Multiple Choice
A certain first-order reaction has a rate constant of 1.0 × 10⁻³ s⁻¹ at 25°C. If the rate constant triples when the temperature is increased to 35°C, what is the activation energy Ea (in kJ/mol) for this reaction?
15. Chemical Kinetics
Arrhenius Equation
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A particular first-order reaction has a rate constant of 1.35 × 10² s⁻¹ at 25.0°C. Using the Arrhenius equation, what is the rate constant (k) at 95.0°C if the activation energy (Ea) is 55.5 kJ/mol?
A
1.35 × 10² s⁻¹
B
5.40 × 10² s⁻¹
C
2.68 × 10³ s⁻¹
D
8.90 × 10² s⁻¹
Verified step by step guidance1
Start by understanding the Arrhenius equation, which is used to calculate the rate constant (k) at different temperatures. The equation is: , where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
Convert the temperatures from Celsius to Kelvin. The temperature at 25.0°C is K and at 95.0°C is K.
Use the Arrhenius equation in its logarithmic form to find the new rate constant at 95.0°C: , where k₀ is the rate constant at the initial temperature, and k is the rate constant at the new temperature.
Substitute the known values into the equation: . Note that the activation energy is converted from kJ/mol to J/mol.
Solve for the new rate constant k by calculating the right side of the equation and then exponentiating both sides to find k. This will give you the rate constant at 95.0°C.
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