Chapter 16: Kinetics: Rates and Mechanism of Chemical Reactions

While developing a catalytic process to make ethylene glycol from synthesis gas $(\mathrm{CO}+H_2)$, a chemical engineer finds the rate is fourth-order in gas pressure. The uncertainty in the pressure reading is 5%. When the catalyst is modified, the rate increases by 10%. If you were the company patent attorney, would you file for a patent on this catalyst modification? Explain.

Assume water boils at ${\mathbf{100}}^{\mathbf{0}}\mathit{C}$ in Houston (near sea level), and at ${\mathbf{90}}^{\mathbf{0}}\mathit{C}$ in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is${\mathbf{E}}_{\mathbf{a}}$ for this process?

For the reaction , sketch two curves on the same set of axes that show (a) The formation of product as a function of time(b) The consumption of reactant as a function of time

Chlorine is commonly used to disinfect drinking water, and the inactivation of pathogens by chlorine follows first-order kinetics. The following data show E. coli inactivation:

(a) Determine the first-order inactivation constant, k. [Hint: % inactivation

$\mathbf{=}\mathbf{100}\mathbf{\times }\left(1-\frac{{\left[A\right]}_t}{{\left[A\right]}_0}\right)$

(b) How much contact time is required for 95% inactivation?

Nitrification is a biological process for removing $\mathit{N}{\mathit{H}}_{\mathbf{3}}$from wastewater as $\mathit{N}{{\mathbf{H}}_{\mathbf{4}}}^{\mathbf{+}}$:

$\mathbf{N}{{\mathbf{H}}_{\mathbf{4}}}^{\mathbf{+}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}{\mathbf{O}}_{\mathbf{2}}\mathbf{\to }\mathbf{N}{\mathbf{O}}_{\mathbf{3}}^{\mathbf{-}}\mathbf{}\mathbf{+}\mathbf{2}{\mathbf{H}}^{\mathbf{+}}\mathbf{}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$

The first-order rate constant is given as

${\mathit{K}}_{\mathbf{1}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{47}{\mathit{e}}^{\mathbf{0}\mathbf{.}\mathbf{095}\left(T°C-15°C\right)}$

Where${\mathit{K}}_{\mathbf{1}}$ is in$\mathit{d}\mathit{a}{\mathit{y}}^{\mathbf{-}\mathbf{1}}$ and T is in°C

1. If the initial concentration$\mathit{N}{\mathit{H}}_{\mathbf{3}}$is 3.0$\mathit{m}\mathit{o}\mathit{l}\mathbf{/}{\mathit{m}}^{\mathbf{3}}$, how long will it take to reduce the concentration to 0.35$\mathit{m}\mathit{o}\mathit{l}\mathbf{/}{\mathit{m}}^{\mathbf{3}}$in the spring (T =20°C)?
2. In the winter (T = 10°C)?
3. Using your answer to part (a), what is the rate of${\mathit{O}}_{\mathbf{2}}$ consumption?

Carbon disulfide, a poisonous, flammable liquid, is an excellent solvent for phosphorus, sulfur, and some other nonmetals. A kinetic study of its gaseous decomposition reveals these data:

(a) Write the rate law for the decomposition of$\mathit{C}{\mathit{S}}_{\mathbf{2}}$ .

(b) Calculate the average value of the rate constant

Like any catalyst, palladium, platinum, and nickel catalyze both directions of a reaction: the addition of hydrogen to (hydrogenation) and its elimination from (dehydrogenation) carbon double bonds.

(a) Which variable determines whether an alkene will be hydrogenated or dehydrogenated?

(b) Which reaction requires a higher temperature?

(c) How can all-trans fats arise during the hydrogenation of fats that contain some cis-double bonds?

The molecular scenes below represent the first-order reaction as cyclopropane (red) is converted to propene (green):

Determine (a) the half-life and (b) the first-order rate constant.

The growth of Pseudomonas bacteria is modelled as a first-order process with k = 0.035 $\mathit{m}\mathit{i}{\mathit{n}}^{\mathbf{-}\mathbf{1}}$ at 37°C. The initial Pseudomonas population density is $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$cells/L.

(a) What is the population density after two h?

(b) What is the time required for the population to go from $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathit{t}\mathit{o}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$cells/ L?

For the reaction , [C] vs. time is plotted:

How do you determine each of the following?

(a) The average rate over the entire experiment

(b) The reaction rate at time x

(c) The initial reaction rate

(d) Would the values in parts (a), (b) and (c) be different if you plotted [D] vs. time? Explain.