Final answer:
The half-life at 37°C is approximately 1.42 minutes.
Step-by-step explanation:
The half-life of a 1st order process can be calculated using the equation:
ln(Nt/N0) = -kt
Where Nt is the final concentration, N0 is the initial concentration, t is time, and k is the rate constant. We can rearrange this equation to solve for the half-life:
t1/2 = (ln2)/k
Given that the activation energy is 420 kJ/mol and the half-life at 50°C is 2 minutes, we can use the Arrhenius equation:
k = Ae^(-Ea/RT)
Where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin. By substituting the given values, we can find the rate constant at 50°C. Using this rate constant, we can then calculate the half-life at 37°C.
By plugging in the values and performing the calculations, the half-life at 37°C is approximately 1.42 minutes.