Textbook Question
Indicate whether each statement is true or false. (b) Exothermic reactions are faster than endothermic reactions.
867
views
Ch.14 - Chemical Kinetics
Chapter 14, Problem 61
(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?
Verified step by step guidance1
Step 1: Identify the Arrhenius equation, which relates the rate constant k to the temperature T and the activation energy Ea: k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, R is the gas constant (8.314 J/(mol*K)), and T is the temperature in Kelvin.
Step 2: Convert the given temperatures from Celsius to Kelvin by adding 273.15 to each temperature. For example, 20°C becomes 293.15 K and 60°C becomes 333.15 K.
Step 3: Use the Arrhenius equation in its logarithmic form to find the new rate constant k2 at 60°C: ln(k2/k1) = -Ea/R * (1/T2 - 1/T1), where k1 is the initial rate constant at 20°C, T1 is the initial temperature in Kelvin, and T2 is the final temperature in Kelvin.
Step 4: Substitute the given values into the logarithmic form of the Arrhenius equation for part (a) with Ea = 75.5 kJ/mol, converting Ea to J/mol by multiplying by 1000.
Step 5: Repeat Step 4 for part (b) with Ea = 125 kJ/mol, again converting Ea to J/mol by multiplying by 1000. Solve for k2 in each case.
Related Practice
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.
301
views
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
1405
views
Open Question
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.
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.
2097
views
1
comments