Suppose an enzyme lowers the activation energy by an order of magnitude.
What is the ratio of catalyzed rate to the uncatalyzed rate at at 25 °C? at 37 °C?
To determine the ratio of the catalyzed rate to the uncatalyzed rate at different temperatures, we need to consider the effect of temperature on reaction rates. The reaction rates depend on the activation energy, which is affected by temperature according to the Arrhenius equation:
k = A * exp(-Ea/RT),
where k is the reaction rate, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
Given that an enzyme lowers the activation energy by an order of magnitude, we can assume that the uncatalyzed rate (k_uncatalyzed) is at the higher activation energy (Ea_uncatalyzed), while the catalyzed rate (k_catalyzed) is at the lower activation energy (Ea_catalyzed = Ea_uncatalyzed / 10).
Now, let's calculate the ratio of the catalyzed rate to the uncatalyzed rate at two different temperatures: 25 °C and 37 °C.
1. Calculate the ratio at 25 °C:
Convert 25 °C to Kelvin: T = 25 + 273.15 = 298.15 K
k_catalyzed = A * exp(-Ea_catalyzed/RT)
k_uncatalyzed = A * exp(-Ea_uncatalyzed/RT)
ratio_25 = k_catalyzed / k_uncatalyzed
2. Calculate the ratio at 37 °C:
Convert 37 °C to Kelvin: T = 37 + 273.15 = 310.15 K
k_catalyzed = A * exp(-Ea_catalyzed/RT)
k_uncatalyzed = A * exp(-Ea_uncatalyzed/RT)
ratio_37 = k_catalyzed / k_uncatalyzed
Please note that the values of A, Ea_uncatalyzed, and Ea_catalyzed are required to calculate the exact ratios.