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).
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32