The rate constant of a first order reaction is 4.60 x 10-4 s-1 at 350 oC. If the activation energy is 104 kJ/mol, calculate the temperature in Kelvin at which its rate constant is 1.80 x 10-3 s-1.
Use the Arrhenius equation.
ln(k2/k Y1) = Ea(1/T1-1/T2)/R
You have k1 and k2; also Ea and T1. Substitute and solve for T2.
To calculate the temperature at which the rate constant is 1.80 x 10^(-3) s^(-1), we can use the Arrhenius equation:
k2 = A * e^(-Ea/RT)
Where:
k2 is the rate constant at the desired temperature,
A is the pre-exponential factor,
Ea is the activation energy,
R is the gas constant, and
T is the absolute temperature in Kelvin.
We are given the rate constant at 350 °C, which is equivalent to 623.15 K. We'll denote this rate constant as k1:
k1 = 4.60 x 10^(-4) s^(-1)
We are also given the activation energy, Ea, which is 104 kJ/mol.
We can rearrange the Arrhenius equation to solve for temperature (T):
T = (-Ea / (R * ln(k))) - 273.15
First, we need to convert the rate constant at 350 °C to its natural logarithmic form:
ln(k1) = ln(4.60 x 10^(-4) s^(-1))
Using the property of logarithms, we can rewrite this as:
ln(k1) = -7.78
Substituting the values into the rearranged formula:
T = (-104 kJ/mol) / (8.314 J/(mol·K) * -7.78) - 273.15
Simplifying:
T ≈ 925.81 K
Therefore, at a temperature of approximately 925.81 K, the rate constant is 1.80 x 10^(-3) s^(-1).