Atomic Structure

---

An atom is the smallest building block of matter. Atoms are made of neutrons, protons and electrons. The nucleus of an atom is extremely small in comparison to the atom. If an atom was the size of the Houston Astrodome, then its nucleus would be the size of a pea.

---

• Introduction to the Periodic Table
• Charges in the Atom
• Atomic Models and the Quantum Numbers
• Determining Electron Configuration

---

Introduction to the Periodic Table

Scientists use the Periodic Table in order to find out important information about various elements. Created by Dmitri Mendeleev (1834-1907), the periodic table orders all known elements in accordance to their similarities. When Mendeleev began grouping elements, he noticed the Law of Chemical Periodicity. This law states, "the properties of the elements are periodic functions of atomic number." The periodic table is a chart that categorizes elements by "groups" and "periods." All elements are ordered by their atomic number. The atomic number is the number of protons per atom. In a neutral atom, the number of electrons equals the number of protons. The periodic table represents neutral atoms. The atomic number is typically located above the element symbol. Beneath the element symbol is the atomic mass. Atomic mass is measured in Atomic Mass Units where 1 amu = (1/12) mass of carbon measured in grams. The atomic mass number is equal to the number of protons plus neutrons, which provides the average weight of all isotopes of any given element. This number is typically found beneath the element symbol. Atoms with the same atomic number, but different mass numbers are called isotopes. Below is a diagram of a typical cells on the periodic table.

There are two main classifications in the periodic table, "groups" and "periods." Groups are the vertical columns that include elements with similar chemical and physical properties. Periods are the horizontal rows. Going from left to right on the periodic table, you will find metals, then metalloids, and finally nonmetals. The 4th, 5th, and 6th periods are called the transition metals. These elements are all metals and can be found pure in nature. They are known for their beauty and durability. The transition metals include two periods known as the lanthanides and the actinides, which are located at the very bottom of the periodic table. The chart below gives a brief description of each group in the periodic table. 

Group 1A	Known as Alkali Metals Very reactive Never found free in nature React readily with water
Group 2A	Known as Alkaline earth elements All are metals Occur only in compounds React with oxygen in the general formula EO (where O is oxygen and E is Group 2A element)
Group 3A	Metalloids Includes Aluminum (the most abundant metal in the earth) Forms oxygen compounds with a X2O3 formula
Group 4A	Includes metals and nonmetals Go from nonmetals at the top of the column to metals at the bottom All oxygen form compounds with a XO2 formula
Group 5A	All elements form an oxygen or sulfur compound with E2O3 or E2S3 formulas
Group 6A	Includes oxygen, one of the most abundant elements. Generally, oxygen compound formulas within this group are EO2 and EO3
Group 7A	Elements combine violently with alkali metals to form salts Called halogens, which mean "salt forming" Are all highly reactive
Group 8A	Least reactive group All elements are gases Not very abundant on earth Given the name noble gas because they are not very reactive

Charges in the Atom

The charges in the atom are crucial in understanding how the atom works. An electron has a negative charge, a proton has a positive charge and a neutron has no charge. Electrons and protons have the same magnitude of charge. Like charges repel, so protons repel one another as do electrons. Opposite charges attract which causes the electrons to be attracted to the protons. As the electrons and protons grow farther apart, the forces they exert on each other decrease.

Atomic Models and the Quantum Numbers

There are different models of the structure of the atom. One of the first models was created by Niels Bohr, a Danish physicist. He proposed a model in which electrons circle the nucleus in "orbits" around the nucleus, much in the same way as planets orbit the sun. Each orbit represents an energy level which can be determined using equations generated by Planck and others discussed in more detail below. The Bohr model was later proven to be incorrect, but provides a useful model for building an explanation.

The "accepted" model is the quantum model. In the quantum model, we state that the electron cannot be found precisely, but we can predict the probability, or likelihood, of an electron being at some location in the atom. You should be familiar with quantum numbers, a series of three numbers used to describe the location of some object (like an electron) in three-dimensional space:

1. n: the principal quantum number, an integer value (1, 2, 3...) that is used to describe the quantum level, or shell, in which an electron resides. The principal quantum number is the primary number used to determine the amount of energy in an atom. Using one of the first important equations in atomic structure (developed by Niels Bohr), we can calculate the amount of energy in an atom with an electron at some value of n:
   

   En = -

   Rhc n2

   where:
   R = Rydberg constant, a value of 1.097 X 10⁷ m^-1
   c = speed of light, 3.00 X 10⁸ m/s
   h = Planck's constant, 6.63 X 10 ^-34 J-s
   n = principal quantum number, no unitFor example, how much energy does one electron with a principal quantum number of n= 2 have?
   
