I've figured out the Ea but I'm not sure how to find the kcal/mol
The gas reaction N2O5 → 2NO2 + 1/2O2 follows the Arrhenius equation k = Ae(-Ea/RT) where R = 8.314 J K-1 mol-1 and 1 calorie = 4.184J. At the temperature T=273K, k = 3.46 x 10-5 s-1, whereas at T = 298K, k = 8.87 x 10-3 s-1. What is the value of the activation energy Ea in kJ/mol and in kcal/mol. What is the rate constant at 100 oC?
ln(3.46 x10-5 s-1)/(8.87 x 10-3 s-1)=Ea/(8.314 J/(K.mol))(1/(298 K)-1/273k)
Ea= 1.50 x 105 J or 150 kJ
150 kJ is correct.
I need to know the kcal/mol. How do I find the kcal/mol??
1 cal = 4.184 J.
1 kcal = 4.184 kJ
To find the value of activation energy (Ea) in kJ/mol and kcal/mol, you can use the equation:
Ea = -(R * ln(k2/k1)) / ((1/T2) - (1/T1))
Here, R is the gas constant (8.314 J K-1 mol-1), ln is the natural logarithm, k1 and k2 are the rate constants at different temperatures (T1 and T2), and T1 and T2 are the corresponding temperatures in Kelvin.
In this case, we are given k1 (3.46 x 10-5 s-1) at T1 (273 K) and k2 (8.87 x 10-3 s-1) at T2 (298 K). Let's calculate Ea in kJ/mol:
Ea = -(8.314 J/K.mol) * ln((8.87 x 10-3 s-1) / (3.46 x 10-5 s-1)) / ((1/298 K) - (1/273 K))
Ea = -(8.314 J/mol) * ln(256) / (0.0034 K)
Ea = -6642.704 J/mol
To convert the units from J/mol to kJ/mol, divide by 1000:
Ea = -6.642704 kJ/mol
To convert the units from kJ/mol to kcal/mol, use the conversion factor 1 kcal = 4.184 kJ:
Ea = -6.642704 kJ/mol * (1 kcal / 4.184 kJ)
Ea = -1.587712 kcal/mol
Therefore, the value of activation energy Ea is approximately 6.64 kJ/mol and -1.59 kcal/mol.
To find the rate constant at 100 oC, convert the temperature to Kelvin (373 K) and use the given Arrhenius equation:
k = Ae(-Ea/RT)
Substituting the values, we have:
T = 373 K
Ea = -150000 J/mol (converted from kJ/mol)
k = A * e^(-150000 J/(8.314 J/(K.mol) * 373 K))
Simplifying the equation, we get:
k = A * e^(-49.133)
Since we don't have the value of the pre-exponential factor A, we cannot calculate the exact value of the rate constant.