Colligative properties and determination of molar mass

Introduction :

The vapour pressure of solution decrease when a non volatile solution is added to a volation solvent. There are many properties of solution which are connected with this decreasing of vapour pressure. These are the relatively of vapour pressure of the solvent, depression of freezing points of the solvent. Elevation of the boiling point of the solvent, osmotic pressure of the solution. Everyone these of the property depend on the numeral of solute particle irrespective of their environment relative.

Relative lowering of vapour pressure:

In colligative properties and determination of molar mass, the vapour pressure of a solvent in solution is less than that of the pure solvent. Raoult recognized that the lower of vapour pressure depends simply on the concentration of the solute particles and it is dependent of their individuality.

`p_(1)=x_(1)p_(1)^(0)`

The reaction of the colligative properties in the vapour pressure of solvent is given as:

`Deltap_(1)=p_(1)^(0)-p_(1)=p_(1)^(0)-p_(1)^(0)x_(1)`

           =`p_(1)^(0)(1-x_(2))`

In a solution colligative properties containing several non volatile solutions, the lowering of the vapour pressure depends sum of the mole fraction of different solutions.

`(Deltap_(1))/(p_(1)^(0))` =`(p_(1^(0))-p_(1))/(p_(1)^(0))` =`x_(2)`

                The expression on the left hand side of the equation as mentioned earlier is called relative lowering of vapour force and is equal to the mole division of the solution of the colligative properties. The above equation can be determinations as:

`(p_(1)^(0)-p_(1))/(p_(1)^(0))` =`(n_(2))/(n_(1)+n_(2))`

                Here n₁ and n₂ are the number of mole of solvent and solute respectively present in the solution.

For dilute solution n₂<<n₁ hence neglection n₂ in the denominator we have

`(p_(1)^(0)-p_(1))/(p_(1)^(0))` =`(w_(2)xxM_(1))/(M_(2)xxW_(1))`

Here w₁ and w₂ are the mass and M₁ and M₂ are the molar mass of the solvent and solute correspondingly.

Elevation of boiling point:

In the colligative determination of molar mass, the vapour pressure of a liquid increase with enhance of temperature.It boils at the warmth at which its vapour pressure is identical to the atmospheric strain. The determination molar boiling point of a solution is always higher than that of the boiling point of the pure solvent.

Depression of freezing points:

The lowering vapour pressure of a solution cause a lowering of the freezing points compared to that of the determination  pure solvent in molar mass. The freezing points of the substance, the solids phase are the dynamic equilibrium with the liquid phases. The freezing points of the substance may be defined as temperature at which the vapour pressure of the substance in its liquid phase is equal to the vapour pressure in the solids state.

Mole chemistry

Introduction:
All substance is made up of smallest particle, called atom. In chemistry, the smallest particle, used for calculation, is said to be a mole. Any chemical equation or a chemical expression is given with moles of a substance under consideration.

Mole Definition:
Mole is the smallest unit used in all calculations in chemistry. Mole is a unit of measurement, which gives the same number of chemical entities (atoms, molecules, ions, electrons), as in number of atoms in 12 grams of carbon.

Mole concept is used in calculation of concentrations of solutions, in the calculation of molecular mass, etc.

Molar mass of a substance is defined as “mass per mole” of a substance.
Mole of a substance can also be defined as: “one mole of a substance contains Avogadro number of molecules or atoms”.
The value of Avogadro’s number is – 6.023 x 10²³
This is given by:

Mole =
Mole Calculation

Many calculations, regarding a chemical compound can be obtained from the mole concept.
Mole of a substance is used to calculate-
a.     Grams of a substance, if molar mass is known.
b.     Molar mass of a substance, if grams are known.
c.      Molarity, molality, mole fraction.
d.     Number of atoms present, with the help of Avogadro’s number.

Thus, moles play a very important role in chemical calculations.

Chemistry Mole Problems-
Example – 1:
A sample of magnesium hydroxide contains 12 grams of the substance. Calculate the number of moles of Mg(OH)₂ present.
Answer:
Molar mass of Magnesium hydroxide is: 58.32

Moles of Magnesium hydroxide = Mass in grams / Molar mass
                                                         = 12 grams / 58.32 grams/mole
                                                        = 0.206 moles.

Example – 2
13.65 moles of methane gas was obtained in a reaction. Find the mass in grams of methane.

Answer:
Molar mass of methane is 16.04 grams/mole.
Moles of methane = Grams of methane / Molar mass
Grams of methane = Moles of methane x Molar mass
                                    = 13.65 moles x 16.04 grams / mole
                                    =   218.94 grams of methane
Mole Problems Chemistry
Finding number of atoms, with Avogadro number
Example – 3
Calculate the number of atoms present in 4.2 moles of Sodium.
Answer:

1 Mole of a substance contains Avogadro number of atoms/molecules/ions.
Therefore, Avogadro’s constant =

We have – 4.2 moles of Sodium.