   

   En = - Rhc n2

   or

   En = - (1.097x107 m-1 ∗ (6.63x10-34 J•s)∗(3.0x108 m•s-1) 22

   = 5.5x10-19 J

   You might ask, well, who cares? In addition to the importance of knowing how much energy is in an atom (a very important characteristic!), we can also derive, or calculate, other information from this energy value. For example, can we see this energy? The table below suggests that we can. For example, suppose that an electron starts at the n=3 level (we'll call this the excited state) and it falls down to n=1 (the ground state). We can calculate the change in energy using the equation:
   
   

   ΔE = hv = RH

   1 ni2

   -

   1 nf2

   Where:
   ΔE = change in energy (Joules)
   h = Planck's constant with a value of 6.63 x 10^-34 (J-s)
   ν is frequency (s^-1)
   R_H is the Rydberg constant with a value of 2.18 x 10^-18J.
   n_i is the initial quantum number
   n_f is the final quantum number
   Using the equation below, we can calculate the wavelength and the frequency of the energy. The wavelength and the frequency give us information about how we might "see" the energy:
   
   

   vλ = c

   Where:
   ν = the frequency of radiation (s^-1)
   λ = the wavelength (m)
   c = the speed of light with a value of 3.00 x 10⁸ m/s in a vacuum
   

   Speed of light =	3.00E+08
   Rydberg constant =	2.18E-18
   Planck's constant =	6.63E-34
   Excited state, n =	3	4	5
   Ground state, n =	2	2	2
   Excited state energy (J)	2.42222E-19	1.363E-19	8.72E-20
   Ground state energy (J)	5.45E-19	5.45E-19	5.45E-19
   ΔE =	-3.02778E-19	-4.09E-19	-4.58E-19
   ν =	4.56678E+14	6.165E+14	6.905E+14
   λ(nm) =	656.92	486.61	434.47

   
   
2. l ("el", not the number 1): the azimuthal quantum number, a number that specifies a sublevel, or subshell, in an orbital. The value of the azimuthal quantum number is always one less than the principal quantum number n. For example, if n=1, then "el"=0. If n=3, then l can have three values: 0,1, and 2. The values of l are typically not identified as "0, 1, 2, and 3" but are more commonly called by their historic names, "s, p, d, and f", respectively. Since the quantum numbers were discovered through the study of light and lines on an electromagnetic spectra, chemists identified the lines by their quality: sharp, principal, diffuse and fundamental. The table below shows the relationship:
   

   Value of l	Subshell designation
   0	s
   1	p
   2	d
   3	f

3. m: the magnetic quantum number. Each subshell is composed of one or more orbitals. In the study of light, it was discovered that additional lines appeared in the spectra produced when light was emitted in a magnetic field. The magnetic quantum number has values between -l and +l. When l =1, for example, m can have three values: -1, 0, and +1. Because you know from the chart above that the subshell designation for l =1 is "p", you now know that the p orbital has three components. In your study of chemistry, you will be presented with p_x, p_y, and p_z. Notice how the subscripts are related to a three-dimensional coordinate system, x, y, and z. The chart below shows a summary of the quantum numbers:
   

   Principal Quantum Number (n)	Azimuthal Quantum Number (l)	Subshell Designation	Magnetic Quantum Number (m)	Number of orbitals in subshell
   1	0	1s	0	1
   2	0 1	2s 2p	0 -1 0 +1	1 3
   3	0 1 2	3s 3p 3d	0 -1 0 +1 -2 -1 0 +1 +2	1 3 5
   4	0 1 2 3	4s 4p 4d 4f	0 -1 0 +1 -2 -1 0 +1 +2 -3 -2 -1 0 +1 +2 +3	1 3 5 7

---

Chemists care about where electrons are in an atom or a molecule. In the early models, we believed that electrons move like billiard balls, and followed the rules of classical physics. The graphic below attempts to show that earlier models thought that we could identify the exact path, position, velocity, etc. of an electron or electrons in an atom:

A more accurate picture is that the electron(s) reside in a "cloud" that surrounds the nucleus of the atom. This concept is shown in the graphic below:

Chemists are interested in predicting the probability that the electron will be at some particular part of this cloud. The cloud is better known as an orbital, and comes in several different types, or shapes. Atomic orbitals are known as s, p, d, and f orbitals. Each type of atomic orbital has certain characteristics, such as shape. For example, as the graphic below shows, an s orbital is spherical in shape:

On this graph, the horizontal (x) axis represents the distance from the nucleus in units of a₀, or atomic units. The value of a₀ is 0.0529 nanometers (nm). The vertical (y) axis represents the probability density. What you should notice is that as the electron moves farther away from the nucleus, the probability of its being found at that distance decreases. In other words, the electron prefers to hang around close to the nucleus.

