Chemical Kinetics

Step 1: Lindemann mechanism overview.
The Lindemann mechanism suggests that the decomposition of a molecule follows first-order kinetics at low pressure, where the rate of decomposition is dependent on the concentration of the reactant. At high pressures, the reaction can follow second-order kinetics due to the increased number of collisions.

Step 2: Analysis of options.
- (1) It follows second order kinetics at high pressure: This is true for high-pressure conditions, but not the best fit for the unimolecular decomposition at low pressure.
- (2) It follows second order kinetics at low pressure: This is not correct; Lindemann mechanism typically follows first-order kinetics at low pressure.
- (3) The kinetics of the reaction does not depend on the gaseous pressure: This is not accurate; the kinetics depend on pressure.
- (4) It follows first order kinetics at low pressure: This is correct according to the Lindemann mechanism.

Step 3: Conclusion.
The correct answer is (4), as the reaction follows first-order kinetics at low pressure.

Step 1: The Arrhenius equation.
The Arrhenius equation relates the rate constant to temperature and the activation energy : Taking the natural logarithm of both sides, we get: This is a linear equation of the form , where the slope is . Thus, the activation energy can be found from the slope of the line.

Step 2: Using the slope to find activation energy.
The slope , where is the universal gas constant ( ). The given slope is . We can solve for as follows:

Step 3: Conclusion.
Thus, the activation energy is , which corresponds to option (1).