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).