The three graphics below show some other orbitals. The first graph (top left) is of a "2s" orbital. Each "s" orbital can hold two electrons in its cloud. Notice how there is a relatively high probability of an electron being near the nucleus, then some space where the probability is close to zero, then the probability increases substantially at some distance from the nucleus. The graphic at the top right shows a "2p" atomic orbital. Orbitals that are "p" orbitals can hold up to six (6) electrons in their cloud. Notice its "dumbbell" or "figure of eight" shape. At the bottom left is a "3s" orbital. Again, notice its spherical shape. Finally, at the bottom right, is a "3p" orbital.

Determining Electron Configuration

One of the skills you will need to learn to succeed in freshman chemistry is being able to determine the electron configuration of an atom. An electron configuration is basically an account of how many electrons there are, and in what orbitals they reside under "normal" conditions. For example, the element hydrogen (H) has one electron. We know this because its atomic number is one (1), and the atomic number tells you the number of electrons. Where does this electron go? The one electron of hydrogen goes into the lowest energy state it possibly can, which means it will start at "level" one and goes into "s" orbitals first. We say that hydrogen has a "[1s¹]" electron configuration. Looking at the next element on the Periodic Table --helium, or He -- we see it has an atomic number of two, so two electrons. Since " s" orbitals can hold up to two electrons, helium has an electron configuration of "[1s²]".

What about larger atoms? Let's look at carbon, with an atomic number of 6. Where do its 6 electrons go?

• First two: 1s²
• Next two: 2s²
• Last two: 2p²

We can therefore say that carbon has the electron configuration of "[1s²2s²2p²]".

The table below shows the subshells, the number of orbitals, and the maximum number of electrons allowed:

Subshell	Number of Orbitals	Maximum Number of Electrons
s	1	2
p	3	6
d	5	10
f	7	14

The Abridged (shortened) Periodic Table below shows the electron configurations of the elements. Notice for space reasons we sometimes leave off a portion of the electron configuration. For example, look at argon (Ar), element 18. The table below shows its electron configuration as "[3s²3p⁶]" (remembering that "p" orbitals can hold up to six (6) electrons). Its actual electron configuration is:

Ar = [1s²2s²2p⁶3s²3p⁶]

Sometimes you will see the notation: "[Ne]3s²3p⁶", which means to include everything that is in neon (Ne, 10) plus the stuff in the "3"-level orbitals.

Energy and Chemical Reaction

Enthalpy changes

Enthalpy = H = heat of reaction at constant pressure = Qp
The enthalpy change is the change in energy that accompany chemical changes incident at a constant pressure.

a. Termination of the bond requires energy (= endothermic)
Example: H 2 → 2H - a kJ; DH = + AKJ

b. Bond formation provides energy (= exothermic)
Example: 2H → H 2 + a kJ; DH =-a kJ

The term used in the enthalpy change:
1. Standard Enthalpy Pembentakan (DHF):
     DH animal lays to form 1 mole of compound directly from its elements were measured at 298 K and pressure of 1 atm.
Example: H 2 (g) + 1/2 O 2 (g) → H 2 0 (l); DHF = -285.85 kJ

2. Enthalpy of decomposition:
     DH from the decomposition of 1 mole of the compound directly into its elements (= opposite of DH formation).
Example: H 2 O (l) → H 2 (g) + 1/2 O 2 (g), DH = +285.85 kJ

3. Standard Enthalpy of Combustion (DHC):
     DH to burn 1 mole of compounds with O 2 from the air measured at 298 K and pressure of 1 atm.
Example: CH 4 (g) + 2O 2 (g) → CO 2 (g) + 2H 2 O (l); DHC = -802 kJ

4. Enthalpy of reaction:
     DH of an equation in which substances contained in the equation is expressed in units of moles and the coefficients of the equation is simple round.
Example: 2AL + 3H 2 SO 4 → Al 2 (SO 4) 3 + 3H 2; DH = -1468 kJ

5. Enthalpy of Neutralization:
     DH generated (always exothermic) in acid or base neutralization reaction.
Example: NaOH (aq) + HCl (aq) → NaCl (aq) + H 2 O (l), DH = -890.4 kJ / mol

6. Lavoisier-Laplace law
     "The amount of heat released in the formation of one mole of a substance from the elements unsurya = amount of heat required to decompose the substance into its constituent elements."
Meaning: If the reaction is reversed the sign of the heat that is formed is also reversed from positive to negative or vice versa
Example:
N 2 (g) + 3H 2 (g) → 2NH 3 (g), DH = - 112 kJ
2NH 3 (g) → N 2 (g) + 3H 2 (g), DH = + 112 kJ
Enthalpy of formation, combustion and decomposition
Thermochemical Data are generally set at a temperature of 25 0 C and a pressure of 1 atm, hereinafter referred to standard conditions. Enthalpy changes were measured at a temperature of 25 0 C and a pressure of 1 atm is called the standard enthalpy change and is expressed with the symbol Δ H 0atau ΔH298. While the changes in enthalpy measurement not refer to the condition of measurement is expressed with the symbol ΔH alone.
Is the molar enthalpy of the reaction enthalpy change associated with the quantity of the substance involved in the reaction. In the known thermochemical various molar enthalpy, such as enthalpy of formation, enthalpy of decomposition, and the enthalpy of combustion.
Enthalpy of Formation
There are a variety of important thermochemical equation associated with the formation of one mole of unsurunsurnya. The enthalpy change associated with this reaction is called the heat of formation or the enthalpy of formation of a given symbol ΔH f. For example, the thermochemical equation for the formation of water and steam at 100 0 C and 1 atm, respectively.



