Half Life

Let's evaluate each statement individually:
Statement (A):
For zero-order reactions, the successive half-lives decrease as time progresses. - The half-life for a zero-order reaction is given by the formula: where represents the initial concentration of the reactant and is the rate constant.
Since the concentration of the reactant decreases over time, the half-life also diminishes. This confirms that the statement is correct.
Statement (B):
A substance that appears as a reactant in the chemical equation may not necessarily influence the rate of reaction. - This statement is true because the order of reaction with respect to a substance does not always align with its stoichiometric coefficient in the equation. A substance can appear in the equation but have a zero-order effect on the reaction, meaning it does not alter the rate. For instance, in a zero-order reaction with respect to a substance, varying its concentration does not affect the rate of the reaction. Hence, this statement is correct.
Statement (C):
Order and molecularity of a chemical reaction can both be fractional numbers. - The order of a reaction refers to the powers of the concentration terms in the rate law and can indeed be fractional, as observed in some reactions. However, molecularity, which refers to the number of reacting particles in an elementary step, must always be a whole number. This is because molecularity counts the species involved in an elementary reaction step. Therefore, this statement is incorrect as molecularity cannot be fractional.
Statement (D):
The rate constant units for zero and second-order reactions are mol L s and mol L s respectively. - In zero-order reactions, the rate law is: The unit for rate is mol L s , and the unit of the rate constant is mol L s . For second-order reactions, the rate law is: The unit for rate is mol L s , and the unit of the rate constant is mol L s . Thus, this statement is correct.
Conclusion:
Statement (A) is correct.
Statement (B) is correct.
Statement (C) is incorrect.
Statement (D) is correct.
Therefore, the number of incorrect statements is 1, and the incorrect statement is (C).