Multiple Choice
Using the Arrhenius Equation, what is the rate constant (k) for the reaction of NO with F2 at a temperature of 298 K?
15. Chemical Kinetics
Arrhenius Equation
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The reaction N2 + O2 → 2NO takes place in the gas phase. The rate constant at 250 K is 4.32 × 10^13 M⁻¹s⁻¹, and at 275 K the rate constant is 8.19 × 10^13 M⁻¹s⁻¹. Calculate the frequency factor (A) for the reaction using the Arrhenius equation.
A
3.45 × 10^14 M⁻¹s⁻¹
B
4.78 × 10^14 M⁻¹s⁻¹
C
1.23 × 10^14 M⁻¹s⁻¹
D
2.56 × 10^14 M⁻¹s⁻¹
Verified step by step guidance1
Understand that the Arrhenius equation is given by: k = A * e^(-Ea/(RT)), 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), and T is the temperature in Kelvin.
To find the frequency factor (A), we need to rearrange the Arrhenius equation to solve for A: A = k / e^(-Ea/(RT)).
Since we have two rate constants at two different temperatures, we can use the Arrhenius equation in its logarithmic form: ln(k2/k1) = -Ea/R * (1/T2 - 1/T1). This allows us to solve for the activation energy (Ea).
Substitute the given values into the logarithmic form: ln(8.19 × 10^13 / 4.32 × 10^13) = -Ea/8.314 * (1/275 - 1/250). Solve this equation to find the value of Ea.
Once Ea is determined, substitute back into the Arrhenius equation to solve for A using one of the rate constants and its corresponding temperature. For example, use k1 = 4.32 × 10^13 M⁻¹s⁻¹ and T1 = 250 K to find A: A = 4.32 × 10^13 / e^(-Ea/(8.314 * 250)).
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