The activation energy of a reaction is typically determined by calculating the rate constant for the reaction at two temperatures and then manipulating the Arrhenius equation. If you determine the reaction rate constants for a particular reaction to be 0.0650 /s at 25.0 C and 0.150 /s at 35.0 C, then what is the activation energy for the reaction? Give the answer in kJ/mol.

So use the Arrhenius equation and calculate it.

To determine the activation energy of a reaction using the Arrhenius equation, you will need to calculate the rate constant at two different temperatures and then solve for the activation energy. The Arrhenius equation is as follows:

k = A * e^(-Ea/RT)

Where:
k = rate constant
A = pre-exponential factor or frequency factor
Ea = activation energy
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin (K)

In this case, you have the rate constants at two temperatures: 0.0650 /s at 25.0°C and 0.150 /s at 35.0°C. However, the temperatures must be converted from Celsius to Kelvin before proceeding with the calculations.

Step 1: Convert temperatures to Kelvin
T1 = 25.0°C + 273.15 = 298.15 K
T2 = 35.0°C + 273.15 = 308.15 K

Step 2: Calculate the ratio of rate constants
k1/k2 = (0.0650 /s) / (0.150 /s)

Step 3: Use the Arrhenius equation to manipulate the ratio and solve for the activation energy.
Taking the natural logarithm of both sides of the equation, we have:

ln(k1/k2) = -Ea/R * ((1/T1) - (1/T2))

Rearranging the equation to solve for Ea:
Ea = -R * ln(k1/k2) / ((1/T1) - (1/T2))

Step 4: Plug in the values and calculate the activation energy.
Ea = - (8.314 J/(mol·K)) * ln(0.0650 / 0.150) / ((1/298.15 K) - (1/308.15 K))

Calculating the above expression will provide the answer in units of J/mol. To convert it to kJ/mol, divide the result by 1000 (since 1 kJ = 1000 J).

Finally, the activation energy for the reaction in kJ/mol is the value obtained from the calculation divided by 1000.