How can we use this equation to get the heat of evaporation of water? What is clear equation (1) we must reverse and then summed with the equation (2). Do not forget to change the sign of ΔH. (If the formation of H 2 O (l) exothermic, as reflected by a negative ΔH f, the reverse process must be endothermic), which means a positive exothermic which means being endothermic.

Exothermic

Exothermic (heat producing)

Endothermic

If we add the equations (1) and (2), we can

And the hot reaction =

Note that the heat of reaction to all the changes with the heat of formation reaction proceeds minus the heat of formation of the reactants. In general it can be written:

Enthalpy change for reaction rates can be affected by the temperature and pressure conditions when measurements. Therefore, the necessary conditions of temperature and pressure must be specified for each data thermochemical.
Enthalpy of Combustion

The reaction of a substance with oxygen reaction called combustion. Substances that are combustible elements carbon, hydrogen, sulfur, and various compounds of these elements. Said to be perfect if the combustion of carbon (c) burned to CO2, hydrogen (H) burned into H2O, sulfur (S) burned to SO2.
Enthalpy change for the combustion of 1 mol of a substance is measured at 298 K, 1 atm is called the standard enthalpy of combustion (standard enthalpy of combustion), which is expressed by Δ Hc 0. Enthalpy of combustion is also expressed in kJ mol -1.
Price enthalpy of combustion of various substances at 298 K, 1 atm are given in Table 3 below.
Table 3. Enthalpy of combustion of various substances at 298 K, 1 atm



Burning gasoline is an exothermic process. If gasoline is considered consisting of isooctane, C8H18 (a component of gasoline) determine the amount of heat released in the combustion of 1 liter of gasoline. Given the enthalpy of combustion of isooctane = -5460 kJ mol -1, and the density of isooktan = 0.7 kg L -1 (H = 1 and C = 12).
Answer:
Enthalpy of combustion of isooctane is - 5460 kJ mol -1. The mass of 1 liter of gasoline = 1 liter x 0.7 kg L-1 = 0.7 kg = 700 grams. Isooctane mole = 700 g mol -1 gram/114 = 6.14 mol. So the heat is released in the combustion of 1 liter of gasoline is: 6.14 x 5460 kJ mol = 33524.4 kJ mol -1.
Combustion Perfect and Imperfect

Fuel combustion in vehicle engines or the industry does not burn completely. Complete combustion of hydro-carbon compounds (fossil fuels) to form carbon dioxide and water vapor. While imperfect combustion to form carbon monoxide and water vapor. For example:
a. Complete combustion of isooctane:
C8H18 (l) +12 ½ O2 (g) -> 8 CO2 (g) + 9 H2O (g) ΔH = -5460 kJ

b. Incomplete combustion of isooctane:
C8H18 (l) + 8 ½ O2 (g) -> 8 CO (g) + 9 H2O (g) ΔH = -2924.4 kJ
The impact is not perfect Burning
As seen in the example above, incomplete combustion produces less heat. Thus, imperfect combustion reduces fuel efficiency. Another disadvantage of incomplete combustion produces gases are carbon monoxide (CO), which are toxic. Therefore, incomplete combustion will pollute the air.

Enthalpy of decomposition

Decomposition reaction is the opposite of a reaction formation. Therefore, in accordance with the principle of conservation of energy, equal to the value of the enthalpy of decomposition enthalpy of formation, but opposite sign.
Example:
Given Δ Hf 0 H2O (l) = -286 kJ mol -1, the enthalpy of decomposition of H2O (l) into hydrogen gas and oxygen gas is + 286 kJ mol -1
H2O (l) -> H2 (g) + ½ O2 (g) ΔH = + 286 kJ

Determination of Reaction Enthalpy Change

The enthalpy change (DH) for a reaction can be determined in various ways, namely through experiments, based on data from the enthalpy change of formation DHf0 Hess law, and based on bond energies.

a. Determination DH Through Experiments

Enthalpy change of the reaction can be determined by using a device called a calorimeter (heat meter). In the calorimeter, a substance that will be reacted reaction put into place. The place is surrounded by water of known mass. Heat of reaction liberated absorbed by water and the water temperature will rise. Changes in water temperature is measured with a thermometer. Calorimeter placed in an insulated container filled with water to prevent the escape of heat.

