Kinetics: Rates and Mechanism of Chemical Reactions

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?

Consider the following organic reaction, in which one halogen replaces another in an alkyl halide: 

${\mathbf{CH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{Br}\mathbf{+}\mathbf{Kl}\mathbf{\to }{\mathbf{CH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{l}\mathbf{+}\mathbf{KBr}$

In acetone, this particular reaction goes to completion because KI is soluble in acetone but KBr is not. In the mechanism, I approach the carbon opposite to the Br (see Figure 16.19, with ${\mathbf{l}}^{\mathbf{-}}$  

instead of OH- ). After Br- has been replaced by ${\mathbf{l}}^{\mathbf{-}}$and precipitates as KBr, other I ions react with the ethyl iodide by the same mechanism. 

(a) If we designate the carbon bonded to the halogen as C-1, what are the shapes around C-1 and the hybridization of C-1 in ethyl iodide? 

(b) In the transition state, one of the two lobes of the unhybridized 2p orbital of C-1 overlaps a p orbital of I, while the other lobe overlaps a p orbital of Br. What are the shape around C-1 and the hybridization of C-1 in the transition state? 

(c) The deuterated reactant, ${\mathbf{CH}}_{\mathbf{3}}\mathbf{CHDBr}$(where D is deuterium, 2 H), has two optical isomers because C-1 is chiral. If the reaction is run with one of the isomers, the ethyl iodide is not optically active. Explain