Number of atoms of Sodium present =


    4.2 moles of Na x   = 25.29 x 10²³ atoms of Na

Example – 4
 There are 3.01 x 10³² molecules of carbon dioxide present. Calculate:

i)                   Number of moles

ii)                Number of grams of CO₂.

Answer:

i)  To calculate the number of moles-

Moles of Carbon dioxide

= 3.01 x 10³² atoms of CO₂ x

= 4.99 x 10⁹ moles of Carbon dioxide

ii)                 To calculate the mass in grams of carbon dioxide –

Mass in grams = Moles of CO2 x Molar mass

                          = 4.99 x 10⁹moles x 44 grams / mole

                           = 219.56 x 10⁹ grams of Carbon dioxide

Molar Mass

Two very important entities of elements that recognise its characteristics are its atomic number and atomic mass. Similarly, mol mass of a compound is very important and is used in almost all stoichiometric calculations of a compound.

Molar Mass Definition

Molecular mass of a compound is the sum of atomic masses of all elements present in it.

Molecular mass is a physical property of a compound. It is denoted by M.

Molar Mass-

Molecular mass can also be calculated using the mass of a substance and the amount of substance present in moles.

Molecular mass = Grams of a substance / Moles

Mol mass is expressed in grams per mole.

Mol mass is used to find the moles of a substance, when its mass is given.

How to Calculate Molar Mass –

Molar mass of a substance can be found from the atomic masses of the elements present in it. Atomic masses of the individual elements can be obtained from the periodic table.

To calculate mol mass, we need to follow the following steps:

1. Write the Formula for Molar Mass of the compound whose mol mass is to be calculated.

Example – Magnesium chloride

MgCl₂

2. Find the subscripts/number of each element present in the compound.

1 x Mg + 2 x Cl

3. Multiply the number of each element present with the atomic mass of that element.

1 x 24.305 (Mg) 2 x 35.453 (Cl)

= 24.305 = 70.906

4. Finally, put all the atomic masses and their multiplied values together and sum it up.

Mg + 2 x Cl

= 24.305 + 70.906

= 95.211 grams/mole

Molar Mass of Water –

Formula of water is H₂O.

To calculate the mol mass of water, we need to have the atomic masses of hydrogen and oxygen.

Atomic mass of hydrogen = 1.008 grams/mole

Atomic mass of Oxygen = 15.994 grams /mole

There are two moles of Hydrogen. Thus, 2 x 1.008 = 2.016

Mol mass of water = 2.016 + 15.994 = 18.01 grams/mole.

Example of molar mass calculations:

To calculate the mol mass of Sodium hydroxide:

Formula of sodium hydroxide is NaOH

There are 1 mole of sodium, Na, 1 mole of hydrogen, and 1 mole of Oxygen.

To find the mol mass, we can add the atomic masses of all the elements.

Atomic mass of Sodium = 22.989 grams/mole

Atomic mass of oxygen = 15.994 grams/mole

Atomic mass of Hydrogen = 1.008 grams/mole

Mol mass of Sodium hydroxide = Na + O + H

= 22.989 + 15.994 + 1.008 = 39.991 grams/mole.

Mol mass of sodium hydroxide is taken approximately for calculations as 40 grams/mole.

Metals Nonmetals and Metalloids

Periodic table consists of an array of elements, with different metallic properties. Some are completely metallic, making them soft or hard metals. Other major type includes the non-metals, which have completely different physical and chemical properties from metals and are easily distinguishable.

Some elements have properties in-between that of a metal and a non-metal. These types of elements are termed as ‘metalloids’.

Characteristics of Metals Nonmetals Metalloids-

Common characteristics through which a metal, non-metal and a metalloid can be differentiated are:

Metals:

An element is called as metal, when, in the process of forming an ionic bond, it donates electrons, to form a positive ion. Thus, the main characteristics of a metal is that, it should have very less first ionization energy, or energy due to removal of outermost electron.

Some common properties of metal are:

1. Metals are mostly solids, hard or soft. Metals of first two groups of the periodic table are soft solids, while transition metals are hard. Mercury is the only metal, which is a liquid.
2. They are malleable and ductile.
3. They transfer heat and electricity due to the presence of ions in their structure. There is a special type of bond called as metallic bond, which gives metals all these distinctive properties.

