In the following pair of halogen compounds, which compound undergoes \( S_N1 \) reaction faster and why?
To solve the problem, we need to determine which halogen compound undergoes an Sₓ1 reaction faster and explain why.
1. Identify the Compounds:
The first compound is a tertiary halide (3°), with Cl attached to a carbon bonded to three other carbons. The second compound is a secondary halide (2°), with Cl attached to a carbon bonded to two other carbons.
2. Understand Sₓ1 Reaction Mechanism:
Sₓ1 reactions proceed via a carbocation intermediate. The rate depends on the stability of the carbocation formed after the leaving group (Cl⁻) departs. The stability order is: tertiary carbocation > secondary carbocation > primary carbocation.
3. Compare Carbocation Stability:
For the first compound (tertiary halide), the carbocation formed is tertiary, which is highly stable due to hyperconjugation and inductive effects from three alkyl groups. For the second compound (secondary halide), the carbocation is secondary, which is less stable than a tertiary carbocation.
4. Determine Reaction Rate:
Since Sₓ1 reaction rate depends on carbocation stability, the tertiary halide will react faster because its carbocation intermediate is more stable.
Final Answer:
The first compound (tertiary halide) undergoes Sₓ1 reaction faster because it forms a more stable tertiary carbocation intermediate compared to the secondary carbocation formed by the second compound.
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 \(P,O,Q\).