Multiple Choice
A reaction is followed and found to have a rate constant of 3.36 x 10^4 M^-1 s^-1 at 344 K and a rate constant of 7.69 M^-1 s^-1 at 219 K. Determine the activation energy for this reaction.
15. Chemical Kinetics
Arrhenius Equation
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At 298 K, the decomposition of ammonia is catalyzed by tungsten. The activation energy for the catalyzed reaction is 163 kJ/mol. If in the absence of a catalyst, the activation energy is 335 kJ/mol, which of the following statements is true with reference to this reaction?
A
The catalyzed reaction has a lower rate constant than the uncatalyzed reaction.
B
The activation energy does not affect the rate constant of the reaction.
C
The catalyzed reaction has the same rate constant as the uncatalyzed reaction.
D
The catalyzed reaction has a higher rate constant than the uncatalyzed reaction.
Verified step by step guidance1
Understand the concept of activation energy: Activation energy is the minimum energy required for a chemical reaction to occur. It influences the rate constant of a reaction, as a lower activation energy typically results in a higher rate constant.
Recognize the role of a catalyst: A catalyst provides an alternative pathway for the reaction with a lower activation energy, thereby increasing the rate of the reaction without being consumed in the process.
Compare the activation energies: The catalyzed reaction has an activation energy of 163 kJ/mol, while the uncatalyzed reaction has an activation energy of 335 kJ/mol. The lower activation energy in the catalyzed reaction suggests a higher rate constant.
Apply the Arrhenius equation: The Arrhenius equation, \( k = A e^{-\frac{E_a}{RT}} \), shows that the rate constant \( k \) is inversely related to the activation energy \( E_a \). A decrease in \( E_a \) leads to an increase in \( k \).
Conclude based on the comparison: Since the catalyzed reaction has a lower activation energy, it will have a higher rate constant compared to the uncatalyzed reaction, making the statement 'The catalyzed reaction has a higher rate constant than the uncatalyzed reaction' true.
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