Non-metals:

An element is said to be a non-metal, when it shows electronegative property than electropositive property. They accept electrons to form an ionic bond. Their first ionization energy is very high.

1. Non-metals are mostly liquids, gases or in some case, amorphous solids.
2. If they are solids, they are brittle solids, and are not malleable and ductile.

Metalloids:

These are elements which have properties in-between that of metals and non-metals. Metalloids are called as semi-metals. They have lustre like metals, but do not conduct electricity.

Metalloids find use as semiconductors. Metalloids are placed with the non-metals in 14^th, 15^th and 16^th Group of the periodic table.

List of Metals Nonmetals and Metalloids

Some of the metals, metalloids and non-metals are listed below:

Metals	Metalloids	Non-metals
Copper- Cu	Silicon -Si	Oxygen-O
Iron- Fe	Germanium - Ge	Chlorine –Cl
Mercury Hg	Antimony -Sb	Nitrogen – N
Cadmium Cd	Arsenic - Sb	Carbon – C
Sodium Na	Tellurium -Te	Sulfur – S
Calcium Ca		Phosphorus -P
Chromium Cr		Bromine -Br

Is Gold a Metal Nonmetal or Metalloid–

Gold, Au, is one of the transition elements. It has an atomic number of 79 and is placed in group 11 of the table. It is a transition metal.

Is Sodium a Metal Nonmetal or Metalloid–

Sodium is placed in the first group of the periodic table. It is a soft metal. Sodium is one of the alkali metals.

Is Calcium a Metal Nonmetal or Metalloid-

Calcium, a white amorphous solid, is a metal, because of its electron donating property. Calcium is an alkaline earth metal.

Ionic Compound

Elements combine together to form compounds. Chemical compounds are of many types, depending upon the bond present in them. Corresponding to the two ways by which any two atoms rearrange to form a compound, two types of bonds are formed.

1. Ionic bond
2. Covalent bond.

Ionic bond or electrovalent bond is established by the transfer of one or more valence electrons from one atom to the other.

Thus, ionic bond is a chemical bond formed between two atoms by the transfer of one or more valence electrons from one atom to the other.

This bond is also called as a polar bond.

Formation of an ionic bond:

Formation of an ionic bond can be explained using the following example:

Consider an atom A , which has two electrons in its outermost shell. Another element B, has 6 electrons in its outermost shell.

The atom A has two electrons in excess, to make it to the Noble gas electronic configuration, while atom B has two electrons less to make it to that level.

Now, atom A gives two of the excess electron to atom B, and by this, atom A attains a completely filled shell, while atom B, having attained the required amount of electrons, also reaches the noble gas configuration.

They therefore form an ionic bond between themselves.

List of Ionic Compound Formula-

Lists of ionic-compounds with their formula are:

S.No	Ionic-compound	Formula
	Sodium chloride	NaCl
2.	Potassium iodide	KI
3.	Lithium iodide	LiI
4.	Aluminium oxide	Al2O3

Ionic Compound Example-

Some examples of ionic compound are:

Magnesium oxide - MgO – Mg²⁺, O^2-

Calcium Fluoride – CaF₂ – Ca²⁺, 2F^-

Aluminium Fluoride – AlF₃ – Al³⁺, F^3-

Properties of an Ionic Compound-

1. Ionic-compounds are three dimensional solids, with well-defined geometrical pattern.
2. Ionic solids conduct electricity when they are in water solution or in the fused state (molten state).
3. They are quite hard, have low volatility and high melting and boiling point.
4. Ionic solids are soluble in polar solvents, due to dissociation of their ions.
5. Ionic solids are very stable and have very high density.

Is NaCl an Ionic Compound-

Sodium chloride, NaCl is ionic in nature.

The formation of sodium chloride is as follows:

Na has an electronic configuration of 2, 8, 1. The last electron, in the third shell, has to be removed, for it to attain noble gas configuration.

Chlorine has a configuration of 2, 8, 7. It needs one extra electron, which it gains from Sodium, thereby getting the required magic number of ‘8’.

Is Salt an Ionic Compound–

Sodium chloride is also called as common salt. Other than this, most of the compounds, commonly known as salts are formed from the neutralization reaction of an acid and a base. They are all ionic-compounds, because they dissociate into ions in their solution.

Bonding and molecular structure

Syllabus : 

Valency electrons, the octet rule. Electrovalent and covalent bonds with examples. Properties of electrovalent and covalent compounds. Limitation of octet rule (examples), coordinate covalent bonds (examples).

Directionality of covalent bonds, shapes of polyatomic molecules (examples), concept of hybridization of atomic orbitals (qualitative pictorial approach): sp³, sp² and sp hybridizations with typical examples. Tetrahedral space model of-carbon atom, single-bond, double- bond and triple - bond involving carbon atom with examples a and 7t bonds.

