Mole Concept Stoichiometry and Behavior of Gases
Mole Concept Stoichiometry and Behavior of Gases Synopsis
Synopsis
Mole Concept
A mole is a collection of 6.022 × 1023 particles.
A mole is the amount of a substance containing elementary particles like atoms, molecules or ions in 12 gram of carbon-12 (12C).
Avogadro’s Number
It is the number of atoms present in 12 gram of C-12 isotope, i.e. 6·023 × 1023 atoms.
It is denoted by NA or L.
NA = 6·023 × 1023
1 mole of atoms = 6·023 × 1023 atoms
1 mole of molecules = 6·023 × 1023 molecules
1 mole of electrons = 6·023 × 1023 electrons
1 mole of a gas = 22·4 litre at STP
Applications of Avogadro’s Law
- It explains Gay-Lussac’s law.
- It determines atomicity of the gases.
- It determines the molecular formula of a gas.
- It determines the relation between molecular mass and vapour density.
- It gives the relationship between gram molecular mass and gram molar volume.
Relative Vapour Density (VD)
Relative vapour density is the ratio between the masses of equal volumes of a gas (or vapour) and hydrogen under the same conditions of temperature and pressure.
According to Avogadro’s law, volumes at the same temperature and pressure may be substituted by molecules.
Hence,
Relative molecular mass of a gas or vapour = 2 × VD
Important Formulae
(GAW = gram atomic weight; GMW = gram molecular weight)
Percentage Composition, Empirical and Molecular Formulae
- Percentage Composition
The percentage by weight of each element present in a compound is called percentage composition of the compound.
- Empirical Formula
It is the chemical formula which gives the simplest ratio in whole numbers of atoms of different elements present in one molecule of the compound. - Empirical Formula Mass
It is the sum of atomic masses of various elements present in the empirical formula.
Empirical Formula Weight (EFW)
The empirical formula weight is the atomic masses of the elements present in the empirical formula.
EFW of H2O2=2 × (H) + 2 × (0)
=2 × 1 + 2 × 16
=34 amu - Molecular Formula
It denotes the actual number of atoms of different elements present in one molecule of the compound.
Molecular formula = Empirical formula × n 
Examples: Molecular formula of
Zinc nitrate: Zn(NO3)2
Butane: C4H10
Glucose: C6H12O6
Relationship between empirical formula and molecular formula
Molecular formula = Empirical formula × n
where ‘n’ is a positive whole number
- Chemical Equation
A shorthand notation of describing an actual chemical reaction in terms of symbols and formulae along with the number of atoms and molecules of the reactants and products is called a chemical equation.
A chemical equation is a balanced account of a chemical transaction.
Information conveyed by the chemical equation:
- Molecular proportion of a substance
In the above reaction, 2 molecules of solid KClO3 on heating in the presence of MnO2 produce 2 molecules of solid KCl and 3 molecules of O2(g). - Relative weights of substances
2 × 122.5g = 245 g of potassium chlorate - Volumes of gaseous substances
3 × 22.4 L = 67.2 L of oxygen at STP is evolved when 245 g of potassium chlorate is heated.
Symbol
The specific abbreviation used to denote the name of an element is called its symbol.
Significance of a Symbol
- A symbol represents a short form of an element.
- A symbol represents one atom of the element.
- It indicates the atomic weight of an element. The quantity of the element is equal to its atomic mass, gram atomic mass or atomic mass unit (amu).
For example, the symbol C
- Stands for the element Carbon
- Represents one atom of Carbon
- Indicates the atomic mass of Carbon, i.e. 12 amu
In 1807, the scientist John Dalton tried to name the various elements based on pictorial symbols. Symbols of some elements as proposed by Dalton are shown in the diagram.
In 1814, the Swedish Chemist Jöns Jakob Berzelius devised a system using letters of the alphabet. He put forward certain points for presentation.
- In most cases, the first letter of the name of an element was taken as the symbol for that element and written in capitals.
- In some cases, the initial letter of the name in capital along with its second letter in small was used.
- Symbols for some elements were derived from their Latin names.
- Symbols of elements used today are those as first suggested by the Swedish chemist Berzelius.
