For the reaction given below, the frequency factor A is 8.7 multiplied by 1012 s-1 and the activation energy is 63 kJ/mol.
NO(g) + O3(g) NO2(g) + O2(g)
What is the rate constant for the reaction at 55°C?
http://en.wikipedia.org/wiki/Arrhenius_equation
To determine the rate constant for the reaction at 55°C, we can use the Arrhenius equation:
k = A * exp(-Ea / (R * T))
where:
k is the rate constant
A is the frequency factor
Ea is the activation energy
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin by adding 273.15:
T = 55°C + 273.15 = 328.15 K
Now we can substitute the given values into the Arrhenius equation:
k = (8.7 × 10^12 s^-1) * exp(-63000 J/mol / (8.314 J/(mol·K) * 328.15 K))
Before calculating the exponent, we need to convert the activation energy from kJ/mol to J/mol:
Ea = 63 kJ/mol * 1000 = 63000 J/mol
Now we can calculate the rate constant:
k = (8.7 × 10^12 s^-1) * exp(-63000 J/mol / (8.314 J/(mol·K) * 328.15 K))
Calculating the exponent:
exp(-63000 J/mol / (8.314 J/(mol·K) * 328.15 K)) ≈ 0.647
Finally, substituting this value into the equation:
k ≈ (8.7 × 10^12 s^-1) * 0.647
k ≈ 5.6 × 10^12 s^-1
Therefore, the rate constant for the reaction at 55°C is approximately 5.6 × 10^12 s^-1.