Step 1: Definition: - The \( S_N1 \) (unimolecular nucleophilic substitution) reaction follows a two-step mechanism. - It occurs in tertiary haloalkanes due to carbocation stability.
Step 2: Mechanism:
Step 2.1: Formation of Carbocation (Rate Determining Step): \[ R-X \rightarrow R^+ + X^- \]
Step 2.2: Nucleophilic Attack: \[ R^+ + Nu^- \rightarrow R-Nu \]
Step 3: Example: \[ (CH_3)_3CBr \xrightarrow{H_2O} (CH_3)_3C^+ + Br^- \] \[ (CH_3)_3C^+ + H_2O \rightarrow (CH_3)_3COH + H^+ \]
(i) What is a rate determining step?
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $