Question

the 1995 nobel prize in chemistry was shared by paul crutzen, f. sherwood rowland, and mario molina for their work concerning the formation and decomposition of ozone in the stratosphere. rowland and molina hypothesized that chlorofluorocarbons (cfcs) in the stratosphere break down upon exposure to uv radiation, producing chlorine atoms. chlorine was previously identified as a catalyst in the breakdown of ozone into oxygen gas. using the enthalpy of reaction for two reactions with ozone, determine the enthalpy of reaction for the reaction of chlorine with ozone. (1) $clo(g)+o_{3}(g)\to cl(g)+2o_{2}(g)$ $delta h_{rxn}^{circ}=-122.8kj$ (2) $2o_{3}(g)\to 3o_{2}(g)$ $delta h_{rxn}^{circ}=-285.3kj$ (3) $o_{3}(g)+cl(g)\to clo(g)+o_{2}(g)$ $delta h_{rxn}^{circ}=?$ $delta h_{rxn}^{circ}=$ kj

Explanation:

Step1: Reverse reaction (1)

When we reverse a reaction, the sign of its enthalpy change changes.
Reversing reaction (1): \(Cl(g)+2O_{2}(g)\to ClO(g) + O_{3}(g)\), \(\Delta H_{rxn}=+ 122.8\space kJ\)

Step2: Manipulate reaction (2)

We want to get \(O_{3}(g)\) and \(Cl(g)\) on the reactant side and \(ClO(g)\) and \(O_{2}(g)\) on the product side.
Let's consider reaction (2): \(2O_{3}(g)\to3O_{2}(g)\), \(\Delta H_{rxn}=-285.3\space kJ\)

If we add the reversed reaction (1) \((Cl(g)+2O_{2}(g)\to ClO(g) + O_{3}(g),\Delta H = + 122.8\space kJ)\) and reaction (2) \((2O_{3}(g)\to3O_{2}(g),\Delta H=-285.3\space kJ)\) in a way that we can get reaction (3).

Let's rewrite the reversed reaction (1) as:
\(Cl(g)+2O_{2}(g)-ClO(g)-O_{3}(g)=0\)
and reaction (2) as: \(2O_{3}(g)-3O_{2}(g)=0\)

If we add them:
\(Cl(g)+2O_{2}(g)-ClO(g)-O_{3}(g)+2O_{3}(g)-3O_{2}(g)=0\)
Simplify to get \(O_{3}(g)+Cl(g)\to ClO(g)+O_{2}(g)\)

The enthalpy change \(\Delta H\) for the overall reaction is the sum of the enthalpy changes of the individual reactions.
Let \(\Delta H_{1}\) be the enthalpy of the reversed reaction (1) (\(\Delta H_{1}=+122.8\space kJ\)) and \(\Delta H_{2}\) be the enthalpy of reaction (2) (\(\Delta H_{2}=-285.3\space kJ\))

We can also use Hess's law formula. If we want to find \(\Delta H\) for \(O_{3}(g)+Cl(g)\to ClO(g)+O_{2}(g)\)

Let’s express the target reaction in terms of the given reactions.
We know that \(\Delta H=\Delta H_{1}+\frac{1}{2}\Delta H_{2}\) (because in the combination of reactions to get the target reaction, reaction (2) is used in a “half - amount” sense in terms of stoichiometry for \(O_{3}\) and \(O_{2}\) balancing)

$$
LATEXBLOCK0
$$

Answer:

\(-19.85\)