IOM 2016, Теория — Задача 4. Radical decomposition

1st Olympiad of Metropolises — Chemistry, Theoretical Problems, Official English version · 7 септември 2016 г.

Условие

Problem 4. Radical decomposition (12 marks)

Almost all halogen oxides are endothermic compounds, i.e. they are formed from elements with absorption of heat. Chlorine (I) oxide, a brownish-yellow gas, is not an exception. Upon mild heating it decomposes exothermically into chlorine and oxygen according to the equation

This reaction is not an elementary one. It proceeds through several consecutive elementary steps:

($k_1$ – $k_3$ are the rate constants, M is any molecule)

1 Using the Hess’ law calculate the reaction enthalpies for all elementary steps and for the overall reaction. For each case note whether the reaction is exothermic (write “$Q>0$”) or endothermic (“$Q<0$”). The necessary data are provided at the end of the problem.

$2\mathrm{Cl_2O}\rightarrow2\mathrm{Cl_2}+\mathrm{O_2}$

$\Delta_\mathrm r H^o=$ ______

$\mathrm{Cl_2O+M\rightarrow Cl\cdot+ClO\cdot+M}$

$\Delta_\mathrm r H^o=$ ______

$\mathrm{Cl\cdot+Cl_2O\rightarrow Cl_2+ClO\cdot}$

$\Delta_\mathrm r H^o=$ ______

$2\mathrm{ClO\rightarrow Cl_2+O_2}$

$\Delta_\mathrm r H^o=$ ______ [12 т.]

2 Which elementary step would you expect to be the slowest one? Tick the appropriate box.

(1) ☐ (2) ☐ (3) ☐ [3 т.]

3 Derive the expression for the rate of $\mathrm{Cl_2O}$ depletion using the steady-state approximation. Do not express [M] in terms of concentrations of specific substances, leave it as it is.

Calculations:

$-\dfrac{d[\mathrm{Cl_2O}]}{dt}=$ ______ [10 т.]

Decomposition of oxygen difluoride, $\mathrm{OF_2}$, to fluorine and oxygen proceeds via a similar mechanism with the notable exception: reaction between two $\mathrm{FO\cdot}$ radicals yields two fluorine atoms rather than a difluorine molecule. This is due to the fact that the reaction

is highly exothermic, and the amount of heat released is enough to break the F–F bond. The fluorine atoms formed then either dimerize or react with $\mathrm{OF_2}$. So, the overall mechanism is as follows:

($k_1$ – $k_4$ are the rate constants, M is any molecule)

Note that this is a chain reaction: $\mathrm{F\cdot}$ radical produces $\mathrm{FO\cdot}$, then $\mathrm{FO\cdot}$ radical produces $\mathrm{F\cdot}$ and the process repeats itself. The radicals $\mathrm{F\cdot}$ and $\mathrm{FO\cdot}$ are the carriers of the chain process.

Under the certain conditions exothermic chain reactions can proceed with increasing rates. There are two possible reasons for this: a) self-heating of the reaction mixture as the reaction proceeds causes the increase of the rate constants which makes the reaction go faster and b) over a cycle of chain propagation the number of the chain carriers increases which leads to exponential growth of their concentrations. These two regimes are called thermal mode and chain-branching mode, respectively.

4a Using the law of mass action derive the expression for the change rate of the total concentration of chain carriers, [CC], in the reaction of $\mathrm{OF_2}$ decomposition. Do not express [M] in terms of concentrations of certain substances. Note that concentrations of radical species are negligible regardless of the reaction mode.

Calculations:

$\dfrac{d[\mathrm{CC}]}{dt}=\dfrac{d([\mathrm F]+[\mathrm{FO}])}{dt}=$ ______ [6 т.]

4b Draw a sketch of dependence of $d[\mathrm{CC}]/dt$ on [CC].

[4 т.]

4c Decide whether $\mathrm{OF_2}$ decomposition is a thermal process or a chain-branching process.

thermal ☐ chain-branching ☐ [4 т.]

5 Using the steady-state approximation, derive the expression for the rate of $\mathrm{OF_2}$ depletion. Do not express [M] in terms of concentrations of specific substances, leave it as it is.

Calculations:

$-\dfrac{d[\mathrm{OF_2}]}{dt}=$ ______ [20 т.]

Standard enthalpies of formation of gaseous compounds and radical species at $298\ \mathrm K$

Решение

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