- The method suggested by Berzelius forms the basis of the IUPAC (International Union of Pure and Applied Chemistry) system of chemical symbols and formulae.
- The names and symbols decided by IUPAC are used all over the world for international trade.
Modern Symbols of Elements
The modern symbols of elements are derived from their English or Latin names which are made up of either the first letter or a letter appearing later in the name.
Valency
Valency is the combining capacity of an atom or a radical.
For example, the valency of carbon is 4 because it combines with four atoms of hydrogen to yield methane (CH4).
Valency with Respect to Hydrogen Atom
The number of hydrogen atoms which combines with or displaces one atom of that element or radical. The valency is taken to be 1 and is considered standard.
Modern Definition of Valency
The number of electrons which an atom can lose, gain or share during a chemical reaction to attain the stable configuration of the nearest inert gas element is called its valency.
Valance Electrons
The electrons present in the outermost shell or valence shell are known as valence electrons.
Definition of Valency with Respect to Valence Electrons
The number of electrons donated or accepted or shared by its atom during a chemical reaction is called valence electrons, and the number of these electrons is called the valency of that element.
Variable Valency
Sometimes, the same element may exhibit one valency in one compound and another valency in other compound. This property is called variable valency.
If an element exhibits two positive valencies, then for lower valency, use the suffix –ous at the end of the name of the element, and for higher valency, use the suffix –ic at the end of the name of the element.
Example: (a) Iron shows two valencies.
Fe2+ or Fe (II) is ferrous.
Fe3+ or Fe (III) is ferric.
(b) Mercury also shows two valencies.
Hg+ or Hg (I) is Mercurous.
Hg2+ or Hg (II) is Mercuric.
Examples of variable valency
Ions or Radicals
An ion or radical is an atom or a group of atoms of the same or different elements which behaves as a single unit with a positive or negative ion.
Radicals have their own combining power based on which they form chemical formulae.
Classification of ions or radicals depending on their number of charges
The number of charges indicates the number of electrons lost or gained by the atom or group of atoms.
Depending on the number of charges, 1, 2, 3 or 4, ions or radicals are described as monovalent, divalent, trivalent and tetravalent, respectively.
List of Common Electrovalent Positive Ions or Radicals
- Monovalent electropositive ions
Ammonium NH4+
Cuprous Cu+
Mercurous Hg+ - Bivalent electropositive ions
Argentic Ag2+
Ferrous Fe2+
Stannous Sn2+
Cupric Cu2+ - Trivalent electropositive ions
Aluminium Al3+
Chromium Cr3+
Arsenic As3+ - Tetra positive ions
Plumbic Pb4+
Stannic Sn4+
List of Common Electrovalent Negative Ions or Radicals
- Monovalent electronegative ions
Acetate CH3COO− Permanganate MnO4−
Bisulphite HSO3− Cyanide CN−
Bisulphate HSO4− Hypochlorite ClO− - Bivalent electronegative ions
Carbonate CO32− Silicate SiO32−
Oxide O2− Chromate CrO42−
Sulphate SO42− Oxalate (COO)22− - Trivalent electronegative ions
Arsenate AsO43−
Phosphide P3−
Phosphate PO43−
Borate BO3- - Tetravalent electronegative ions
Carbide C4−
Ferro cyanide [Fe(CN)6]4−
Molecular Formula or Chemical Formula
A molecular formula, also known as chemical formula, is a combination of elemental symbols and subscript numbers used to show the composition of a compound.
Examples:
Silica is represented as SiO2.
Marble is represented as CaCO3.
Writing Chemical Formulae
Step 1: Write the symbol of a basic radical (element with positive valency) to the left-hand side and that of the acid radical (element with negative valency) to the right-hand side.
Step 2:Write the valency of each of the respective radicals at the right hand top of its symbol.
Step 3: Divide the valency by their highest common factor (HCF), if any, to get the simple ratio. Ignore (+) or (−) symbols of the radicals.
Step 4: Cross the reduced valencies. If 1 appears, then ignore it. If a group of atoms receives a valency more than 1, then enclose it within brackets.
Example of magnesium chloride and ammonium sulphate (refer to the diagram below)
Significance of Molecular Formula
The molecular formula of a compound has quantitative significance. It represents
- The name of the substance.
