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).
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}
The equilibrium constant for decomposition of $ H_2O $ (g) $ H_2O(g) \rightleftharpoons H_2(g) + \frac{1}{2} O_2(g) \quad (\Delta G^\circ = 92.34 \, \text{kJ mol}^{-1}) $ is $ 8.0 \times 10^{-3} $ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ($ \alpha $) of water is _____ $\times 10^{-2}$ (nearest integer value). [Assume $ \alpha $ is negligible with respect to 1]