 Figure Calorimeter

Based on this research, to raise the temperature of 1 kg of water at 10C required heat of 4.2 kJ or 1 kcal. Water required to heat 1 gram of 4.2 A or 1 cal. Amount of heat is called the specific heat of water with the symbol c. The amount of heat that is absorbed into the water is calculated by multiplying three factors: the mass of water in the calorimeter (g), changes in water temperature (0C), and the specific heat of water. The formula is written: q = heat released or absorbed

m = mass of water (g)

c = heat capacity of water (J)

Dt = change in temperature (0C)

b. DH Determination Under DHf0

Based on the change in the standard enthalpy of formation of substances that are present in the reaction, the reaction enthalpy change can be calculated by the formula:

 DHr0 = standard reaction enthalpy change enthalpy of formation of some substance changes can be seen in the table below.

 Table: Changes in the enthalpy of formation of some substance (t = 250C)

Enthalpy change of reaction sometimes can not be determined directly but must go through the stages of the reaction. For example, to determine the change in enthalpy of formation of CO2 can be done in various ways.

 In one way, the reaction is a single stage, while a 2 way and 3 way last two stages. Apparently a number of ways, the same enthalpy change is -394 kJ.

A scientist, German Hess, had done some research enthalpy change and the result is that the reaction enthalpy change of a reaction does not depend on the course of reaction, whether the reaction takes place one stage or several stages. This discovery is known as Hess's Law, which reads:

 According to Hess's study, the change in enthalpy of a reaction can not be determined with the calorimeters can be determined by calculation. Here is an example of the determination of the enthalpy change calculations.

c. Determination DH Based Energy Association

A chemical reaction caused by chemical bonds breaking and formation of chemical bonds of the new. At the time of the formation of chemical bonds of atoms will be the release of energy, whereas the energy required to break the tie. The amount of energy required to break the tie antaratom in 1 mole of gaseous molecules called bonding energy. The stronger the bond the greater the energy required. Some bond energy prices can be seen in the following table:

Table: Some bond energy prices

 Price of the bond energy can be used to determine the H 􀀨 a reaction.

 With this formula can also be determined average bond energy of a molecule and the energy needed to break a bond or bond dissociation energy of a molecule. Here is an example calculation using the DH bond energy prices.

Thermochemistry is a branch of chemistry that
study the relationship between the reaction with
heat.

THINGS LEARNED
• energy changes that accompany chemical reactions
• A chemical reaction takes place spontaneously
• Chemical reactions in the equilibrium position


1. Exothermic reaction
Is a reaction that takes place when accompanied by the release of heat or heat. The heat of reaction is written with a positive sign.
Example:
          N2 (g) + 3H2 (g) 2NH3 (g) + 26.78 kcal
2. REACTION endothermic
Is a reaction that takes place when needed heat. The heat of reaction written de
with a negative sign
Example:
         2NH3 N2 (g) + 3H2 (g) - 26.78 kcal



I Law of Thermodynamics: Law of conservation of mass and
energy, ie energy can not be created and dimusnah
it.
Mathematically formulated as follows:
1. Whenever there is a change in the energy system, the amount of energy change is determined by two factors:
    a. heat energy absorbed (q)
    b. effort (work) done by the system (w)

For systems that absorb heat → q: positive (+)
For systems that emit heat → q: negative (-)

For systems that do business (working) → w: positive
If efforts are made to system → w: negative

Energy system will increase if: q (+) and w (-)
Energy system will be reduced if: q (-) and w (+)
Applicable:
ΔE = q - w

ΔE = change in energy
  q = heat energy absorbed
  w = work done by system

2. His relationship with the enthalpy (H)
The definition of enthalpy:

H = E + P.V

- If P is fixed, ΔH:
ΔH = H2 - H1
= (E2 + P2. V2) - (E1 + P1.V1)
= (E2 - E1) - (P2.V2 - P1.V1)
= (E2 - E1) + P (V2 - V1)
ΔH = ΔE + P.ΔV
Since ΔE = qp - P.ΔV, then:
ΔH = qp-P.ΔV + P.ΔV
ΔH = qp
So the change in enthalpy = heat changes that occur
In the (P, T fixed)



HK. II. THERMODYNAMICS:
• NOT formulated MATHEMATICAL
• Explained SOME EVENTS ASSOCIATED WITH BOTH HK THERMODYNAMICS
1. Spontaneous Processes and Not Spontaneous
Spontaneous process: a process that can take place by itself and can not return without outside influence. Example:
a. Heat always flows from high temperature to tem
peratur low.
b. Gas flows from high pressure to low pressure
c. Water flows from a high to a low.

The process is not spontaneous: a process can not take place without any outside influence. Example:
heat can not flow from low temperature to a high temperature without any outside influence.

