Haloalkanes and Haloarenes: General Concepts

Arenes: Arenes are aromatic hydrocarbons—a class of organic compounds containing one or more special rings of carbon atoms with delocalized pi electrons. They are cyclic unsaturated (having atleast one double or triple bonds) organic compunds. 

Key Features

Structure: Built on flat, cyclic rings (such as benzene rings) with alternating single and double bonds that achieve special stability through resonance. 
The Term "Aromatic": Originally described sweet-smelling plant extracts, but today it defines electronic stability and ring conjugation rather than odor. 
Properties: Typically hydrophobic (water-fearing), non-polar, and prone to burning with a sooty flame due to a high carbon-to-hydrogen ratio.

 

Why Markovnikov rule applies only to asymmetric alkenes:

Just like haloalkanes are classified as primary,  secondary and tertiary according to the nature of carbon atom to which halogen atom is attached, amines are also classified as primary,  secondary and tertiary. 

For example in above diagram, Aniline is a primary aromatic amine, n-methylbenzenamie is a secondary aromatic amine and n,n dimethylbenzenamine is a tertiary aromatic amine.

The Amino functional group -NH2

Notice that Benzenediamine is not a secondary amine.

Meaning of 'in situ' reaction:

In situ preperation of Phosphorous Tribromide.

Ampere's circuital law

 Ampere's circuital law states that the line integral of a magnetic field around any closed loop is equal to the permeability of free space multiplied by the net electric current enclosed by that loop.

While the Biot-Savart Law gives the magnetic field at a point due to a current element using vector calculus, Ampere’s law provides a simpler alternative when symmetry is present. For instance, in the case of a long straight wire, a toroid, or a solenoid, the law allows for a direct and often less mathematically intensive calculation of the magnetic field. The law states that the line integral of the magnetic field around any closed loop is proportional to the net current enclosed by that loop. However, it is important to note that Ampere’s law is strictly valid for steady currents, meaning the current must remain constant with time. The complications that arise in time-varying situations lead to the introduction of the concept of displacement current, which extends the law to dynamic fields, a topic explored in later chapters.

We draw a circular loop with radius ' r' passing through point  'P', with the current-carrying wire lying on its axis. This loop is called an Amperian loop.

The Amperian loop can be of any shape, but for practical calculations, it is often chosen with symmetry to simplify the mathematics.

It is important to choose the direction of the current and the direction in which you traverse the loop properly; this is determined by the right-hand rule. If you curl the fingers of your right hand in the direction you traverse the loop, then your right thumb points in the direction in which the current is considered positive.

Pythagorous theorem for sides of a triangle of any angle theta

 Expansion of the Pythagorous theorem for a triangle with any angle other than 90 degree....also called as Law of Cosines.

Law of Cosines...gives general relation between the three sides of any triangle ( it is also true for right angle triangles).

For small x, the expression (1+x)^n approximates to 1+nx.

 

What are cis trans isomers

 Cis and trans isomers are [stereoisomers] (molecules with the same formula and bonds, but different 3D shapes). In a cis isomer, the same or high-priority groups sit on the same side of a rigid structure (like a double bond or ring). In a trans isomer, those groups sit on opposite sides.

Is there some rotation too when a ball is slipping?

 

A solid sphere (A) of mass 5m and a spherical shell (B) of mass m, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of a and b, respectively. The ratio of a and b is?