calculate the rate of a constant reaction at 293 kelvin when the energy of activation is 103 kilo joules per mole and the rate constant at 273 kelvin is 7.87*10 to the power -7...
To calculate the rate of a constant reaction at 293 Kelvin, we can use the Arrhenius equation. The Arrhenius equation is as follows:
k = Ae^(-Ea/RT)
Where:
- k is the rate constant at a given temperature,
- A is the pre-exponential factor (also called the frequency factor),
- Ea is the energy of activation,
- R is the gas constant (8.314 J/mol·K), and
- T is the temperature in Kelvin.
Given that the rate constant at 273 Kelvin (k1) is 7.87*10^(-7) and the energy of activation (Ea) is 103 kJ/mol, we can calculate the pre-exponential factor (A) using the following steps:
1. Convert the energy of activation from kJ/mol to J/mol:
Ea = 103 kJ/mol * 1000 J/kJ = 103,000 J/mol
2. Plug the values into the Arrhenius equation to solve for the pre-exponential factor (A):
k1 = A*e^(-Ea/RT1)
Rearranging the equation, we get:
A = k1 / (e^(-Ea/RT1))
Substituting the given values:
A = 7.87*10^(-7) / (e^(-103000 J/mol / (8.314 J/mol·K * 273 K))
Using a calculator, evaluate the exponential term:
e^(-103000 J/mol / (8.314 J/mol·K * 273 K))
Then divide k1 by the result to find A.
Once you have determined the pre-exponential factor (A), you can calculate the rate constant (k2) at 293 Kelvin using the same formula:
k2 = Ae^(-Ea/RT2)
Substituting the values:
k2 = A*e^(-103000 J/mol / (8.314 J/mol·K * 293 K))
Again, you can use a calculator to evaluate the exponential term and then multiply A by the result to find k2, the rate constant at 293 Kelvin.
Keep in mind that the rate of a constant reaction is directly proportional to the rate constant. So once you have the rate constant at 293 Kelvin, you can compare it to the rate constant at 273 Kelvin to determine the change in the reaction rate.