Physics, Chemistry & Maths Glossary

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A

Alcohol Oxidation with Potassium Dichromate

Potassium dichromate oxidises 1^o and 2^o alcohols and gets reduced to green Cr³⁺ ion.

In case of 3^o alcohols the bright orange colour of dichromate ion remains as it is indicating no reaction.

The colour change can be used to indicate a reaction. If the orange colour changes to green or blue green a reaction has occurred.

fig.

Alkyl Halide Nucleophilic Substitution/Elimination

Primary: Generally S_N2 is better than E2. E2 is favoured by strong bulky base with heating as bulky base finds is harder to reach C than H due to steric hindrance

Secondary: S_N2 is favoured over E2 if nucleophile is weak base and the solvent is polar and aprotic. E2 is favoured over S_N2 if strong base is used in protic solvent. Heating further favours E2 over S_N2. Reactions can go via S_N1 and E1 mechanisms in protic solvents.

Tertiary: E2 is almost exclusive in the presence of strong base and protic solvent.

B

Bayes' Theorem

While may be interesting to think about the future outcome of an event, many times it is important to know the likelihood of something once an event has happened.

Let B₁, B₂, …, B_n be n mutually exclusive and exhaustive events in a sample space S. Let A be any event in S intersecting every B_i, (i = 1,2,…,n) and \(P(A)\neq 0\). Then

\(P(B_i /A) = {\rm{ }}{{{\rm{P(B}}_{\rm{i}} )P(A/B_i )} \over {\sum\limits_{j = 1}^n {P(B_j )P(A/B_j )} }}\)

Think of it as A has happened and one of the Bs must have happened. So, here we are interested to know the probability that after A has happened what are the chances of a specific B happening.

C

Cauchy-Bunyakovsky Inequality

\(\left|{\int\limits_a^b{f(x)g(x)dx}}\right|\le\sqrt{\int\limits_a^b {f^2 (x)dx}}\sqrt{\int\limits_a^b{g^2(x)dx}}\)

Class 01 - Chemical Bonding

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Class 01 - Trigonometric Equations

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Class 01 - Work & Energy

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Conditional Probability

\(P(A \cap B) = P(A)P(B/A)\)

Here, event A has taken place before B.

\(P(A \cap B) = P(B)P(A/B)\)

Here, event B has taken place before A.

Conservation of Angular Momentum

Conservation of angular momentum (COAM) is applicable to a system experiencing no net external torque.

It says that internal torques alone cannot change the angular momentum of the system. In other words, the angular momentum of the system is conserved in the absence of external torques.

Conservation of Linear Momentum

Conservation of linear momentum (COLM) is applicable to a system experiencing no net external force.

It says that internal forces alone cannot change the momentum of the system. In other words, the momentum of the system is conserved in the absence of external forces.

A typical example is that of a bullet fired from the gun. Initially, the bullet is inside the gun and the momentum of the system (gun + bullet) is zero. Now, when the gun fires the bullet, the bullet has forward momentum. However, the forces between the bullet and the gun are internal forces. So, the overall momentum must be zero later as well. So, the gun moves backwards and has backwards momentum. This ensures the overall zero momentum of the system.

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