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- The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128 s−1 at 150 K. If the surface is initially completely covered, what fraction will remain covered after 10 s? After 20 s?
Problem 97
Problem 97a
The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128/s at 150 K. a. What is the half-life of the desorption reaction?-
Problem 97b
The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128/s at 150 K. b. If the surface is initially completely covered with n-butane at 150 K, how long will it take for 25% of the molecules to desorb (leave the surface)? For 50% to desorb?
- What fraction of the film is left after 10 s, assuming the same initial coverage as in part a, given that the evaporation of a 120-nm film of n-pentane from a single crystal of aluminum oxide is zero order with a rate constant of 1.92 * 10^13 molecules/cm^2 * s at 120 K?
Problem 98
Problem 98a
The evaporation of a 120-nm film of n-pentane from a single crystal of aluminum oxide is zero order with a rate constant of 1.92⨉1013 molecules/cm2•s at 120 K. a. If the initial surface coverage is 8.9⨉1016 molecules/cm2, how long will it take for one-half of the film to evaporate?
Problem 99b
The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)
C2H5Br(aq) + OH- (aq) → C2H5OH(l) + Br- (aq)
Temperature (°C) k (L,mol •s)
25 8.81⨉10-5
35 0.000285
45 0.000854
55 0.00239
65 0.00633
b. Determine the rate constant at 15 °C.
Problem 100
The reaction 2 N2O5 → 2 N2O4 + O2 takes place at around room temperature in solvents such as CCl4. The rate constant at 293 K is found to be 2.35⨉10-4 s-1, and at 303 K the rate constant is found to be 9.15⨉10-4 s-1. Calculate the frequency factor for the reaction.
Problem 101a
This reaction has an activation energy of zero in the gas phase: CH3 + CH3 → C2H6 a. Would you expect the rate of this reaction to change very much with temperature?
Problem 102a
Consider the two reactions:
O + N2 → NO + N Ea = 315 kJ/mol
Cl + H2 → HCl + H Ea = 23 kJ/mol
a. Why is the activation barrier for the first reaction so much higher than that for the second?
Problem 102b
Consider the two reactions:
O + N2 → NO + N Ea = 315 kJ/mol
Cl + H2 → HCl + H Ea = 23 kJ/mol
b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.
Problem 103
Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon- 14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 19.5% of the C-14 found in living organisms. How old is the bone?
- How old is a rock that contains 83.2% of the amount of uranium-238 it contained when it was formed?
Problem 104
Problem 105a
Consider the gas-phase reaction: H2(g) + I2(g) → 2 HI(g) The reaction was experimentally determined to be first order in H2 and first order in I2. Consider the proposed mechanisms. Proposed mechanism I: H2(g) + I2(g) → 2 HI(g) Single step Proposed mechanism II: I2(g) Δk1k-12 I(g) Fast H2( g) + 2 I( g) → k22 HI( g) Slow a. Show that both of the proposed mechanisms are valid.
Problem 105b
Consider the gas-phase reaction: H2(g) + I2(g) → 2 HI(g) The reaction was experimentally determined to be first order in H2 and first order in I2. Consider the proposed mechanisms. Proposed mechanism I: H2(g) + I2(g) → 2 HI(g) Single step Proposed mechanism II: I2(g) Δk1k-12 I(g) Fast H2( g) + 2 I( g) → k22 HI( g) Slow b. What kind of experimental evidence might lead you to favor mechanism II over mechanism I?
Problem 106
Phosgene (Cl2CO), a poison gas used in World War I, is formed
by the reaction of Cl2 and CO. The proposed mechanism for the
reaction is:
Cl2Δ2 Cl (fast, equilibrium)
Cl + COΔClCO (fast, equilibrium)
ClCO + Cl2¡Cl2CO + Cl (slow)
- What rate law corresponds to the proposed mechanism for the formation of hydrogen bromide, which can be written in a simplified form as: Br2(g) → 2Br(g) (Fast) Br(g) + H2(g) → HBr(g) + H(g) (Slow) H(g) + Br2(g) → HBr(g) + Br(g) (Fast)?
Problem 107
- What rate law corresponds to the proposed mechanism for the formation of hydrogen iodide, which can be written in simplified form as: I2 Δk1k-1 2I (Fast), I + H2 Δk2k-2 H2I (Fast), H2I + I ¡k3 2HI (Slow)?
Problem 108
Problem 109
A certain substance X decomposes. Fifty percent of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is (c) second order?
Problem 110
The half-life for radioactive decay (a first-order process) of plutonium- 239 is 24,000 years. How many years does it take for one mole of this radioactive material to decay until just one atom remains?
- The energy of activation for the decomposition of 2 mol of HI to H2 and I2 in the gas phase is 185 kJ. The heat of formation of HI(g) from H2(g) and I2(g) is -5.65 kJ/mol. Find the energy of activation for the reaction of 1 mol of H2 and 1 mol of I2 to form 2 mol of HI in the gas phase.
Problem 111
- Ethyl chloride vapor decomposes by the first-order reaction: C2H5Cl -> C2H4 + HCl. The activation energy is 249 kJ/mol, and the frequency factor is 1.6 * 10^14 s^-1. Find the temperature at which the rate of the reaction would be twice as fast.
Problem 112
Problem 112a
Ethyl chloride vapor decomposes by the first-order reaction: C2H5Cl → C2H4 + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉1014 s-1. Find the value of the rate constant at 710 K.
Problem 112b
Ethyl chloride vapor decomposes by the first-order reaction: C2H5Cl → C2H4 + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉1014 s-1. What fraction of the ethyl chloride decomposes in 15 minutes at this temperature?