The rate constant of the reaction between CO2 and OH - in aqueous solution to give the HCO3- ion is 1.5 1010 1/(M·s) at 25°C. Determine the rate constant at blood temperature (37°C), given that the activation energy for the reaction is 38 kJ/mol.
units 1/(M·s)
Can't you use the Arrhenius equation?
I did that for both temperatures and divided both of them by each other but my answer is incorrect.
i got the answer!
To determine the rate constant at a different temperature, you can use the Arrhenius equation, which relates the rate constant (k) to the temperature (T) and the activation energy (Ea):
k = A * e^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor, which is a constant
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
First, you need to convert the activation energy from kJ/mol to J/mol by multiplying it by 1000. So, Ea = 38 kJ/mol * 1000 = 38000 J/mol.
Next, convert both temperatures to Kelvin. The given temperature, 25°C, is equivalent to 25 + 273 = 298 K. The desired temperature, 37°C, is equivalent to 37 + 273 = 310 K.
Now, you need to calculate the ratio of rate constants at the two temperatures:
k2 / k1 = (A * e^(-Ea/RT2)) / (A * e^(-Ea/RT1))
Simplifying:
k2 / k1 = e^(-Ea/R) * (1/T2 - 1/T1)
Substituting the given values into the equation:
k2 / (1.5 * 10^10) = e^(-38000 / (8.314 * 298)) * (1/310 - 1/298)
Solving the equation gives:
k2 = (1.5 * 10^10) * e^(-38000 / (8.314 * 298)) * (1/310 - 1/298)
Calculating this expression will give you the rate constant at blood temperature (37°C) in units of 1/(M·s).