B.sc. 2nd Part Chemistry Subsidiary Notes
93Np239 --- -β---> 94Pu239.
Other examples are-
13Al27 + 2He4 ———–> 15P30 + 0n1
15P30 ———–> 14Si30 + 1e0
5B10 + 2He4 ———–> 7N13 + 0n1
E = mc2
where E is the energy, m is the mass and c is the velocity of light and according to which the energy and mass are inter-convertible.
Nucleus contains mainly two particles – protons and neutrons- in addition to many other elementary particles. Thus, the mass of the nucleus is the masses of protons and neutrons, but the experiments have shown that the sum of the masses of protons and neutrons is always greater than experimentally determined nuclear mass.
This mass difference is called Mass Defect or binding energy of nucleus.
In order to bind protons and neutrons together, some energy is needed, which is taken out of the masses of protons and neutrons. Some of the masses of protons and neutrons converted into an energy and utilizes that energy to bind the protons and neutrons within the nucleus.
The stability of nuclei of different mass number and the same mass number can be explained on the basis of binding energy per nucleon. The nucleus with large binding energy per nucleon is more stable. When a graph is plotted between binding energy per nucleon and mass number of different nuclei, the given grapg is obtained. This curve is called nuclear binding energy curve.
Except 2He4, 6C12 and 8O16, all the elements lie on this curve. Binding energy per nucleon of heavy elements is small. So, these elements are radioactive. The heavy elements are disintegrated and after disintegration, stable nuclei are formed because these stable nuclei have larger binding energy per nucleon.
The maximum binding energy per nucleon is 8.7 MeV of iron. So, iron is found in nature in large abundant. Maximum stable nuclei have near about 8MeV.
Other examples are-
13Al27 + 2He4 ———–> 15P30 + 0n1
15P30 ———–> 14Si30 + 1e0
5B10 + 2He4 ———–> 7N13 + 0n1
Radioactivity
Radioactivity is the process by which the nucleus of an unstable atom loses energy by emitting radiation, including alpha particles, beta particles, gamma rays and conversion electrons Although radioactivity is observed as a natural occurring process, it can also be artificially induced typically via the bombarding atoms of a specific element by radiating particles, thus creating new atoms.Nuclear Binding Energy
The nuclear binding energy is an energy required to break up a nucleus into its components protons and neutrons. In essence, it is a quantitative measure of the nuclear stability. The concept of nuclear binding energy is based on Einstein's equation-E = mc2
where E is the energy, m is the mass and c is the velocity of light and according to which the energy and mass are inter-convertible.
Nucleus contains mainly two particles – protons and neutrons- in addition to many other elementary particles. Thus, the mass of the nucleus is the masses of protons and neutrons, but the experiments have shown that the sum of the masses of protons and neutrons is always greater than experimentally determined nuclear mass.
This mass difference is called Mass Defect or binding energy of nucleus.
In order to bind protons and neutrons together, some energy is needed, which is taken out of the masses of protons and neutrons. Some of the masses of protons and neutrons converted into an energy and utilizes that energy to bind the protons and neutrons within the nucleus.
The stability of nuclei of different mass number and the same mass number can be explained on the basis of binding energy per nucleon. The nucleus with large binding energy per nucleon is more stable. When a graph is plotted between binding energy per nucleon and mass number of different nuclei, the given grapg is obtained. This curve is called nuclear binding energy curve.
Except 2He4, 6C12 and 8O16, all the elements lie on this curve. Binding energy per nucleon of heavy elements is small. So, these elements are radioactive. The heavy elements are disintegrated and after disintegration, stable nuclei are formed because these stable nuclei have larger binding energy per nucleon.
The maximum binding energy per nucleon is 8.7 MeV of iron. So, iron is found in nature in large abundant. Maximum stable nuclei have near about 8MeV.
