Values of the rate constant for the decomposition of N2O5 at four different temperatures are as follows:
T(K) k(s^-1)
658....2.14*10^5
673....3.23*10^5
688....4.81*10^5
703....7.03*10^5
The activation energy is 1.02*10^2 kJ/mol. Calculate the value of the rate constant at 300 K
I keep trying that and it is saying that I have the wrong answer. here is my work:
slope: -1.19*10^4 y-intercept= 30.439
Ea: -(-1.19*10^4 K) *(8.314J/moK)= 9.89*10^4 J/mol
A= e^30.439= 1.65*10^13
(1.65*10^13) e^-(9.89*10^4J/mol/8.314*300 K)= 9.98*10^-5
I keep getting different answers, and each time they are saying it is wrong. Can you tell me where I am going wrong? And am I supposed to convert the Ea into joules/mole?
To calculate the value of the rate constant at 300 K, we can use the Arrhenius equation:
k = A * exp(-Ea / (R * T))
Where:
- k is the rate constant
- A is the pre-exponential factor or the frequency factor
- Ea is the activation energy
- R is the ideal gas constant (8.314 J/(mol K))
- T is the temperature in Kelvin
First, we need to convert the activation energy from kJ/mol to J/mol:
Ea = 1.02 * 10^2 kJ/mol * (1000 J/kJ) = 1.02 * 10^5 J/mol
Next, we can choose one set of temperature and rate constant values from the given data. Since the rate constant is temperature-dependent, the choice of T doesn't matter as long as it corresponds to one of the given rate constants. Let's choose T = 658 K as an example:
T = 658 K
k = 2.14 * 10^5 s^-1
Now we can substitute these values into the Arrhenius equation and solve for A:
2.14 * 10^5 s^-1 = A * exp((-1.02 * 10^5 J/mol) / (8.314 J/(mol K) * 658 K))
Dividing both sides by exp((-1.02 * 10^5 J/mol) / (8.314 J/(mol K) * 658 K)) gives us:
A = (2.14 * 10^5 s^-1) / exp((-1.02 * 10^5 J/mol) / (8.314 J/(mol K) * 658 K))
Using a calculator, we find A ≈ 6.42 * 10^11 s^-1.
Finally, we can substitute the calculated value of A and the desired temperature, T = 300 K, into the Arrhenius equation to find the rate constant, k, at 300 K:
k = (6.42 * 10^11 s^-1) * exp((-1.02 * 10^5 J/mol) / (8.314 J/(mol K) * 300 K))
Calculating this expression gives us the value of the rate constant, k, at 300 K.
Can't you use the Arrhenius equation?
Use two T values with corresponding k values. One T will be 300 and k at that T will be the unknown.