A certain first order reaction has a rate constant of 3.75x10^-2 s^-1 at 25.0C. What is the value of k at 70.0C when the activation energy is 135 kj/mol?
Would I use the formula K=Ae ^-Ea/RT even though I have two temperatures?
I would use ln(k2/k1) = Ea/R(1/T1 - 1/T2)
Yes, you can use the Arrhenius equation to determine the value of k at 70.0°C given the activation energy and the rate constant at 25.0°C. The Arrhenius equation relates the rate constant (k) to the activation energy (Ea), the gas constant (R), the absolute temperature (T), and a constant factor (A).
The general form of the Arrhenius equation is:
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) or 0.008314 kJ/(mol·K))
T = temperature in Kelvin (K)
To use the Arrhenius equation, you need to convert the temperatures to Kelvin. The equation requires temperature in Kelvin, so you can add 273.15 to both temperatures:
25.0°C + 273.15 = 298.15 K
70.0°C + 273.15 = 343.15 K
Now you can plug in the values into the Arrhenius equation:
k1 = 3.75x10^-2 s^-1 (rate constant at 25.0°C)
T1 = 298.15 K (temperature at 25.0°C)
T2 = 343.15 K (temperature at 70.0°C)
Ea = 135 kJ/mol (activation energy)
k2 = A * e^(-Ea/RT2)
To find A, you can rearrange the equation as follows:
k1 = A * e^(-Ea/RT1)
Then, solve for A by dividing both sides of the equation by e^(-Ea/RT1):
A = k1 / e^(-Ea/RT1)
Now substitute the values into the equation for k2:
k2 = (k1 / e^(-Ea/RT1)) * e^(-Ea/RT2)
By plugging in the values, you can calculate the value of k2 at 70.0°C using the given activation energy and rate constant at 25.0°C.