- Both molecule and molecular mass of the compound.
- The respective numbers of different atoms present in one molecule of a compound.
- The ratios of the respective masses of the elements present in the compound.
Example: The formula CO2 means that
- CO2 represents carbon dioxide.
- The molecular formula of carbon dioxide is CO2.
- Each molecule contains one carbon atom joined by chemical bonds with two oxygen atoms.
- The molecular mass of carbon dioxide is 44, given that the atomic mass of carbon is 12 and that of oxygen is 16.
Rules in Naming Certain Chemical Compounds
4. Nomenclature of acids
- Binary acids
The names of binary acids are given by adding the prefix hydro– and the suffix –ic to the name of the second element.
Example: HCl – Hydrochloric acid
HF – Hydrofluoric acid - Acids containing radicals of polyatomic groups
The names of acids containing radicals of polyatomic groups such as sulphate SO4, nitrate NO3 etc. are given on the basis of the second element present in the molecule, and the prefix hydro– is not used.
Example: H2SO4: The second element is sulphur; thus, the name sulphuric acid.
HNO3: The second atom is nitrogen; thus, the name nitric acid.
5.Trivial names
Names of certain compounds do not follow any systematic rule. Such names are called trivial names or common names, and they are widely accepted.
Kinetic Molecular Theory of Gases
Assumptions or postulates of the kinetic molecular theory of gases:
- Gases consist of a large number of minute identical particles (atoms or molecules) which are very small.
- Gas molecules are so far apart from each other that the actual volume of the molecules is negligible as compared to the total volume of the gas. They are thus considered point masses.
- There is no force of attraction between the particles of a gas at ordinary temperature and pressure.
- Particles of a gas are always in constant and random motion.
- Particles of a gas move in all possible directions in straight lines. During their random motion, they collide with each other and with the walls of the container. Pressure is exerted by the gas as a result of collision of the particles with the walls of the container.
- Collisions of gas molecules are perfectly elastic, i.e. the total energy of molecules before and after the collision remains the same. Although energy is exchanged between colliding molecules, their individual energies may change, but the sum of their energies will remain constant.
- At any particular time, different particles in the gas have different speeds and hence different kinetic energies.
- In kinetic theory, it is assumed that the average kinetic energy of the gas molecules is directly proportional to the absolute temperature.
where
p = Pressure exerted by the gas
V = Volume of the gas
m = Mass of each molecule of the gas
c = Root mean square of the gas
Deviations from Ideal Behaviour
- Gases show deviation from ideal behaviour because of two faulty assumptions:
- There is no force of attraction between the molecules of a gas.
- Volume of the molecules of a gas is negligibly small compared to the space occupied by the gas.
- At low temperature and high pressure, gases deviate from ideal behaviour, i.e. gases behave as real gases.
- At low pressure and high temperature, gases show ideal behaviour, i.e. gases behave as ideal gases.
- Gases which are soluble in water are easily liquefiable, i.e. gases such as CO2, SO2 and NH3 show larger deviations than gases such as H2, O2 and N2.
- Van der Waals equation of state:
where a and b are Van der Waals constants, and n is the number of moles of the gas. - The deviation from ideal behaviour can be measured in terms of the compressibility factor Z, which is the ratio of the product of pV and nRT.
For ideal gas: Z = 1
For real gas: If Z < 1, it is called negative deviation.
If Z > 1, it is called positive deviation. - Compressibility factor (Z) versus pressure (p) for some gases:
- Deviations from ideal behaviour decrease with an increase in temperature.
- The temperature at which a real gas obeys the ideal gas law over an appreciable range of pressure is called Boyle temperature or Boyle point.
Differences between an Ideal Gas and a Real Gas
The Gas Laws
- The behaviour of a gas under known conditions of temperature, pressure and volume is described by laws known as gas laws.
- The standard variables used for gas laws are pressure (P), temperature (T) and volume (V).
Pressure–Volume Relationship in Gases
At constant temperature, the volume of a fixed mass of a gas decreases when the pressure increases and increases when the pressure decreases.
Temperature–Volume Relationship in Gases
At constant pressure, the volume of a fixed mass of a gas increases with an increase in temperature and decreases with a decrease in temperature.
