Which equation correctly expresses the Arrhenius relationship between the rate constant and temperature?

• A. k = A exp(-Ea/(RT))
• B. k = A exp(Ea/(RT))
• C. k = A/(RT) exp(-Ea)
• D. k = R T exp(-Ea/(A))

Answer: (A)

The rate constant depends on temperature through an exponential term that has a negative Ea/(RT). This means higher activation energy makes the rate smaller at a given temperature, and raising the temperature makes this exponent less negative, increasing k. The proper Arrhenius form is k = A exp(-Ea/(RT)) because the exponent must reflect Ea divided by RT, ensuring the correct temperature dependence and the exponential growth of k with temperature.

The other forms misplace the temperature dependence or sign. A positive sign in the exponent would imply k grows as temperature drops, which contradicts observed behavior. Putting exp(-Ea) outside of the temperature-dependent piece removes the essential T dependence from the exponential and introduces a mismatched factor like 1/T, which disrupts the proper scaling. Using exp(-Ea/A) mixes energy units with a factor that isn’t a temperature, leading to incorrect temperature behavior and dimensional issues.