Kinetics

Step 1: First Order Integrated Rate Law.
For a first-order reaction, the integrated rate law is: Where: - is the initial concentration of the reactant, - is the concentration of the reactant at time , - is the rate constant, - is the time. Step 2: Time for 90\% Completion.
For 90\% completion, the concentration of the reactant is 10\% of its initial concentration: Step 3: Time for 99.9\% Completion.
For 99.9\% completion, the concentration of the reactant is 0.1\% of its initial concentration: Thus, the time required for 99.9\% completion is three times the time required for 90\% completion. Step 4: Electronic Configuration of Gd (Z = 64).
The electronic configuration of Gd (Z = 64) is: Step 5: Nano Structured Material in Tyres.
The nano-structured material used in car tyres to increase their life is silica.

Pseudo First-Order Reaction:
A reaction that is not actually first-order but behaves as if it were first-order is called a pseudo-first-order reaction. This typically occurs when one of the reactants is in excess and its concentration remains almost constant during the reaction, making the reaction rate depend only on the concentration of the limiting reactant. For example, the hydrolysis of an ester in water is a second-order reaction overall but is often treated as a pseudo-first-order reaction if the concentration of water is in large excess. Step 1: Zero Order Integrated Rate Law.
For a zero-order reaction, the rate law is given by: Where is the rate constant. The integrated rate law for a zero-order reaction is derived from the equation: Integrating with respect to time: This is the integrated rate law for a zero-order reaction.