Activation Energy of the Hydrogen Reaction at 500 K
The activation energy (Ea) of a chemical reaction is the minimum amount of energy required to initiate the reaction. In the case of the hydrogenation of ethylene (CH2=CH2) to ethane (CH3-CH3) at 500 K, the activation energy can be calculated based on the reaction mechanism and rate constants.

Reaction Mechanism
The hydrogenation of ethylene involves the breaking of the double bond and the addition of hydrogen atoms to each carbon atom. This process occurs in multiple steps, with the formation of an intermediate species before the final product is obtained.

Rate Constants
The rate of the hydrogenation reaction is dependent on the rate constants of each step in the mechanism. By measuring the reaction rate at different temperatures, the activation energy can be determined using the Arrhenius equation:
k = A * exp(-Ea/RT)
Where:
k = rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant
T = temperature in Kelvin

Calculation
By conducting experiments at 500 K and measuring the reaction rate, the rate constant can be determined. By plotting the natural logarithm of the rate constant against the inverse of the temperature, the activation energy can be calculated from the slope of the line.
In conclusion, the activation energy of the hydrogenation of ethylene to ethane at 500 K can be determined experimentally by measuring the reaction rate at that temperature and analyzing the data using the Arrhenius equation. This information is crucial for understanding the kinetics of the reaction and optimizing reaction conditions in industrial processes.

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