For the reaction
NO(g) + O3(g) „_ NO2(g) + O2(g)
The frequency factor A is 8.7 X 1012 s-1 and the activation energy is 63kJ/mol. What is the rate constant for the reaction at 75 ¢XC?
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To determine the rate constant (k) for the reaction at 75 ¢XC, we'll need to 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 ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (K)
To solve for k at 75 ¢XC, we first need to convert the temperature to Kelvin:
T = 75 ¢C + 273.15 = 348.15 K
Now we can substitute the given values into the Arrhenius equation:
k = (8.7 X 10^12 s^(-1)) * exp(-63,000 J/mol / (8.314 J/(mol·K) * 348.15 K))
Calculating the exponential term, we have:
exp(-63,000 J/mol / (8.314 J/(mol·K) * 348.15 K)) ≈ exp(-22.48)
Using a scientific calculator or a calculator with an "exp" function, we find:
exp(-22.48) ≈ 7.85 X 10^(-10)
Substituting this back into the previous equation, we can calculate the rate constant:
k = (8.7 X 10^12 s^(-1)) * (7.85 X 10^(-10))
Multiplying the two values together, we get:
k ≈ 6.82 s^(-1)
So, the rate constant for the reaction at 75 ¢XC is approximately 6.82 s^(-1).