groups have low electron affinities.

In a period, the halogens will have the highest electron affinity; while the noble gas will have the lowest electron affinity. Electron affinity decreases moving down a group because a new electro would be further from the nucleus of a large atom.


Electro-negativity is a measure of the attraction of an atom for the electrons in a chemical bond. The higher the electro-negativity of an atom, the greater its attraction will be for bonding electrons. Electro-negativity is related to ionization energy. Electrons with low ionization energies have low electro-negativities because their nuclei exert a strong attractive force on electrons. Elements with high ionization energies have high electro-negatives due to the strong pull exerted on electrons by the nucleus. in a group, the electro-negativity decreases as atomic number increases, as a result of increased distance between the valence electron and nucleus (greater atomic radius).

Summary of trends

Moving left to right

  1. Atomic radius decreases
  2. Ionization energy increases
  3. Electron affinity generally increases
  4. Electro-negativity increases

Moving top to bottom

  1. atomic radius increases
  2. ionization energy decreases
  3. electron affinity generally decreases
  4. electro-negativity decreases
Periodic Table Trends

Empirical, Molecular and Structural Formulas

There are three main types of chemical formulas: empirical, molecular and structural. Empirical formulas show the simplest whole-number ratio of atoms in a compound, molecular formulas show the number of each type of atom in a molecule, and structural formulas show how the atoms in a molecule are bonded to each other.

Empirical Formula

The empirical formula shows the simplest whole number ratio of the atoms in a molecule. For example: the empirical formula of hydrogen peroxide is HO.

The determination of the empirical formula of an organic compound involves combustion. A known mass of the compound is burned completely in excess oxygen.

There are several crucial steps in determining the empirical formula of a compound.

Steps for determining an empirical formula

Step 1 – Start with the number of grams of each element, given in the problem. If percentages are given, assume that the total mass is 100g therefore the percent given is equal to the mass of each element present.

Step 2 – Convert the mass of each element to moles using the molar mass in the periodic table

Step 3 – Divide each mole value by the smallest mole that was calculated

Step 4 – Round off to the nearest whole number

Now lets use an example to help us understand exactly how to do this.

Question Compound X contains 45.9% carbon, 32% hydrogen 13.5% nitrogen and 8.6% oxygen. Calculate the empirical formula of compound X.

Step 1 – The mass of each element based on the question

C – 45.9g

H – 32g

N – 13.5g

O – 8.6g

Step 2 – Convert the mass to moles using the molar masses in the periodic table

C          45.9 / 12 = 3.825

H         32 / 1 = 32

N         13.5 / 14 = 0.9643

O         8.6 / 16 = 0.5375

Step 3 – Divide each mole by the smallest number of moles calculated. Remember to round off to the nearest whole number.

C          3.825/0.5375 = 7

H         32 / 0.5375 = 2

N         0.9643 / 0.5375 = 2

O         0.5375 / 0.5375 = 1

Empirical Formula of Compound X – C7H2N2O

Molecular Formula

The molecular formula shows the actual number of atoms of each element in a molecule of the compound. E.g. the molecular formula of the compound hydrogen peroxide is H2O2

Molecular formula can be determined if the molar mass of the compound is known. To find this, calculate the mass of the empirical formula and divide the molar mass of the compound by the empirical formula. Use the number calculated and multiply all the atoms by this ratio to find the molecular formula.

Using an example should make this much easier to understand.

Using the same question above:

Compound X contains 45.9% carbon, 32% hydrogen 13.5% nitrogen and 8.6% oxygen. Calculate the empirical formula of compound X. The molar mass of compound X is 482g/mol

With the empirical formula calculated to be C7H2N2O. We can now go ahead and calculate the molar mass.

C7H2N2O = (7x12g) + (2×1) + (14×2) + (16×1)

84 + 2+ 98 + 16 = 200g/mol

Molar Mass / empirical formula =

482g/mol / 200 g/mol = 2

Therefore multiply the atoms in C7H2N2O by 2

The molecular formula of C7H2N2O is C14H4N4O2

Structural Formula

The structural formula shows the actual number of atoms and the bonds between them; that is the arrangement of atoms in the molecule. The structural formula of hydrogen peroxide is H-O-O-H. The structural formula shows how the various atoms are bonded.

structural formula

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