Valence shell Electron Pair Repulsion (VSEPR) concept (elementary idea) - shapes of H₂0, H₂S,
CH₄, NH₃, C0₂, N0₂ and S0₂ molecules. Concept of resonance (elementary idea), resonance structures (examples). Elementary idea about electronegativity, bond polarity and dipole moment. Hydrogen bonding (inter - & intra molecular structures) and its effects on physical properties (mp, gp, and solubility).

Double salts and complex salts, and coordination compounds (examples only), coordination number (examples with C.N 4 and 6 only).

Valency Electrons and the Octet rule

When details of the electronic configurations of the elements came to be known, it was found tha the arrangement of energy levels in different orbits round the nucleus was different for different elements. Chemical union between atoms to form molecules are energetically favoured only if the chemical combination leads to lowering of energy of the system i.e, if the energy of the combined atoms i.e., the product molecule is less than the sum of the energies of the reactant molecules.

Chemical combination of atoms involves electrons of the two atoms and nuclei take no active part in chemical combination. In each individual atom, the outermost electrons have the highest energy amongst all its electrons. So the lowering of energy must be through the interactions of the outermost electrons of the two interacting atoms. Thus chemical combination in all probabilities, should involve only the outermost electrons of the participating atoms and the interactions should be such that it causes lowering of energy w.r.t. to the initial condition when the atoms lay separated from each other.

A close study of chemical properties of the different classes of elements led us to the fact that the noble gases were the most chemically inactive species amongest all the elements. They had no tendency to combine with themselves or with other elements. They were so inert that they even did not like to form molecules by the combination of two atoms. Inert gas molecules are monatomic — or in other words their atoms do not form molecules. They are devoid of any chemical affinity. mSo it may be seen in the light of our discussion above that their outer electronic configurations are most stable amongest all the elements and no further stabilization is possible by further interaction among themselves or with electrons in other elements.

The extra nuclear electrons present in n successive inert gases are 2,10,18, 36,54 and 86. These numbers were termed magic numbers as the presence of electrons in any one of these numbers in an atom gives special stability to the atom. This stability is lost if this number is changed even by 1 unit on either side.

The arrangement of the electrons in the inert gases can be described as follows :
He — 2
Ne — 2-8
Ar — 2-8-8
Kr —2-8-18-8
Ne —2-8-18-18-8

Molecular mass of polymers

Introduction :  
Several simple organic molecules of one or two types combine with each other by chemical bonds forming macro molecules the product is called a polymer. Simple organic molecules which can form polymers by chemical bonding are called monomers while this process of chemical combination is called polymerisation. In any sample or monomers there are very large number of molecules of lower masses same molecular weights and similar physical and chemical properties.

Polymers:

Ehereas in polymer sample having same molecular weights the number of molecules are very small. The polymers have comparatively very high molecular weight but all molecules do not have comparatively very high molecular weight but all molecules do not have identical molecular weights. Polymers prepared from the same monomer in different conditions do not have all the properties identical. Depending on reaction conditions polymer products have different proportions of molecules of lower and higher masses.

Molecular mass of Polymers:
Overall molecules of ethene combine with each other by addition reaction and give polyethene. This reaction at the first stage two molecules of ethene monomer combine together giving a dimer. A third molecule of ethene combines with this dimer giving a trimer and a forth molecule combine further gives a tetramer. This way monomer molecules go on joining and chain becomes longer. As result very large chain is former which is called macro molecule or polymer.
CH₂ = CH₂ `stackrel(CH_2=CH_2)(->)` CH₃-CH₂-CH = CH₂ `stackrel(CH_2=CH_2)(->)`
CH₃-CH₂-CH₂-CH₂-CH=CH₂ `stackrel(CH_2=CH_2)(->)`
CH₃-CH₂-CH₂-CH₂-CH₂-CH₂-CH=CH₂
`stackrel(nCH_2=CH_2)(->)`  [-CH₂-CH₂-]_n

The polymer chain can be lengthen upto certain limit at laboratory cantons. The tendency of this long chain then decrease to combine with further monomers. Thus in any condition polymers resulting from monomers do not increase in weight more than a certain limit. Generally any polymer asmple contains varying chain-lengths, its molecular mass is always an average molecular mass. The molecular mass of a polymer is expressed as number average molecular mass `barM_n` or weight average molecular mass `barM_w`.
`barM_n = (sumN_tM_t)/(sum tN_t)`
`barM_w = (sumN_tM^2_t)/(sumtN_tM_t)`
Where N_t = number of molecules
M_t = molecular mass.