State first law of thermodynamics and prove ΔE = qv.

First Law of Thermodynamics

"This law is also called the law of conservation of energy. This law is stated as, "energy of the universe is constant".

(OR)

"Energy can neither be created nor destroyed but can change from one form to another."

In other words, a system cannot destroy or create energy. However, it can exchange energy with its surrounding in the form of heat or work. Thus the energy change is the sum of both heat and work so that the total energy of the system and its surroundings remains constant.

Consider a gas enclosed in a cylinder having a piston. Suppose the internal energy of the system is E1. A quantity of heat q is given to the system and work W is done on the piston to keep it in its original position. During these operations, the internal energy of the system changes to E2, the change in internal ΔE is given by the following equation, which is the mathematical form of the first law of thermodynamics.

                    E2 - E1  =  ΔE = q + W

                    ΔE  = q + W

Sign of q will be positive when heat is supplied to the system and q is negative when heat flows out side across the boundary. W is negative when work is done by the system and W is positive when work is done in the system. Pressure volume work is given mathematically as:

                    Work = Force  x  Distance

An external pressure P exerted by a force F, spreads over the area A, as pressure is force per unit area.

                    P  =  F/A    or     F  =  P x A

The volume of the gas in the cylinder is equal to cross-section area A multiplied by the height of the column of the gas h.

                    V  =  A  x  h 

Now, let us assume that the gas expands and does work by pushing the piston against external pressure, "A" remains the same but "h" changes.

               ΔV  =  V2  -  V1

                    ΔV  =  Ahf  -  Ahi

                    ΔV  =  A (hf - hi)

                    ΔV  =  A  Δh

Work done by expansion of gas against constant pressure is given by

                    W  =  -F  x  Δh

                    W  =  -P  x  A  x  Δh

                    W  =  -P ΔV

The negative sign indicates that work is done by the system on the surrounding. So first law of thermodynamics can be written as:

                    ΔE  =  q  -  P ΔV

Energy changes at constant volume

If the volume of gas does not change, no work is done, (ΔV  =  0). By applying the first law of thermodynamics.

                    ΔE  =  qv  -  P ΔV

                    ΔE  =  qv  -  0      (ΔV = 0)

                    ΔE  =  qv

So the increase of heat at constant volume (qv) increases only the internal energy (ΔE) of the system and work done is zero.

What is hybridization? Explain sp² hybridization with example.

"The process of mixing orbitals of different energy and shape to form set of new orbital of the same energy and same shape is called Hybridization and orbitals obtained are called hybrid orbitals".

sp²-Hybridization

The process of mixing one 's' and two 'p' orbitals to form three equivalent sp² hybrid orbitals is called sp2-Hybridization.

Each sp² orbital consists of 's' and 'p' in the ratio of 1 : 2 respectively.

sp²-hybrid orbitals lie at the angle of 120° in a plane. The geometry of the molecules is trigonal planar.

Formation of Ethylene or Ethane (C2H4) Molecule

Electron configuration of C (6) = 1s ⇵, 2s ⇵, 2px↑, 2py↑, 2pz

Excited state = 1s ⇵, 2s ↑, 2px ↑, 2py ↑, 2pz ↑

One s and two p orbitals intermix to form three hybrid (sp²) orbitals. The geometry of molecules depends upon the number of hybrid orbitals. Hybrid orbitals are trigonal planar and are oriented at the angle of 120°. Each atom is left with one half filled p-orbital perpendicular to the planar sp² hybrid orbitals. Each carbon atom undergeos sp² -s, overlaps with two hydrogen atoms and sp² -sp² overlap between themselves to form sigma bonds. These overlaps lead to the following shapes. The partially filled p-orvbitals undergo overlap sideways to form a pi-bond. So, a pi-bond is formed by the sideways overlap of two half filled co-planar p-orbital in such a way that the probability of finding the electron is maximum perpendicular to the line joining the two should be made clear that a π-bond is formed between two atoms only, when the with a sigma bond.

What are London forces? Explain various factors affecting it.

Induced Dipole - Induced Dipole Forces or (Instantaneous Dipole) or (London Dispersion Forces)

Neither dipole - dipole nor dipole induced dipole forces can explain the fact that helium becomes a liquid at temperature below 4.2K. Non-polar gases like noble gases (He, Ne, Ar, Kr, Xe), methane, chlorine etc, becomes liquid at low temperature and high pressure.

A German physicist Fritz London in 1930 offered a simple explanation for these weak attractive forces between non-polar molecules.

In helium gas, the electrons of one atom influence the moving electrons of the other atom. Electrons repel each other and they tend to stay as far apart as possible. When the electrons of one atom move nearer to the electron of other atom, they are pushed away from each other. In this way a temporary dipole is created in the atom as shown in the Figure.

The result is that, at any moment, the electron density of the atom is no more symmetrical. It has more negative charge on one side than one the other. At that particular instant, the atom becomes a dipole. This is called instantaneous dipole. This instantaneous dipole then disturbs the electronic could of other molecule and forms induced dipole.

"The momentary force of attraction created between instantaneous dipole and the induced dipole is called Instantaneous dipole or induced dipole - induced dipole interaction or London forces."