객관식
The activation energy for a first-order reaction is 26.5 kJ/mol. At 10.0°C, the rate constant is 0.020 s⁻¹. Calculate the temperature at which the rate constant is 0.040 s⁻¹ using the Arrhenius Equation.
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15. Chemical Kinetics
Arrhenius Equation
객관식
Using the Arrhenius Equation, what is the rate constant (k) for the reaction of NO with F2 at a temperature of 298 K, given that the activation energy (Ea) is 6.30 kJ/mol and the frequency factor (A) is 6.00 × 10^8 M⁻¹·s⁻¹?
A
k = 5.67 × 10^9 M⁻¹·s⁻¹
B
k = 4.56 × 10^8 M⁻¹·s⁻¹
C
k = 1.23 × 10^7 M⁻¹·s⁻¹
D
k = 2.45 × 10^7 M⁻¹·s⁻¹
검증된 단계별 안내1
Start by recalling the Arrhenius Equation, which is used to calculate the rate constant (k) of a reaction: \( k = A \cdot e^{-\frac{E_a}{RT}} \), where \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.
Convert the activation energy \( E_a \) from kJ/mol to J/mol to match the units of the gas constant \( R \). Since 1 kJ = 1000 J, multiply 6.30 kJ/mol by 1000 to get 6300 J/mol.
Use the universal gas constant \( R = 8.314 \) J/(mol·K) and the given temperature \( T = 298 \) K in the Arrhenius equation.
Substitute the values into the Arrhenius equation: \( k = 6.00 \times 10^8 \cdot e^{-\frac{6300}{8.314 \times 298}} \).
Calculate the exponent \( -\frac{6300}{8.314 \times 298} \), then find the value of \( e \) raised to this power, and finally multiply by the frequency factor \( A = 6.00 \times 10^8 \) to find the rate constant \( k \).
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