Problem 97 - Chemistry: An Atoms-Focused Approach

Question

Chemical Weapon Phosgene, \(\mathrm{COCl}_{2}\), gained notoricty as a chemical weapon in World War I. Phosgene is produced by the reaction of carbon monoxide with chlorine: $$ \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) $$ \(K_{c}=5.0\) for this reaction at \(600 \mathrm{K} .\) What are the equilibrium partial pressures of the three gases if a reaction vessel initially contains a mixture of the reactants in which \(P_{\mathrm{CO}}=P_{\mathrm{Cl}_{1}}=0.265\) atm and \(P_{\mathrm{COC}_{1}}=0.000\) atm?

Step-by-Step Solution

Answer

Answer: At equilibrium, the partial pressures are: \(P_{CO} = 0.205\) atm \(P_{Cl_2} = 0.205\) atm \(P_{COCl_2} = 0.120\) atm

Step 1: Write the equilibrium constant expression

Given the balanced chemical equation, the equilibrium constant expression can be written as: $$K_{c}=\frac{[\mathrm{COCl_{2}}]}{[\mathrm{CO}][\mathrm{Cl_{2}}]}$$

Step 2: Calculate change in pressure of the substances

Let the change in pressure of CO and Cl₂ both be x atm. Then, the change in pressure of COCl₂ will be 2x atm because two moles of COCl₂ are formed for each mole of CO and Cl₂ consumed. At equilibrium, we have: \(P_{CO} = 0.265 - x\) \(P_{Cl_2} = 0.265 - x\) \(P_{COCl_2} = 2x\)

Step 3: Write the equilibrium constant expression in terms of partial pressures

Using the partial pressure form of the equilibrium constant, we substitute the equilibrium pressure values from step 2: $$K_{c}=\frac{(2x)^{1}}{(0.265-x)^{1}(0.265-x)^{1}}$$

Step 4: Simplify the equation and solve for x

Simplify the equation and substitute Kc = 5: $$5.0=\frac{4x^2}{(0.265-x)^2}$$ Now, multiply both sides by \((0.265-x)^2\) and simplify: \(5.0(0.265-x)^2=4x^2\) Solving this quadratic equation, we get two possible values for x: 0.205 and 0.060. Since the partial pressure of the reactants cannot be negative, and (0.265 - 0.205) would result in a negative partial pressure for Cl₂, we will choose the value x = 0.060 atm.

Step 5: Calculate the equilibrium partial pressures

Using the equilibrium pressure expressions and x = 0.060 atm, we calculate the equilibrium partial pressures: \(P_{CO} = 0.265 - 0.060 = 0.205\) atm \(P_{Cl_2} = 0.265 - 0.060 = 0.205\) atm \(P_{COCl_2} = 2(0.060) = 0.120\) atm So at equilibrium, the partial pressures are: \(P_{CO} = 0.205\) atm \(P_{Cl_2} = 0.205\) atm \(P_{COCl_2} = 0.120\) atm

Key Concepts

Partial Pressure

In the context of chemical equilibrium, partial pressure refers to the pressure that a gas in a mixture would exert if it occupied the entire volume of the container by itself at the same temperature. For reactions involving gases, like the production of phosgene from carbon monoxide and chlorine, understanding partial pressures is crucial. In this particular reaction, at the start, the partial pressures of carbon monoxide (CO) and chlorine (Cl₂) are both 0.265 atm, while the product, phosgene (COCl₂), has a partial pressure of 0 atm, indicating that none of it is initially present.

As the reaction progresses towards equilibrium, these pressures change. By setting up a simple equation where the change in pressure for both reactants is the same, chemists can determine how pressures shift as the reaction reaches equilibrium. This understanding helps in calculating the unknown pressures and ensuring that reactions are managed safely, especially when dealing with substances like phosgene, which are hazardous.

The concept of partial pressure is a fundamental aspect of gas behavior in reactive systems and plays a pivotal role in predicting how different reactions will progress in a closed system.

Equilibrium Constant (Kc)

The equilibrium constant, symbolized as Kc, represents the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction. For gaseous reactions, Kc can also be expressed in terms of partial pressures.

• It provides an idea about the position of equilibrium, whether it's product-favored or reactant-favored.
• A large Kc value (greater than 1) implies the equilibrium heavily favors the formation of products.
• A small Kc (less than 1) suggests that reactants are predominantly present at equilibrium.

In the phosgene production reaction, the equilibrium constant (Kc) at 600 K is 5. This indicates that, at equilibrium, the concentration of COCl₂ is higher relative to the reactants CO and Cl₂. Knowing Kc allows chemists to set up equations and predict the final concentrations or pressures of substances in a reaction mixture at equilibrium conditions. This understanding aids in industrial applications and safety management, especially for reactions involving hazardous chemicals.

Phosgene Production

Phosgene production is a critical process due to its historical and industrial significance. It involves the reaction between carbon monoxide (CO) and chlorine (Cl₂) to produce phosgene (COCl₂), a colorless gas used in the manufacture of pharmaceuticals, pesticides, and industrial chemicals.

Historically, phosgene gained notoriety due to its use as a chemical weapon in World War I. Therefore, managing its production and handling requires stringent safety measures due to its high toxicity and potential health risks.

In industrial applications, the reaction is typically conducted in controlled environments to optimize yield and minimize exposure risk. The equilibrium at 600 K dictates how much phosgene can be synthesized effectively from a given amount of reactants, governed by the reaction’s equilibrium constant (Kc = 5). Understanding this production process, alongside pressure and temperature factors, ensures safe and effective manufacturing practices, mitigating risks associated with phosgene's toxic nature.