Final answer:
The frequency factor, A, cannot be accurately calculated using the options provided (a-d). It must be calculated using the Arrhenius equation, which requires simultaneous equations derived from the logarithmic form of the equation at two different temperatures.
Step-by-step explanation:
To calculate the frequency factor A, given the rate constants at two different temperatures (k1 at T1 and k2 at T2), we must employ the Arrhenius equation:
k = Ae-Ea/RT
Where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
By taking the natural logarithm of the Arrhenius equation, we obtain:
ln k = ln A - Ea/(RT)
For the known rate constant k1 at temperature T1 and unknown rate constant k2 at temperature T2, we have two equations:
ln k1 = ln A - Ea/(RT1)
ln k2 = ln A - Ea/(RT2)
By solving these equations simultaneously, we can calculate the frequency factor A. However, none of the options (a) A = k1/k2, (b) A = k1 × T1, (c) A = T1/T2, or (d) A = k1 + k2 represent the correct mathematical relationship to determine A. The correct approach involves using the natural logarithm and the Arrhenius equation as outlined above.