For rate-concentration graphs:
• Linear regions indicate first-order behavior.
• A constant rate indicates zero-order behavior.
• Non-linear regions suggest fractional orders of reaction.
1. Analysis of the Graph:
- In region-I, the rate of reaction increases linearly with the concentration, which is characteristic of a first-order reaction.
- In region-II, the graph shows non-linear behavior, indicating that the reaction order is fractional (in the range of 0.1 to 0.9).
- In region-III, the rate becomes constant, indicating a zero-order reaction.
2. Verification of Statements:
- (A) Incorrect. The overall order cannot be determined directly from the graph as it changes across regions.
- (B) Incorrect. The order can be inferred for specific regions.
- (C) Correct. Region-I corresponds to first-order behavior, and region-III corresponds to zero-order behavior.
- (D) Incorrect. In region-II, the reaction is not of first order.
- (E) Correct. In region-II, the reaction order lies between 0.1 and 0.9.
3. Conclusion:
- The correct statements are (C) and (E).
The correct order of the rate of reaction of the following reactants with nucleophile by \( \mathrm{S_N1} \) mechanism is:
(Given: Structures I and II are rigid) 
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]