Problem 2 - Chemistry Matter and Change

Question

Challenge Write the chemical equation that has the equilibrium constant expression \(K_{\mathrm{eq}}=\frac{[\mathrm{CO}]^{2}\left[\mathrm{O}_{2}\right]}{\left[\mathrm{CO}_{2}\right]^{2}}\).

Step-by-Step Solution

Answer

2CO₂ ↔ 2CO + O₂

Step 1: Understanding the Equilibrium Constant Expression

Identify the reactants and products based on the equilibrium expression. - The numerator ([CO]²[O₂]) of the expression represents the concentration of products. This implies that the products are CO and O₂. - The denominator ([CO₂]²) represents the concentration of reactants. This indicates that CO₂ is the reactant.

Step 2: Balancing the Chemical Equation

Start with the unbalanced equation based on the equilibrium expression: CO₂ ↔ CO + O₂. To balance the chemical equation, ensure the number of atoms of each element on the reactant side equals the number on the product side.

Step 3: Final Balanced Equation

The balanced chemical equation is achieved by balancing the coefficients: 2CO₂ ↔ 2CO + O₂. This satisfies the requirement of the equilibrium expression, with the concentration of products as CO and O₂, and the concentration of reactants as CO₂, matching the given expression: \[ K_{eq} = \frac{[CO]^2[O_2]}{[CO_2]^2} \]

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_{eq} \), is a value that expresses the ratio of products to reactants at equilibrium for a reversible reaction. It provides insight into the composition of a reaction mixture at equilibrium. Consider the general reversible reaction:\[ aA + bB \rightleftharpoons cC + dD \]The equilibrium constant expression for this reaction is defined in terms of concentrations as:\[ K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]Here, the square brackets \([ ]\) express molar concentrations, and the coefficients \(a, b, c,\) and \(d\) from the balanced chemical equation become the exponents in the equilibrium constant expression.The value of \( K_{eq} \) tells us about the position of equilibrium:

• If \( K_{eq} \) is much greater than 1, the products are favored at equilibrium.
• If \( K_{eq} \) is much less than 1, the reactants are favored.
• If \( K_{eq} \) is around 1, neither reactants nor products are favored.

Knowing \( K_{eq} \) allows chemists to predict the concentrations of different species when the reaction reaches equilibrium, aiding in process design and optimization.

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants transforming into the products. The equation spells out the substances involved, typically using their chemical formulas.An example of a simple chemical equation is: \[ \text{CO}_2 \rightarrow \text{CO} + \text{O}_2 \]This notation signifies a potential reaction where carbon dioxide (\(\text{CO}_2\)) would break down into carbon monoxide (\(\text{CO}\)) and oxygen (\(\text{O}_2\)).The arrow (\(\rightarrow\)) represents the direction of the reaction—from reactants to products. Sometimes, a double arrow (\(\rightleftharpoons\)) is used to indicate that the reaction can proceed in both directions, emphasizing its reversible nature.Chemical equations enable scientists to:

• Visualize the substances involved in a reaction.
• Identify the nature of chemical transformations.
• Predict the outcome of reactions.

Understanding the symbolic language of chemical equations is fundamental to mastering chemistry.

Balancing Chemical Equations

Balancing chemical equations ensures that the Law of Conservation of Mass is respected; that is, matter cannot be created or destroyed. In a balanced equation, the number of each type of atom on the reactant side is equal to the number of each type on the product side. For example, in balancing:\[ \text{CO}_2 \rightarrow \text{CO} + \text{O}_2 \]You notice that on the left side, there are two oxygen atoms and one carbon atom in \(\text{CO}_2\). On the right in \(\text{CO}\) and \(\text{O}_2\), there are three oxygen atoms and one carbon atom. This equation is not balanced.The correctly balanced version would be:\[ 2\text{CO}_2 \rightleftharpoons 2\text{CO} + \text{O}_2 \]Here, the coefficients (the numbers before the compounds) have been adjusted to achieve balance:

• 2 carbon atoms and 4 oxygen atoms on both sides.

Balancing is crucial for correctly determining how much reactant is needed and how much product will be formed, as well as interpreting equilibrium constants accurately.