Problem 31 - Chemistry and Chemical Reactivity

Question

\(K_{\mathrm{p}}\) for the formation of phosgene, \(\mathrm{COCl}_{2},\) is \(6.5 \times 10^{11}\) at \(25^{\circ} \mathrm{C}\) $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) $$ What is the value of \(K_{p}\) for the dissociation of phosgene? $$ \operatorname{COCl}_{2}(g) \rightleftarrows \operatorname{CO}(g)+\mathrm{Cl}_{2}(g) $$

Step-by-Step Solution

Answer

The equilibrium constant \( K'_p \) for the dissociation of phosgene is approximately \( 1.538 \times 10^{-12} \).

Step 1: Understand the Reaction and Its Equilibrium Expression

The initial reaction for the formation of phosgene is \( \text{CO}(\text{g}) + \text{Cl}_2(\text{g}) \rightleftharpoons \text{COCl}_2(\text{g}) \). The given equilibrium constant \( K_p \) for this reaction at \( 25^{\circ} \text{C} \) is \( 6.5 \times 10^{11} \).For the reverse reaction, \( \text{COCl}_2(\text{g}) \rightleftharpoons \text{CO}(\text{g}) + \text{Cl}_2(\text{g}) \), we need to find the equilibrium constant \( K'_p \) which corresponds to the dissociation of phosgene.

Step 2: Relationship Between Forward and Reverse Reaction Equilibrium Constants

For any reversible reaction \( aA + bB \rightleftharpoons cC + dD \), if the equilibrium constant for the forward reaction is \( K_p \), then the equilibrium constant for the reverse reaction is given by \( K'_p = \frac{1}{K_p} \). Therefore, for the dissociation of phosgene, we have:\[ K'_p = \frac{1}{K_p} \].

Step 3: Calculate the Equilibrium Constant for the Reverse Reaction

Using the relationship from the previous step, substitute the given \( K_p \) value:\[ K'_p = \frac{1}{6.5 \times 10^{11}} \].This gives:\[ K'_p \approx 1.538 \times 10^{-12} \].

Step 4: Conclude the Result

The equilibrium constant \( K'_p \) for the dissociation of phosgene is approximately \( 1.538 \times 10^{-12} \). This indicates that under the given conditions at 25°C, the reaction predominantly favors the formation of phosgene.

Key Concepts

Equilibrium Constants

Equilibrium constants are crucial in understanding chemical reactions that reach a state of balance where the rate of the forward reaction equals the rate of the reverse reaction. In the context of phosgene formation, we are dealing with the equilibrium constant for reactions involving gaseous compounds, hence the use of the notation \( K_{p} \).
An equilibrium constant \( K_{p} \) represents the ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients, when the reaction is at equilibrium.

• For a reaction \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant \( K_{p} \) is defined as \( K_{p} = \frac{[C]^c [D]^d}{[A]^a [B]^b} \).

In the phosgene formation reaction:

• Carbon monoxide (CO) and chlorine gas (Cl\(_2\)) react to form phosgene (COCl\(_2\)).
• The given \( K_{p} = 6.5 \times 10^{11} \) illustrates that at 25°C, the formation of phosgene is highly favored.

Given such a large \( K_{p} \) value implies that, at equilibrium, there is significantly more phosgene than carbon monoxide and chlorine.

Reversible Reactions

Reversible reactions are chemical processes where the reactants form products, which can themselves react to give back the reactants. These reactions will eventually reach a state of equilibrium, where the conversion of reactants and products occurs at an equal rate, stabilizing their concentrations.
In the phosgene formation exercise, the reaction can be represented both ways:

• The forward reaction: \( \text{CO}( ext{g}) + \text{Cl}_2( ext{g}) \rightleftharpoons \text{COCl}_2( ext{g}) \).
• The reverse reaction: \( \text{COCl}_2( ext{g}) \rightleftharpoons \text{CO}( ext{g}) + \text{Cl}_2( ext{g}) \).

When discussing reversible reactions, it is essential to understand that their equilibrium state depends on various factors:

• Concentration: Changes can shift the equilibrium point according to Le Chatelier's principle.
• Pressure: Affects reactions involving gases, like in the case of phosgene.
• Temperature: Can alter the equilibrium constant \( K_{p} \), impacting the concentrations at equilibrium.

These reactions demonstrate the dynamic nature of chemical equilibria, highlighting how systems adjust to changes and maintain a balance.

Phosgene Formation

Phosgene (COCl\(_2\)) is a significant industrial chemical, produced through the reaction of carbon monoxide and chlorine gas. This reaction is exothermic, meaning it releases heat, and is highly favored at lower temperatures, as evidenced by the large \( K_{p} \) value given at 25°C.
The reaction, which is reversible, is as follows:

• Forward: \( \text{CO}( ext{g}) + \text{Cl}_2( ext{g}) \rightleftharpoons \text{COCl}_2( ext{g}) \)
• Reverse: \( \text{COCl}_2( ext{g}) \rightleftharpoons \text{CO}( ext{g}) + \text{Cl}_2( ext{g}) \)

Phosgene is also highly toxic and was historically used as a chemical weapon, although now it is primarily used in the production of pharmaceuticals and as a chemical reagent for the synthesis of different organic compounds.
For chemists and industry professionals, controlling the conditions to ensure the safe formation and handling of phosgene is crucial. Factors such as temperature, pressure, and reaction containment need careful management to prevent unwanted decomposition or exposure.
Despite its dangers, phosgene remains a cornerstone in chemical manufacturing due to its effectiveness and versatility as a reagent.