It is measured in the Kelvin or Absolute scale.
Boyle’s Law
In 1662, an Anglo–Irish scientist Robert Boyle stated that the pressure of a fixed amount (i.e. number of moles, n) of gas varies inversely with its volume at constant temperature. This is known as Boyle’s law.
- At constant temperature, the volume of a given mass of a dry gas is inversely proportional to its pressure.
Hence, PV= K1=Constant - Boyle's law can also be stated as ‘for a given mass of a gas the product of pressure and volume is always constant at constant temperature’.
- If P1, P2 and P3 are the pressures of the given masses of a gas and V1, V2 and V3 are the volumes at constant temperature, then according to Boyle’s law:
P1V1=P2V2=P3V3=K1= Constant
- Charles’s Law
- At constant pressure, the volume of a given mass of a dry gas increases or decreases by
of its original volume at 0°C for each degree centigrade rise or fall in temperature.
V ∝ T (at Constant Pressure) - At temperature T1 (K) and volume V1 (cm3),
- At temperature T2 (K), volume is V2 (cm3).
Graphical Representation of Charles’s Law
Absolute Zero
The lowest hypothetical or theoretical temperature of −273°C at which a gas is supposed to have zero volume is called absolute zero.
As V and 273 are constant,
or V = kTAbsolute or Kelvin Scale of Temperature
The temperature scale with its zero at −273°C and each degree equal to one degree on the Celsius scale is called the Kelvin or absolute scale of temperature.
Conversion of Temperature from the Celsius Scale to the Kelvin Scale and vice versa
The value on the Celsius scale can be converted to the Kelvin scale by adding 273 to it.
Example: 20°C = 20 + 273 = 293 K
Gay-Lussac’s Law/Amonton's Law (Pressure–Temperature Relationship)
- The French chemist and physicist Joseph Louis Gay-Lussac made several observations on variation of pressure of a gas with temperature.
- At constant volume, the pressure of a given mass of a gas increases or decreases by of its pressure at 0°C for every 1°C rise or fall in temperature.
, i.e. P = kT 
- Pressure versus temperature (Kelvin) graph at constant molar volume.
Avogadro Law (Volume–Amount Relationship)
- In 1811, the Italian scientist Amedeo Avogadro proposed that equal volumes of gases at the same temperature and pressure should contain equal number of molecules.
V ∝ n
where n is the number of moles of the gas (P and T are constant)
Þ V = k4 n
Number of molecules = Number of moles × Avogadro's number
= 6.022 × 1023 × n
Where d is the density of the gas.
Ideal Gas
- A gas which follows Boyle’s law, Charles’ law and Avogadro’s law strictly is called an ideal gas.
- It is an imaginary gas which has 0 volume at 0 K.
- The gas equation is an equation used in chemical equations for calculating the changes in volume of gases when pressure and temperature both undergo a change, thereby giving a simultaneous effect of changes of temperature and pressure on the volume of a given mass of a dry gas.
According to Charles' law: V∝ T Constant P ….. (2)
According to Avogadro's law: V∝ n at constant T and P … (3)
where n is the number of molecules
- Different values of the universal gas constant:
R = 8.314 Pa m3 K−1 mol−1
= 8.314 × 10−2 bar L K−1 mol−1
= 8.314 J K−1 mol−1 - If the volume of a given mass of a gas changes from V1 to V2, its pressure changes from P1 to P2 and its temperature changes from T1 to T2, then
The above equation is called the gas equation. This equation is also called the combined gas equation.
Density and Molar Mass of a Gaseous Substance - Ideal gas equation can be rearranged as follows:
Dalton’s Law of Partial Pressures
- According to Dalton’s law of partial pressures, the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases.
Mathematically, it is written as
ptotal = p1 + p2 + p3
ptotal is the pressure exerted by the mixture of gases
where p1 + p2 + p3 are partial pressures of gases - Pressure of a dry gas is calculated as
pDry gas = ptotal − Aqueous tension - Pressure exerted by saturated water vapour is called aqueous tension.
- Partial pressure in terms of mole fraction is expressed as
pi = xi × ptotal
where pi is partial pressure of ith gas and xi is the mole fraction of ith gas.
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