Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
A particular first-order reaction has a rate constant of 1.35 × 10^2 s⁻¹ at 25.0°C. What is the magnitude of the rate constant k at 95.0°C if the activation energy Ea is 55.5 kJ/mol?
A
5.40 × 10^2 s⁻¹
B
2.70 × 10^3 s⁻¹
C
1.35 × 10^2 s⁻¹
D
1.35 × 10^3 s⁻¹
Verified step by step guidance
1
First, identify the Arrhenius equation, which relates the rate constant k to the temperature T and activation energy Ea: k = A * exp(-Ea / (R * T)).
Recognize that the problem requires using the Arrhenius equation in its two-point form to find the new rate constant at a different temperature. The two-point form is: ln(k2/k1) = (-Ea/R) * (1/T2 - 1/T1).
Convert the activation energy Ea from kJ/mol to J/mol by multiplying by 1000, since R (the gas constant) is typically expressed in J/(mol*K). Ea = 55.5 kJ/mol * 1000 = 55500 J/mol.
Substitute the known values into the two-point Arrhenius equation: k1 = 1.35 × 10^2 s⁻¹, T1 = 25.0°C = 298 K, T2 = 95.0°C = 368 K, Ea = 55500 J/mol, and R = 8.314 J/(mol*K).
Solve the equation for k2, the rate constant at 95.0°C, using the expression: ln(k2/k1) = (-55500 J/mol / 8.314 J/(mol*K)) * (1/368 K - 1/298 K). Calculate the value of k2 from this expression.