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6.3 Practice Problems

6.3 Practice Problems#

  1. Consider the following reaction,

\[\ce{4 NO2 + O2 -> 2 N2O5}\]

At a particular time during the reaction, is being consumed at the rate of \(\pu{1.3e-3 mol L-1 s-1}\). (a) At what rate is being consumed? (b) At what rate is being produced? Answer: (a) \(\pu{-3.25e-4mol L-1 s-1}\), (b) \(\pu{6.5e-4 mol L-1 s-1}\)

  1. The solvent methylene chloride (\(\ce{CH2Cl2}\)) reacts with bisulfide (\(\ce{HS-}\)) to form dithiomethane (\(\ce{CH2(SH)2}\)) as shown in this reaction:

\[\ce{CH2Cl2 + 2 HS- -> CH2(SH)2 + 2 Cl-}\]

This reaction is monitored by measuring the rate of production. If after \(\pu{2 min}\), appears at a rate of \(\pu{10 mmol L-1 min-1}\), what is the reaction rate at which is being consumed? Answer: \(\pu{-5 mmol L-1 min-1}\)

  1. Write the rate expressions and determine the reaction order in the following reactions.

\[\begin{split} \begin{align} \ce{ 2 A &-> C\\ 2 A + B &-> C } \end{align}\end{split}\]

Answer: (1) 2, 2 (2) 2, 1, 3

  1. The decomposition of hydrogen peroxide is first order in \(\ce{H2O2}\).

\[\ce{ 2 H2O2 -> 2 H2O + O2 }\]

The rate constant for this reaction at \(\pu{20 ^\circ C}\) is \(\pu{1.8e-5 s-1}\). The starting concentration of is \(\pu{0.75 M}\). Determine (a) the concentration of remaining after \(\pu{3 h}\). Answer: \(\pu{0.62 M}\) and (b) how long it will take for the concentration to drop to \(\pu{0.10 M}\). Answer: \(\pu{31 h}\).

  1. The decomposition of ethane (\(\ce{C2H6}\)) to methyl radicals (\(\ce{.CH3}\)) is a first-order reaction with a rate constant of \(\pu{5.36e-1 s-1}\) at \(\pu{700 ^\circ C}\). Calculate the half-life of this reaction in minutes. Answer: \(\pu{21.5 min}\)

  2. Auto-oxidation of \(\ce{Fe^2+}\) occurs when exposed to the atmosphere due to the presence of \(\ce{O2(g)}\). The table below shows the observed \(\ce{Fe^2+}\) oxidation data. Determine (a) the reaction order, (b) the rate constant for this reaction, and (c) the half-life of \(\ce{Fe^2+}\).

Time, \(\pu{min}\)

Conc, \(\pu{\mu g L-1}\)

0

500

10

320

20

200

30

130

40

80

60

35

  1. A researcher has monitored the treatment of an organic pollutant using a naturally-occurring mineral compound. The table below shows the kinetics data. Determine (a) the reaction order, (b) the rate constant for this reaction, and (c) the half-life of pollutant.

Time, \(\pu{h}\)

Conc, \(\pu{\mu mol L-1}\)

1.5

137

18

98.6

42.5

68

71.5

38.4

91.5

23.7

115

12.2

138.5

8.4