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?
See your post below.
To calculate the rate constant for the reaction at 55°C, we can use the Arrhenius equation:
k = Ae^(-Ea/RT)
where:
k - rate constant
A - frequency factor
Ea - activation energy
R - gas constant (8.314 J/(mol·K))
T - temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
T = 55°C + 273.15 = 328.15 K
Now, we can substitute the values into the Arrhenius equation:
k = (8.7 x 10^12 s^(-1)) * e^(-(63 kJ/mol) / (8.314 J/(mol·K) * 328.15 K))
k = (8.7 x 10^12) * e^(-190840 J / (8.314 J/(mol·K) * 328.15 K))
k = (8.7 x 10^12) * e^(-190840 / (8.314 * 328.15))
Calculating this expression will give us the rate constant for the reaction at 55°C.
To find the rate constant for the reaction at 55°C, we can use the Arrhenius equation:
k = A * exp(-Ea / (R * T))
Where:
k: rate constant
A: frequency factor
Ea: activation energy
R: gas constant (8.314 J/(mol*K))
T: temperature in Kelvin
First, let's convert the temperature from Celsius to Kelvin:
T = 55°C + 273.15 = 328.15 K
Now, we can plug in the values into the Arrhenius equation:
k = (8.7 * 10^12 s^(-1)) * exp(-(63 * 10^(3) J/mol) / (8.314 J/(mol*K) * 328.15 K))
To calculate this, we need to evaluate the exponential term:
exp(-(63 * 10^(3) J/mol) / (8.314 J/(mol*K) * 328.15 K))
Let's do the calculation step by step:
1. Divide the activation energy by the gas constant times the temperature:
(63 * 10^(3) J/mol) / (8.314 J/(mol*K) * 328.15 K) = 23.317
2. Take the exponential of the result:
exp(23.317) ≈ 2.55 * 10^10
Now, substitute this value back into the equation for the rate constant:
k ≈ (8.7 * 10^12 s^(-1)) * (2.55 * 10^10)
Multiply the two values together:
k ≈ 2.228 * 10^23 s^(-1)
Therefore, the rate constant for the reaction at 55°C is approximately 2.228 * 10^23 s^(-1).