ENTROPY (s)
• In addition to the change in enthalpy, chemical or physical change involves a change in the chaos (disorder) relative of atoms, molecules or ions. Chaos (disorder) of a system called ENTROPY
Example:
• The gas is contained in a 1 L flask has a greater entropy than the same quantity of gas to be placed in a 10 ml flask.
• Sodium Chloride ions in the form of gas has higher entropy than the solid crystalline form.
• Water (liquid) at a temperature of 0oC has higher entropy than the ice at the same time.

The amount of entropy in the universe always increases
The more irregular: S increased.

Statement of Third Law of Thermodynamics:
• A perfect crystal at absolute zero temperature has the perfect order → entropy is zero.
• Entropy of a substance compared to the entropy in the form of a perfect crystal at absolute zero, is called the Absolute Entropy
• The higher the temperature of the substance, the greater the absolute entropy

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers. For example, in a reaction that forms ammonia (NH₃), exactly one molecule of nitrogen (N₂) reacts with three molecules of hydrogen (H₂) to produce two molecules of NH₃:

N₂ + 3H₂ → 2NH₃

Stoichiometry can be used to find quantities such as the amount of products (in mass, moles, volume, etc.) that can be produced with given reactants and percent yield (the percentage of the given reactant that is made into the product). Stoichiometry calculations can predict how elements and components diluted in a standard solution react in experimental conditions. Stoichiometry is founded on the law of conservation of mass: the mass of the reactants equals the mass of the products.

Reaction stoichiometry describes the quantitative relationships among substances as they participate in chemical reactions. In the example above, reaction stoichiometry describes the 1:3:2 ratio of molecules of nitrogen, hydrogen, and ammonia.

Composition stoichiometry describes the quantitative (mass) relationships among elements in compounds. For example, composition stoichiometry describes the nitrogen to hydrogen ratio in the compound ammonia: 1 mol of ammonia consists of 1 mol of nitrogen and 3 mol of hydrogen. As the nitrogen atom is about 14 times heavier than the hydrogen atom, the mass ratio is 14:3, thus 17 kg of ammonia contains 14 kg of nitrogen and 3 kg of hydrogen.

A stoichiometric amount or stoichiometric ratio of a reagent is the optimum amount or ratio where, assuming that the reaction proceeds to completion:

1.       All of the reagent is consumed,

2.       There is no shortfall of the reagent,

3.       There is no excess of the reagent.

A non-stoichiometric mixture, where reactions have gone to completion, will have only the limiting reagent consumed completely.

While almost all reactions have integer-ratio stoichiometry in amount of matter units (moles, number of particles), some nonstoichiometric compounds are known that cannot be represented by a ratio of well-defined natural numbers. These materials therefore violate the law of definite proportions that forms the basis of stoichiometry along with the law of multiple proportions.

Gas stoichiometry deals with reactions involving gases, where the gases are at a known temperature, pressure, and volume, and can be assumed to be ideal gases. For gases, the volume ratio is ideally the same by the ideal gas law, but the mass ratio of a single reaction has to be calculated from the molecular masses of the reactants and products. In practice, due to the existence of isotopes, molar masses are used instead when calculating the mass ratio.

Etymology

The term stoichiometry is derived from the Greek words στοιχεῖον stoicheion "element" and μέτρον metron "measure". In patristic Greek, the word Stoichiometria was used byNicephorus to refer to the number of line counts of the canonical New Testament and some of the Apocrypha.

Definition

Stoichiometry rests upon the very basic laws that help to understand it better, i.e., law of conservation of mass, the law of definite proportions (i.e., the law of constant composition) and the law of multiple proportions. In general, chemical reactions combine in definite ratios of chemicals. Since chemical reactions can neither create nor destroy matter, nortransmute one element into another, the amount of each element must be the same throughout the overall reaction. For example, the amount of element X on the reactant side must equal the amount of element X on the product side.

Chemical reactions, as macroscopic unit operations, consist of simply a very large number of elementary reactions, where a single molecule reacts with another molecule. As the reacting molecules (or moieties) consist of a definite set of atoms in an integer ratio, the ratio between reactants in a complete reaction is also in integer ratio. A reaction may consume more than one molecule, and the stoichiometric number counts this number, defined as positive for products (added) and negative for reactants (removed).^[1]

Different elements have a different atomic mass, and as collections of single atoms, molecules have a definite molar mass, measured with the unit mole (6.02 × 10²³ individual molecules, Avogadro's constant). By definition, carbon-12 has a molar mass of 12 g/mol. Thus to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction. The mass ratios can be calculated by dividing each by the total in the whole reaction.

Balancing chemical reactions

Stoichiometry is often used to balance chemical equations (reaction stoichiometry). For example, the two diatomic gases, hydrogen and oxygen, can combine to form a liquid, water, in an exothermic reaction, as described by the following equation:

2H₂ + O₂ → 2H₂O

Reaction stoichiometry describes the 2:1:2 ratio of hydrogen, oxygen, and water molecules in the above equation.

