Textbook Question
Indicate whether each statement is true or false. (c) If you double the temperature for a reaction, you cut the activation energy in half.
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Ch.14 - Chemical Kinetics
Chapter 14, Problem 62
Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to N2 and O2 is second order with a rate constant of 0.0796 M-1s-1 at 737 _x001E_C and 0.0815 M-1s-1 at 947 _x001E_C. Calculate the activation energy for the reaction.
Verified step by step guidance1
Step 1: Use the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea), temperature (T), and the pre-exponential factor (A): k = A * e^(-Ea/(RT)), where R is the gas constant (8.314 J/mol·K).
Step 2: Take the natural logarithm of both sides of the Arrhenius equation to linearize it: ln(k) = ln(A) - Ea/(RT).
Step 3: Set up two equations using the given rate constants and temperatures. Convert the temperatures from Celsius to Kelvin by adding 273.15.
Step 4: Use the two equations to eliminate ln(A) and solve for Ea. This can be done by subtracting one equation from the other, resulting in: ln(k2/k1) = -Ea/R * (1/T2 - 1/T1).
Step 5: Rearrange the equation to solve for Ea: Ea = -R * ln(k2/k1) / (1/T2 - 1/T1). Substitute the known values for k1, k2, T1, and T2 to find the activation energy.
Related Practice
Textbook Question
Based on their activation energies and energy changes and assuming that all collision factors are the same, rank the following reactions from slowest to fastest. (a) Ea = 45 kJ>mol; E = -25 kJ>mol (b) Ea = 35 kJ>mol; E = -10 kJ>mol (c) Ea = 55 kJ>mol; E = 10 kJ>mol
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Open Question
(a) A certain first-order reaction has a rate constant of 2.75 * 10^-2 s^-1 at 20 _x001E_C. What is the value of k at 60 _x001E_C if Ea = 75.5 kJ/mol? (b) Another first-order reaction also has a rate constant of 2.75 * 10^-2 s^-1 at 20 _x001E_C. What is the value of k at 60 _x001E_C if Ea = 125 kJ/mol?
Open Question
The rate of the reaction CH3COOC2H5(aq) + OH-(aq) → CH3COO-(aq) + C2H5OH(aq) was measured at several temperatures, and the following data were collected: Temperature (°C) k (M⁻¹ s⁻¹) 15 0.0521 25 0.101 35 0.184 45 0.332. Calculate the value of Ea by constructing an appropriate graph.
Textbook Question
The temperature dependence of the rate constant for a reaction is tabulated as follows: Temperature (K) k 1M 1 s1 2 600 0.028 650 0.22 700 1.3 750 6.0 800 23 Calculate Ea and A.
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Textbook Question
(b) What is the difference between a unimolecular and a bimolecular elementary reaction?
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