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Problem 83

High levels of ozone $\left(\mathrm{O}_{3}\right)$ cause rubber to deteriorate, green plants to turn brown, and many people to have difficulty breathing. (a) Is the formation of $\mathrm{O}_{3}$ from $\mathrm{O}_{2}$ favored at all $T,$ no $T,$ high $T$ or low $T ?$ (b) Calculate $\Delta G^{\circ}$ for this reaction at 298 $\mathrm{K}$ .

(c) Calculate $\Delta G$ at 298 $\mathrm{K}$ for this reaction in urban smog where

Answer

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## Discussion

## Video Transcript

The question here gives us this reaction, and it wants us to calculate the value of Delta, G and K. So, first of all, to calculate Delta G, we take, um, products minus reactant. So when we calculate this, it should give us a value off negative 198 killer Jules promote. And from here, we can take Delta G is equal to negative, Artie, the natural log of K. And basically, when we plug it in at 298 Kelvin, negative 198 is equal to negative. Negative are which is the ideal gas constant times 298 Kelvin Natural log of K. And when we solve for kay here, this should give us the value of 5.7 times 10 to the power for negative to the power of 34. Rather, And that's the answer to the question here. So K is equal to that value

## Recommended Questions

One of the reactions that destroys ozone in the upper atmosphere is

$$\mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$

Using data from Appendix $4,$ calculate $\Delta G^{\circ}$ and $K(\text { at } 298 \mathrm{K})$

for this reaction.

The ozone in the earth's ozone layer decomposes according to the equation

$$2 \mathrm{O}_{3}(\mathrm{g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{g})$$

The mechanism of the reaction is thought to proceed through an initial fast equilibrium and a slow step:

Step 1 $\quad$ Fast, Reversible $\quad \mathrm{O}_{3}(\mathrm{g}) \rightleftarrows \mathrm{O}_{2}(\mathrm{g})+\mathrm{O}(\mathrm{g})$

Step 2 Slow $\quad \mathrm{O}_{3}(\mathrm{g})+\mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{g})$

Show that the mechanism agrees with this experimental rate law: $-\Delta\left[\mathrm{O}_{3}\right] / \Delta t=k\left[\mathrm{O}_{3}\right]^{2} /\left[\mathrm{O}_{2}\right]$

The following reaction represents the removal of ozone in the stratosphere: $2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)$ Calculate the equilibrium constant $\left(K_{P}\right)$ for the reaction. In view of the magnitude of the equilibrium constant, explain why this reaction is not considered a major cause of ozone depletion in the absence of man-made pollutants such as the nitrogen oxides and CFCs. Assume the temperature of the stratosphere to be $-30^{\circ} \mathrm{C}$ and $\Delta G_{\mathrm{f}}^{\circ}$ to be temperature independent.

Ozone, $\mathrm{O}_{3}(g),$ is a form of elemental oxygen that plays an important role in the absorption of ultraviolet radiation in the stratosphere. It decomposes to $\mathrm{O}_{2}(g)$ at room temperature

and pressure according to the following reaction:

$$2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g) \quad \Delta H=-284.6 \mathrm{kJ}$$

(a) What is the enthalpy change for this reaction per mole of $\mathrm{O}_{3}(g) ?$

(b) Which has the higher enthalpy under these conditions, 2 $\mathrm{O}_{3}(g)$ or 3 $\mathrm{O}_{2}(g) ?$

Ozone, $\mathrm{O}_{3},$ in the earth's upper atmosphere decomposes according to the equation

$$2 \mathrm{O}_{3}(\mathrm{g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{g})$$

The mechanism of the reaction is thought to proceed through an initial fast, reversible step followed by a slow, second step.

Step 1 $\quad$ Fast, reversible $\mathbf{O}_{3}(\mathrm{g}) \rightleftarrows \mathrm{O}_{2}(\mathrm{g})+\mathrm{O}(\mathrm{g})$

Step 2 Slow $\quad \mathrm{O}_{3}(\mathrm{g})+\mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{g})$

(a) Which of the steps is rate-determining?

