Problem 3 - Chemistry Matter and Change

Question

Write equilibrium constant expressions for these heterogeneous equilibria. a. \(C_{10} \mathrm{H}_{8}(\mathrm{s}) \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{8}(\mathrm{g})\) b. \(\mathrm{H}_{2} \mathrm{O}(1) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) c. \(\mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\) d. \(\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})\) e. \(\mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\)

Step-by-Step Solution

Answer

The equilibrium constant expressions for the given heterogeneous equilibria are: a. \( K_p = [\mathrm{C}_{10}\mathrm{H}_{8}(\mathrm{g})] \) b. \( K_p = [\mathrm{H}_{2}\mathrm{O}(\mathrm{g})] \) c. \( K_p = [\mathrm{CO}_{2}(\mathrm{g})] \) d. \( K_p = \frac{[\mathrm{CO}(\mathrm{g})][\mathrm{H}_{2}(\mathrm{g})]}{[\mathrm{H}_{2}\mathrm{O}(\mathrm{g})]} \) e. \( K_p = \frac{[\mathrm{CO}_{2}(\mathrm{g})]}{[\mathrm{CO}(\mathrm{g})]} \)

Step 1: Identify the gases in the equilibrium

C10H8 (g) is the only gas participating in the equilibrium process. So we only have this component in the equilibrium constant expression.

Step 2: Write the equilibrium constant expression

The equilibrium constant expression for the given reaction is: \[ K_p = [\mathrm{C}_{10}\mathrm{H}_{8}(\mathrm{g})] \] b. H2O(l) ⇌ H2O(g)

Step 1: Identify the gases in the equilibrium

H2O (g) is the only gas participating in the equilibrium process. So we only have this component in the equilibrium constant expression.

Step 2: Write the equilibrium constant expression

The equilibrium constant expression for the given reaction is: \[ K_p = [\mathrm{H}_{2}\mathrm{O}(\mathrm{g})] \] c. CaCO3(s) ⇌ CaO(s) + CO2(g)

Step 1: Identify the gases in the equilibrium

CO2 (g) is the only gas participating in the equilibrium process. So we only have this component in the equilibrium constant expression.

Step 2: Write the equilibrium constant expression

The equilibrium constant expression for the given reaction is: \[ K_p = [\mathrm{CO}_{2}(\mathrm{g})] \] d. C(s) + H2O(g) ⇌ CO(g) + H2(g)

Step 1: Identify the gases in the equilibrium

In this reaction H2O, CO, and H2 are gases participating in the equilibrium process.

Step 2: Write the equilibrium constant expression

The equilibrium constant expression for the given reaction is: \[ K_p = \frac{[\mathrm{CO}(\mathrm{g})][\mathrm{H}_{2}(\mathrm{g})]}{[\mathrm{H}_{2}\mathrm{O}(\mathrm{g})]} \] e. FeO(s) + CO(g) ⇌ Fe(s) + CO2(g)

Step 1: Identify the gases in the equilibrium

In this reaction, CO and CO2 are gases participating in the equilibrium process.

Step 2: Write the equilibrium constant expression

The equilibrium constant expression for the given reaction is: \[ K_p = \frac{[\mathrm{CO}_{2}(\mathrm{g})]}{[\mathrm{CO}(\mathrm{g})]} \]

Key Concepts

Heterogeneous Equilibria

When you come across a chemical reaction where the reactants and products are in different phases, such as solid, liquid, and gas, you are dealing with a heterogeneous equilibrium. These kinds of equilibria can seem a bit confusing at first, but they're based on a fundamental principle: in a chemical equation, you only include the concentrations of gaseous substances and substances in solution in the equilibrium expression.

For instance, in the reaction of aphthalene sublimating, which is the process of turning from a solid directly into a gas, the solid phase isn't included in the equilibrium expression. So, the equilibrium constant for naphthalene sublimating (C_{10}H_{8}(s) rightleftharpoons C_{10}H_{8}(g)) is simply K_p = [C_{10}H_{8}(g)]. This expression indicates that although the solid naphthalene is essential for the equilibrium, its concentration remains constant throughout the process and thus is not included in the expression.

Chemical Equilibrium

In chemistry, a chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain unchanged over time, leading to a state of dynamic balance, not static. It's important to understand that reactions at equilibrium haven't stopped; they're still occurring, but changes are not observable at the macroscopic level.

When writing equilibrium constant expressions, remember to include concentrations for aqueous solutions and partial pressures for gases. Solids and pure liquids don't appear in the equations because their concentrations are essentially constant. For the dehydration of water, for example, only the water in the gas phase is included in the expression K_p = [H_{2}O(g)], which indicates how the position of equilibrium is dependent on the vapor pressure of water in the gas phase alone.

Le Chatelier’s Principle

Understanding how a system at equilibrium responds to changes is critical and that’s where Le Chatelier’s principle comes into play. It predicts that if a stress, such as a change in concentration, pressure, or temperature, is applied to a system at equilibrium, the equilibrium will shift to counteract that stress and re-establish equilibrium.

For instance, if you increase the concentration of CO(g) in the reaction involving iron(III) oxide and carbon monoxide, FeO(s) + CO(g) rightleftharpoons Fe(s) + CO_{2}(g), the system will shift towards the right to produce more CO_{2}(g) and Fe(s), trying to reduce the concentration of CO(g) and re-balancing the equilibrium. This principle is not only fascinating but is also very useful in industrial chemical processes where maximum yield is desired.