Question

Calculate the rate constant, , for a reaction at 66.0 °C that has an activation energy of 77.7 kJ/mol and a frequency factor of 4.29×1011 s−1.

Answer 1

To calculate the rate constant of a reaction at 66.0 °C, use the Arrhenius equation and plug in the known values of activation energy, frequency factor, and temperature.

Step-by-step explanation:

The rate constant, k, can be calculated using the Arrhenius equation:

k = Ae-Ea/RT

where A is the frequency factor, Ea is the activation energy, R is the ideal gas constant (8.314 J/mol/K), and T is the temperature in Kelvin.

Given the activation energy (77.7 kJ/mol), frequency factor (4.29×1011 s-1), and temperature (66.0 °C = 339.15 K), we can plug these values into the equation to calculate the rate constant:

k = (4.29×1011 s-1) * e-77.7 kJ/mol / (8.314 J/mol/K * 339.15 K)

Solving this equation will give us the value of k.

Answer 2

To calculate the rate constant at 66.0 °C for a reaction with an activation energy of 77.7 kJ/mol and a frequency factor of 4.29×1011 s-1, the Arrhenius equation should be applied using the conversion of Celsius to Kelvin and kJ/mol to J/mol.

Step-by-step explanation:

To calculate the rate constant for a reaction with a given activation energy (Ea) and frequency factor (A) at a certain temperature, the Arrhenius equation is used:
k = Ae-Ea/RT

Where:
k is the rate constant,
A is the frequency factor,
Ea is the activation energy in joules per mole (to convert from kJ/mol to J/mol, multiply by 1000),
R is the ideal gas constant (8.314 J/mol/K),
T is the absolute temperature in Kelvin (K).

To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. Therefore, T = 66.0 °C = 66.0 + 273.15 = 339.15 K.
For the given activation energy, Ea = 77.7 kJ/mol, we convert it to J/mol: 77.7 × 1000 = 77700 J/mol.
The frequency factor is given: A = 4.29×1011 s-1.

The rate constant can then be calculated:

k = 4.29×1011 s-1 × e-77700/(8.314×339.15)

After calculating the exponent and the entire expression, you will get the rate constant k at the specified temperature of 66.0 °C.