Answer :
Final answer:
The activation energy (Ea) can be calculated using the Arrhenius equation, which relates the rate constant increase and temperature change. By taking the natural logarithm of the rate increase factor and temperature change in Kelvin, we find that Ea is approximately 54 kJ/mol.The correct option is (b) 25.7 kJ/mol
Explanation:
To calculate the activation energy (Ea) for a reaction using the change in reaction rate with temperature, we can use the Arrhenius equation that establishes a relationship between reaction rate constants at two different temperatures.
Since we know the reaction rate increases 2.21 times as the temperature changes from 70°C to 80°C, we can use the two temperatures (converted to Kelvin) and the rate increase factor to find Ea.
The formula derived from the Arrhenius equation is:
ln(k2/k1) = (-Ea/R) × (1/T2 - 1/T1)
Here, k1 and k2 are the rate constants at temperatures T1 and T2, R is the gas constant 8.314 J/mol·K, and Ea is the activation energy we need to calculate.
Applying the temperatures in Kelvin (343 K for 70°C and 353 K for 80°C) and the given fact that k2/k1 = 2.21, we can solve the rearranged equation for Ea.
After calculations, which include using natural logarithm of the rate increase (ln(2.21)) and the temperature change in Kelvin, Ea is found to be approximately 54 kJ/mol, indicating that option 25.7 kJ/mol is not the correct answer because it is significantly lower than the calculated value.