Arrange the following compounds in increasing order of their reactivity towards \( S_N2 \) displacement: 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane.
To solve the problem, we need to arrange the compounds 2-Bromo-2-methylbutane, 1-Bromopentane, and 2-Bromopentane in increasing order of their reactivity towards Sₓ2 displacement.
1. Understand Sₓ2 Reaction Mechanism:
Sₓ2 reactions involve a backside attack by the nucleophile, requiring access to the carbon attached to the leaving group (Br⁻). Reactivity decreases with increasing steric hindrance: primary (1°) > secondary (2°) > tertiary (3°).
2. Classify the Compounds:
- 2-Bromo-2-methylbutane: The carbon with Br is bonded to three other carbons (two methyl groups and one ethyl group), making it a tertiary (3°) halide.
- 1-Bromopentane: The carbon with Br is bonded to one other carbon, making it a primary (1°) halide.
- 2-Bromopentane: The carbon with Br is bonded to two other carbons, making it a secondary (2°) halide.
3. Assess Steric Hindrance:
- Tertiary (2-Bromo-2-methylbutane): High steric hindrance due to three alkyl groups, least reactive in Sₓ2.
- Secondary (2-Bromopentane): Moderate steric hindrance, more reactive than tertiary but less than primary.
- Primary (1-Bromopentane): Low steric hindrance, most reactive in Sₓ2.
4. Arrange in Increasing Order:
Reactivity increases as steric hindrance decreases: tertiary < secondary < primary.
Final Answer:
The compounds in increasing order of reactivity towards Sₓ2 displacement are: 2-Bromo-2-methylbutane < 2-Bromopentane < 1-Bromopentane.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).