The term stoichiometry is also often used for the molar proportions of elements in stoichiometric compounds (composition stoichiometry). For example, the stoichiometry of hydrogen and oxygen in H₂O is 2:1. In stoichiometric compounds, the molar proportions are whole numbers.

Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting from grams to moles, or from grams to millilitres. For example, to find the number of moles in 2.00 g of NaCl, one would do the following:

In the above example, when written out in fraction form, the units of grams form a multiplicative identity, which is equivalent to one (g/g=1), with the resulting amount of moles (the unit that was needed), is shown in the following equation,

Stoichiometry is also used to find the right amount of reactants to use in a chemical reaction (stoichiometric amounts). An example is shown below using the thermite reaction,

This equation shows that 1 mole of aluminium oxide and 2 moles of iron will be produced with 1 mole of iron(III) oxide and 2 moles of aluminium. So, to completely react with 85.0 g of iron(III) oxide (0.532 mol), 28.7 g (1.06 mol) of aluminium are needed.

 

 

 

Different stoichiometries in competing reactions

Often, more than one reaction is possible given the same starting materials. The reactions may differ in their stoichiometry. For example, the methylation of benzene (), through a Friedel-Crafts reaction using  as catalyst, may produce singly methylated , doubly methylated , or still more highly methylated  products, as shown in the following example,

 

In this example, which reaction takes place is controlled in part by the relative concentrations of the reactants.

Stoichiometric coefficient

In layman's terms, the stoichiometric coefficient (or stoichiometric number in the IUPAC nomenclature^[2]) of any given component is the number of molecules which participate in the reaction as written.
For example, in the reaction CH₄ + 2 O₂ → CO₂ + 2 H₂O, the stoichiometric coefficient of CH₄ would be 1 and the stoichiometric coefficient of O₂ would be 2.

In more technically-precise terms, the stoichiometric coefficient in a chemical reaction system of the i–th component is defined as

 

or

 

where N_i is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37 & 62).

The extent of reaction ξ can be regarded as a real (or hypothetical) product, one molecule of which is produced each time the reaction event occurs. It is the extensive quantity describing the progress of a chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation on a molecular scale, divided by the Avogadro constant (it is essentially the amount of chemical transformations). The change in the extent of reaction is given by dξ = dn_B/ν_B, where ν_B is the stoichiometric number of any reaction entity B (reactant or product) an dn_B is the corresponding amount.^[3]

The stoichiometric coefficient ν_i represents the degree to which a chemical species participates in a reaction. The convention is to assign negative coefficients to reactants (which are consumed) and positive ones to products. However, any reaction may be viewed as "going" in the reverse direction, and all the coefficients then change sign (as does the free energy). Whether a reaction actually will go in the arbitrarily-selected forward direction or not depends on the amounts of the substances present at any given time, which determines the kinetics and thermodynamics, i.e., whether equilibrium lies to the right or the left.

If one contemplates actual reaction mechanisms, stoichiometric coefficients will always be integers, since elementary reactions always involve whole molecules. If one uses a composite representation of an "overall" reaction, some may be rational fractions. There are often chemical species present that do not participate in a reaction; their stoichiometric coefficients are therefore zero. Any chemical species that is regenerated, such as a catalyst, also has a stoichiometric coefficient of zero.

The simplest possible case is an isomerism

in which ν_B = 1 since one molecule of B is produced each time the reaction occurs, while ν_A = −1 since one molecule of A is necessarily consumed. In any chemical reaction, not only is the total mass conserved but also the numbers of atoms of each kind are conserved, and this imposes corresponding constraints on possible values for the stoichiometric coefficients.

There are usually multiple reactions proceeding simultaneously in any natural reaction system, including those in biology. Since any chemical component can participate in several reactions simultaneously, the stoichiometric coefficient of the i–th component in the k–th reaction is defined as

so that the total (differential) change in the amount of the i–th component is

Extents of reaction provide the clearest and most explicit way of representing compositional change, although they are not yet widely used.

With complex reaction systems, it is often useful to consider both the representation of a reaction system in terms of the amounts of the chemicals present { N_i } (state variables), and the representation in terms of the actual compositional degrees of freedom, as expressed by the extents of reaction { ξ_k }. The transformation from a vector expressing the extents to a vector expressing the amounts uses a rectangular matrix whose elements are the stoichiometric coefficients [ ν_i k ].

The maximum and minimum for any ξ_k occur whenever the first of the reactants is depleted for the forward reaction; or the first of the "products" is depleted if the reaction as viewed as being pushed in the reverse direction. This is a purely kinematic restriction on the reaction simplex, a hyperplane in composition space, or N‑space, whose dimensionality equals the number of linearly-independent chemical reactions. This is necessarily less than the number of chemical components, since each reaction manifests a relation between at least two chemicals. The accessible region of the hyperplane depends on the amounts of each chemical species actually present, a contingent fact. Different such amounts can even generate different hyperplanes, all of which share the same algebraic stoichiometry.

