Question

For each of the questions, four choices have been provided. Select the correct alternative. The equilibrium constant for the given reaction, \(\mathrm{CaCO}_{3(\mathrm{~s})} \mathrm{CaO}_{(\mathrm{s})}+\mathrm{CO}_{2}(\mathrm{~g})\) is given by (a) \(\mathrm{K}_{\mathrm{c}}=\frac{[\mathrm{CaO}] \cdot\left[\mathrm{CO}_{2}\right]}{\left[\mathrm{CaCO}_{3}\right]}\) (b) \(\mathrm{K}_{\mathrm{c}}=\frac{[\mathrm{CaO}]}{\left[\mathrm{CaCO}_{3}\right]}\) (c) \(\mathrm{K}_{\mathrm{c}}=\left[\mathrm{CO}_{2}\right]\) (d) \(\mathrm{K}_{\mathrm{c}}=\frac{[\mathrm{CaO}]}{\left[\mathrm{CO}_{2}\right]}\)

Short answer

Answer: Kc = [CO2]

Step-by-step solution

Review the equilibrium constant formula

The equilibrium constant (Kc) for a chemical reaction is given by the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, with each term raised to the power of its stoichiometric coefficient. We can write this as: Kc = ([products])^p / ([reactants])^r Keep in mind that for solid and liquid substances, their concentration remains constant, and we don't include them in the Kc expression.

Analyze the given reaction

Let's analyze the given chemical reaction: CaCO3(s) -> CaO(s) + CO2(g) Reactant: CaCO3(s) Products: CaO(s) and CO2(g)

Write the Kc expression for the given reaction

Using the equilibrium constant formula and the fact that we don't include solid substances, the Kc expression for the given reaction would be: Kc = ([CO2])^1

Select the correct alternative

Now, we will compare the obtained Kc expression with the given choices: Option (a): Kc = [CaO]·[CO2] / [CaCO3] Option (b): Kc = [CaO] / [CaCO3] Option (c): Kc = [CO2] Option (d): Kc = [CaO] / [CO2] Clearly, our Kc expression matches Option (c), which means the correct alternative is: (c) Kc = [CO2]

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to a balance where the concentrations of reactants and products remain constant over time. Despite this constancy, the reactions are still occurring; however, the rates of the forward and reverse reactions are equal, ensuring no net change in the concentrations of chemical species.

This state can be dynamic, meaning that individual molecules continue to react, but as one substance is formed, another is consumed, keeping the overall system in balance. Chemical equilibrium is applicable in various scenarios, including biological systems and industrial processes, and understanding it is critical for predicting how concentrations will change under different conditions.

Reversibility and Closed Systems

• Reversibility: In an equilibrium, the reactions are reversible, meaning the reactants can produce the products, and the products can reform the reactants.
• Closed System: Equilibrium can only be reached in a closed system, where no new materials are introduced, nor are any products removed.

Equilibrium Constant Expression

The equilibrium constant expression is a way to quantify the position of equilibrium. For a balanced chemical equation, this expression is written in terms of the concentrations of the reactants and products at equilibrium. The general form of the equilibrium constant (often denoted as Kc when dealing with concentrations) is given as the ratio of the products' concentrations raised to their stoichiometric coefficients to the reactants' concentrations raised to their stoichiometric coefficients.

For the reaction: \[ aA + bB \rightleftharpoons cC + dD \], the equilibrium constant expression is: \[ K_c = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b} \]

However, it's important to note that the concentrations of pure solids and liquids are not included in the Kc expression, as their concentrations are effectively constant. Therefore, only the gases and aqueous solutions are typically included in the equilibrium constant expression.

Unitless Nature of Equilibrium Constant

Even though equilibrium concentrations are often measured in mol/L, the equilibrium constant itself is unitless. This is because the concentrations are raised to the power of their stoichiometric coefficients, resulting in the cancellation of units.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves the use of the coefficients from the balanced chemical equations to understand the relative quantities of substances involved. These coefficients indicate not only the proportions in which different substances react but also the ratios in which they are produced.

Stoichiometry is fundamental in determining the equilibrium constant expression, as the concentrations of reactants and products in the equilibrium constant are raised to the power of their respective stoichiometric coefficients. A proper understanding of stoichiometry is essential for students to grasp how to derive the correct Kc expression for a reaction.

Link to Equilibrium

For any chemical reaction at equilibrium, the stoichiometry of the reaction helps to understand the proportionality of reactants to products. This ratio, in turn, provides valuable insights into the reaction mechanism and the conditions required to achieve a desired level of product yield.