Number of Phases
A phase is defined as an homogeneous, physically distinct and mechanically separable portion of system, which is separated from other such parts of the system by definite boundary surfaces.Solid Phase
Each solid forms a separate phase. The number of solid phase depends on the number of solids present in it.
Example- Many forms of sulphur can exist together, but these are all separate phases.
Liquid Phase
If two liquids are immiscible, they will form two separate liquid phases.
Examples- Water and Oil.
If two liquids are miscible they will form one liquid phase only.
Water and Ethyl alcohol
Gaseous phase
Since a gaseous mixture are completely miscible in all proportions so, it will form one phase only. Example : a mixture of N2 and H2 forms one phase only.
A solution of a substance in a solvent consists of one phase only, e.g. NaCl solution.
A heterogeneous mixture like CaCO3(s) ⇌ CaO(s) + CO2(g)consists of three phases (i.e., two solids and one gaseous).
At freezing point, water consists of three phases
Ice(S) ⇌ Water(L) ⇌ Water Vapour(G)
The chemical component of all the three phases is H2O and therefore it is one component system.
A homogeneous solid solution of a salt forms a single phase.
Example- Mohr’s salt [ FeSO4. (NH4)2SO4.6H2O] solution has a single phase.
Degree of Freedom
It is defined as the minimum number of independent variable factors such as temperature, pressure and concentration of the phases, which must be fixed in order to define the condition of a system completely.A system having 1,2,3 or 0 degrees of freedom is called univariant, bivariant, trivariant and nonvariant respectively.
It is calculated by formula
F = C − P + 2
Ice(S) ⇌ Water(L) ⇌ Water Vapour(G)
The three phases can be in equilibrium only at particular temperature and pressure. Therefore, when all the three phases are present in equilibrium, then no condition need to be specified. The system is therefore zero variant or invariant or has no degree of freedom.
F = C − P + 2
In the water system-
C = 1 and P = 3
So, F = 1 − 3 + 2 = 0. So, it is a zero variant or invariant or has no degree of freedom.
In this system, if pressure or temperature is altered , three phases will not remain in equilibrium and one of the phases disappears.
If we consider a system consisting of water in contact with its vapour,
Water(l) ⇌ Water vapour(g)
we must state either the temperature or pressure Thus degree of freedom is one and the system is univariant.
If we consider a system consisting of water vapour phase only, we must state the values of both the temperature and pressure in order to define the system completely. Hence the system is bivariant or has two degrees of freedom.
Component
It is defined as the smallest number of independently variable constituents by means of which the composition of each phase can be expressed in the form of a chemical equation.Ice(S) ⇌ Water(L) ⇌ Water Vapour(G)
The chemical component of all the three phases is H2O and so it is an one component system.
Sulphur exists in four phases namely rhombic sulphur, monoclinic sulphur, liquid sulphur and vapour sulphur, but the chemical composition of all phases is S. So, it is an one component system.
Phase Rule
Phase rule was deduced by the American physicist J. Willard Gibbs and stated as "If the equilibrium between any number of phases is not influenced by gravity, electrical, magnetic forces or by surface action but are influenced only by temperature, pressure and concentration , then the number of degrees of freedom (F) of the system is related to the number of components (C ) and number of phases (P) by the following equation"-F = C − P + 2
Eutectic Point
It is the lowest freezing point that can be reached for a eutectic combination (which means lowest melting point).In the solid-liquid system where all three phases, namely the liquid melt of the two metals and the solid phases of each of the components, are in equilibrium at eutectic point.
The melting point of the mixture corresponding to the eutectic point is the lowest. At this stage, the system is invariant (i.e., the degrees of freedom or variance are zero) and has a fixed temperature and composition.
Phase Diagram
It is a graph obtained by plotting one degree of freedom against another. If the phase diagram is plotted between temperature against pressure, the diagram is called P-T diagram. P-T diagram is used for one component system.If the phase diagram is drawn between temperature against composition, the diagram is called T-C diagram. T-C diagram is used for two component system.
