Answer :
The ratio of f at the higher temperature to f at the lower temperature is (A₂/A₁) × 0.8458.
The ratio of the rate constant (f) at higher temperature to the rate constant at lower temperature can be calculated by using the Arrhenius equation. The Arrhenius equation relates the rate constant of a reaction to the activation energy, temperature, and frequency factor (pre-exponential factor) of the reaction.
The Arrhenius equation can be written as follows: k = Ae^(-Ea/RT)
where
k = rate constant
A = frequency factor (pre-exponential factor)
Ea = activation energy
R = gas constant
T = temperature
The ratio of the rate constant at a higher temperature to the rate constant at a lower temperature is given by the following equation:
K₂/K₁ = (A₂/A₁) * e^(-Ea/R) * (1/T₁ - 1/T₂)
The values given in the question are as follows:
Ea = 175 kJ/mol
T₁ = 465 K
T₂ = 485 K
We need to find the ratio of f at the higher temperature to f at the lower temperature.
K₂/K₁ = (A₂/A₁) * e^(-Ea/R) * (1/T₁ - 1/T₂)
= (A₂/A₁) * e^(-175000 J/mol / (8.314 J/mol K) * ((1/465) - (1/485)))
= (A₂/A₁) * e^(-0.1671)
Taking natural logarithms on both sides of the equation gives:
ln(K₂/K₁) = ln(A₂/A₁) - 0.1671
Taking the antilog of both sides of the equation gives:
K₂/K₁ = e^(ln(A₂/A₁) - 0.1671)
= e^(ln(A₂/A₁)) * e^(-0.1671)
= (A₂/A₁) × 0.8458
The ratio of f at the higher temperature to f at the lower temperature is (A₂/A₁) × 0.8458. However, we cannot determine this value without knowing the value of the frequency factor (A). Therefore, the answer is dependent on the value of A, which is not given in the question.
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