(b) Write the rate equation for the rate-determining step.

A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms with ozone:

$$\mathrm{O}(g)+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)$$

At 298 $\mathrm{K}$ the rate constant for this reaction is $4.8 \times 10^{5}$ $M^{-1} \mathrm{s}^{-1} .$ (a) Based on the units of the rate constant, write the likely rate law for this reaction. (b) Would you expect this reaction to occur via a single elementary process? Explain why or why not. (c) Use $\Delta H_{f}^{\circ}$ values from Appendix $C$ to estimate the enthalpy change for this reaction. Would this reaction raise or lower the temperature of the stratosphere?

Ozone Layer The following reaction plays a key role in the destruction of ozone in the atmosphere:

$$\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)

$$.The standard entropy change $\left(\Delta S_{\mathrm{rxn}}^{\circ}\right)$ is $19.9 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})$.Use the standard molar entropies $\left(S^{\circ}\right)$ in Appendix 4 to calculate the $S^{\circ}$ value of $\mathrm{ClO}(g)$.

In the lower troposphere, ozone is one of the components of photochemical smog. It is generated in air when nitrogen dioxide, formed by the oxidation of nitrogen monoxide from car exhaust, reacts by the following mechanism:

$$

\begin{array}{l}{\text { (1) } \mathrm{NO}_{2}(g) \frac{k_{1}}{h v} \mathrm{NO}(g)+\mathrm{O}(g)} \\ {\text { (2) } \mathrm{O}(g)+\mathrm{O}_{2}(g) \frac{k_{2}}{\ln v} \mathrm{O}_{3}(g)}\end{array}

$$

Assuming the rate of formation of atomic oxygen in step 1 equals the rate of its consumption in step 2, use the data below to calculate (a) the concentration of atomic oxygen [O]; (b) the rate of ozone formation.

$$

\begin{array}{ll}{k_{1}=6.0 \times 10^{-3} \mathrm{s}^{-1}} & {\left[\mathrm{NO}_{2}\right]=4.0 \times 10^{-9} \mathrm{M}} \\ {k_{2}=1.0 \times 10^{6} \mathrm{L} / \mathrm{mol} \cdot \mathrm{s}} & {\left[\mathrm{O}_{2}\right]=1.0 \times 10^{-2} \mathrm{M}}\end{array}

$$

Stratospheric Ozone Depletion Chlorine monoxide (C1O) plays a major role in the creation of the ozone holes in the stratosphere over Earth's polar regions.

a. If $\Delta[\mathrm{ClO}] / \Delta t$ at $298 \mathrm{K}$ is $-2.3 \times 10^{7} M / \mathrm{s},$ what is the rate of change in $\left[\mathrm{Cl}_{2}\right]$ and $\left[\mathrm{O}_{2}\right]$ in the following reaction?

$$

2 \mathrm{ClO}(g) \rightarrow \mathrm{Cl}_{2}(g)+\mathrm{O}_{2}(g)

$$

b. If $\Delta[\mathrm{ClO}] / \Delta t$ is $-2.9 \times 10^{4} M / s,$ what is the rate of formation of oxygen and $\mathrm{ClO}_{2}$ in the following reaction?

$$

\mathrm{ClO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{ClO}_{2}(g)

$$

Mechanism of Ozone Destruction Ozone decomposes thermally to oxygen in the following reaction:

$$

2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)

$$

The following mechanism has been proposed:

$$

\begin{array}{l}

\quad \mathrm{O}_{3}(g) \rightarrow \mathrm{O}(g)+\mathrm{O}_{2}(g) \\

\mathrm{O}(g)+\mathrm{O}_{3}(g) \rightarrow 2 \mathrm{O}_{2}(g)

\end{array}

$$

The reaction is second order in ozone. What properties of the two elementary steps (specifically, relative rate and reversibility) are consistent with this mechanism?