In accord with the principles of chemical kinetics and thermodynamic equilibrium, every chemical reaction is reversible, at least to some degree, so that each equilibrium point must be an interior point of the simplex. As a consequence, extrema for the ξ's will not occur unless an experimental system is prepared with zero initial amounts of some products.

The number of physically-independent reactions can be even greater than the number of chemical components, and depends on the various reaction mechanisms. For example, there may be two (or more) reaction paths for the isomerism above. The reaction may occur by itself, but faster and with different intermediates, in the presence of a catalyst.

The (dimensionless) "units" may be taken to be molecules or moles. Moles are most commonly used, but it is more suggestive to picture incremental chemical reactions in terms of molecules. The N's and ξ's are reduced to molar units by dividing by Avogadro's number. While dimensional mass units may be used, the comments about integers are then no longer applicable.

Stoichiometry matrix

In complex reactions, stoichiometries are often represented in a more compact form called the stoichiometry matrix. The stoichiometry matrix is denoted by the symbol, .

If a reaction network has  reactions and  participating molecular species then the stoichiometry matrix will have corresponding  rows and  columns.

For example, consider the system of reactions shown below:

S₁ → S₂

5S₃ + S₂ → 4S₃ + 2S₂

S₃ → S₄

S₄ → S₅.

This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:

where the rows correspond to S₁, S₂, S₃, S₄ and S₅, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix. This means that it is not always possible to recover the original reaction scheme from a stoichiometry matrix.

Often the stoichiometry matrix is combined with the rate vector, v to form a compact equation describing the rates of change of the molecular species:

 

Gas stoichiometry

Gas stoichiometry is the quantitative relationship (ratio) between reactants and products in a chemical reaction with reactions that produce gases. Gas stoichiometry applies when the gases produced are assumed to be ideal, and the temperature, pressure, and volume of the gases are all known. The ideal gas law is used for these calculations. Often, but not always, the standard temperature and pressure (STP) are taken as 0 °C and 1 bar and used as the conditions for gas stoichiometric calculations.

Gas stoichiometry calculations solve for the unknown volume or mass of a gaseous product or reactant. For example, if we wanted to calculate the volume of gaseous NO₂produced from the combustion of 100 g of NH₃, by the reaction:

4NH₃ (g) + 7O₂ (g) → 4NO₂ (g) + 6H₂O (l)

we would carry out the following calculations:

There is a 1:1 molar ratio of NH₃ to NO₂ in the above balanced combustion reaction, so 5.871 mol of NO₂ will be formed. We will employ the ideal gas law to solve for the volume at 0 °C (273.15 K) and 1 atmosphere using the gas law constant of R = 0.08206 L · atm · K⁻¹ · mol⁻¹ :

Gas stoichiometry often involves having to know the molar mass of a gas, given the density of that gas. The ideal gas law can be re-arranged to obtain a relation between thedensity and the molar mass of an ideal gas:

     and     

and thus:

where:

	= absolute gas pressure
	= gas volume
	= number of moles
	= universal ideal gas law constant
	= absolute gas temperature
	= gas density at  and
	= mass of gas
	= molar mass of gas

Stoichiometry of combustion

In the combustion reaction, oxygen reacts with the fuel, and the point where exactly all oxygen is consumed and all fuel burned is defined as the stoichiometric point. With more oxygen (overstoichiometric combustion), some of it stays unreacted. Likewise, if the combustion is incomplete due to lack of sufficient oxygen, fuel remains unreacted. (Unreacted fuel may also remain because of slow combustion or insufficient mixing of fuel and oxygen - this is not due to stoichiometry.) Different hydrocarbon fuels have a different contents of carbon, hydrogen and other elements, thus their stoichiometry varies.

Fuel	By mass [4]	By volume [5]	Percent fuel by mass
Gasoline	14.7 : 1	—	6.8%
Natural gas	17.2 : 1	9.7  : 1	5.8%
Propane (LP)	15.67 : 1	23.9 : 1	6.45%
Ethanol	9 : 1	—	11.1%
Methanol	6.47 : 1	—	15.6%
Hydrogen	34.3 : 1	2.39 : 1	2.9%
Diesel	14.5 : 1	0.094 : 1	6.8%

Gasoline engines can run at stoichiometric air-to-fuel ratio, because gasoline is quite volatile and is mixed (sprayed or carburetted) with the air prior to ignition. Diesel engines, in contrast, run lean, with more air available than simple stoichiometry would require. Diesel fuel is less volatile and is effectively burned as it is injected, leaving less time for evaporation and mixing. Thus, it would form soot (black smoke) at stoichiometric ratio.