From the phase diagram, it is possible to predict whether an eutectic alloy or a solid solution is formed on cooling a homogeneous liquid containing mixture of two metals. Phase diagrams are useful in understanding the properties of materials in the heterogeneous equilibrium system.
Phase Diagram of Ice-Water Vapour System
Watre is an one component system which is chemically a single compound involved in the system. The three possible phases in this system are ice(solid phase), water(liquid phase) and vapour(gaseous phase).Hence, water constituetes a three phase and one component system. Since water is a three phase system, it can have the following three equilibria-
Ice ⇌ Vapour
Ice ⇌ Water
Water ⇌ Vapour
i.e. Ice ⇌ Water ⇌ Vapour
Each equilibrium involves in two phases. The nature of these phases which exist in equilibrium at any time depends on the conditions of temperature and pressure. These conditions have been determined and summarized in the pressure-temperature diagram in which pressure is treated as independent variable.
The phase diagram consists of-
1.Curves: There are three curves OA, OB and OC
2.Areas: Three curves OA , OB and OC divide the diagram into three areas AOB, AOC and BOC.
3.Triple point: The above three curves meet at the point O and is known as triple point.
4.Metastable equilibrium: The curve OA represents the metastable equilibrium.
Curve OA
The curve OA is called vapourisation curve and represents the equilibrium between water and vapour. At any point on the curve the following equilibrium will exist-
Water ⇌ Water vapour
Applying phase rule equation on this curve-
F = C – P + 2
or, F = 1 – 2 + 2
or, F = 1
The degree of freedom of the system is one, i.e, univariant.
Curve OB
The curve OB is called sublimation curve of ice and represents the equilibrium between ice and vapour. At any point on the curve the following equilibrium will exist-
Ice ⇌ Vapour Applying phase rule equation on this curve-
F = C – P + 2
or, F = 1 – 2 + 2
or, F = 1
The degree of freedom of the system is one, i.e., univariant.
Curve OC
The curve OC is called melting point curve of ice and represents the equilibrium between ice and water. At any point on the curve the following equilibrium will exist-
Ice ⇌ Water
The curve OC is slightly inclined towards pressure axis. This shows that melting point of ice decreases with increase of pressure.
The degree of freedom of the system is also one. i.e., univariant.
Areas
Area AOC, BOC , AOB represents water, ice and vapour respectively. In order to define the system at any point in the areas, it is essential to specify both temperature and pressure.
Applying phase rule equation on the area-
F = C – P + 2
or, F = 1 – 1 +2
or, F = 2
So, the degree of freedom of the system is two. i.e., Bivariant.
Triple point (Point 'O')
At triple point all the three phases (i.e. ice, water and vapour) coexist. Thus the value of Phase(P) is 3. Applying phase rule equation, the degree of freedom at this point is zero. It means that three phases can coexist in equilibrium only at a definite temperature and pressure.
At this triple point, neither pressure nor temperature can be altered even slightly without causing the disappearance of one of the phases.
Curve OA' ( Metastable equilibrium)
The curve OA' is called vapour pressure curve of the super-cool water or metastable equilibrium. The following equilibrium will exist-
Super-cool water ⇌ Vapour
Supercooled water is unstable and it can be converted into solid by slight disturbance.
Summary of Water System
| Curve/Area/Point | System Name | Phases in Equilibrium | Number of Phases | Degree of Freedom |
|---|---|---|---|---|
| Curve OB | Vaporization | Liquid & Vapour | 2 | 1 |
| Curve OA | Sublimation | Solid & Vapour | 2 | 1 |
| Curve OC | Fusion | Solid& Liquid | 2 | 1 |
| Curve OA' | Metastable | Liquid & Vapour | 2 | 1 |
| Area AOC | Ice | 1 | 2 | |
| Area BOC | Water | 1 | 2 | |
| Area AOB | Vapour | 1 | 2 | |
| Point O | Ice, Water & Vapour | 3 | 0 |