Question

When steam is passed over iron filings, solid iron(III) oxide and gaseous hydrogen are produced in a reversible reaction. Write the balanced chemical equation and the equilibrium constant expression for the reaction, which yields iron(III) oxide and hydrogen gas.

Short answer

The balanced chemical equation for the given reversible reaction is: \(2Fe(s) + 3H_2O(g) \rightleftharpoons Fe_2O_3(s) + 3H_2(g)\). The equilibrium constant expression (Kc) for this reaction is \(K_c = \frac{[H_2]^3}{[H_2O]^3}\).

Step-by-step solution

Identify reactants and products

In the reversible reaction, we have the following reactants and products: Reactants: Steam (water in gaseous form) and Iron filings Products: Iron(III) oxide (solid) and Hydrogen gas

Write the balanced chemical equation

To write a balanced chemical equation, we need to place coefficients in front of each compound so that the number of atoms of each element is equal on both sides of the equation. Unbalanced equation: \(Fe + H_2O \rightleftharpoons Fe_2O_3 + H_2\) Balancing the equation: To balance the equation, we will first balance the iron atoms. We will need two iron atoms on the left side, so we will place a coefficient of 2 in front of the iron. \(2Fe + H_2O \rightleftharpoons Fe_2O_3 + H_2\) Now, let's balance the oxygen atoms. Since there are 3 oxygen atoms in iron(III) oxide, we need 3 water molecules on the left side to match them. So, we will place a coefficient of 3 in front of the water molecule: \(2Fe + 3H_2O \rightleftharpoons Fe_2O_3 + H_2\) Now, we need to balance the hydrogen atoms. We have 6 hydrogen atoms on the left side of the reaction (3 water molecules with two hydrogen atoms each). So, we need 3 hydrogen gas molecules (3 molecules with 2 hydrogen atoms each) on the right side of the reaction. We will place a coefficient of 3 in front of the hydrogen gas: \(2Fe + 3H_2O \rightleftharpoons Fe_2O_3 + 3H_2\) Now, the balanced chemical equation is: \(2Fe(s) + 3H_2O(g) \rightleftharpoons Fe_2O_3(s) + 3H_2(g)\)

Find the equilibrium constant expression

To find the equilibrium constant expression (Kc), we write an expression that involves the concentration of products divided by the concentration of reactants, all raised to the power of their coefficients in the balanced equation. In the equilibrium constant expression, we will only consider the gaseous species because the concentrations of solids remain constant. The equilibrium constant expression is as follows: \(K_c = \frac{[H_2]^3}{[H_2O]^3}\) In this case, the concentration of iron and iron(III) oxide are not included in the expression, since they are in solid form and have constant concentrations.

Key concepts

Balancing Chemical Equations

Balancing chemical equations is essential for accurately representing chemical reactions. It involves ensuring that the number of each type of atom is the same on both sides of the equation. To achieve this, we adjust the coefficients before each substance in the equation. Let's take the reaction between iron filings and steam as an example. Initially, we wrote the equation as \[ Fe + H_2O \rightleftharpoons Fe_2O_3 + H_2 \]. This equation is not balanced because different numbers of iron, hydrogen, and oxygen atoms appear on both sides. To balance it, we adjust the coefficients: - First, balance the iron atoms by placing a '2' in front of Fe: \[ 2Fe + H_2O \rightleftharpoons Fe_2O_3 + H_2 \].- Next, balance the oxygen atoms by placing a '3' in front of \( H_2O \): \[ 2Fe + 3H_2O \rightleftharpoons Fe_2O_3 + H_2 \].- Finally, balance the hydrogen atoms by adding a '3' in front of \( H_2 \): \[ 2Fe + 3H_2O \rightleftharpoons Fe_2O_3 + 3H_2 \].Now the equation is balanced, ensuring the conservation of mass. Each element has the same number of atoms on both sides.

Equilibrium Constant Expression

The equilibrium constant expression, denoted as \( K_c \), is central to understanding reversible chemical reactions. It quantitatively describes the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their respective coefficients. For the balanced reaction between iron filings and steam, represented as: \[ 2Fe(s) + 3H_2O(g) \rightleftharpoons Fe_2O_3(s) + 3H_2(g) \],we only include gases in the expression because solids' concentrations are constant and do not change during the reaction. Hence, the equilibrium constant expression is:\[ K_c = \frac{[H_2]^3}{[H_2O]^3} \].This expression indicates how the concentration of hydrogen gas cubes over the concentration of water vapor cubes. A larger \( K_c \) implies a reaction that favors products, while a smaller \( K_c \) suggests reactants are favored. By using these calculations, chemists can predict the extent of a reaction and its behavior under different conditions.

Reversible Reactions

Reversible reactions are fundamental in chemical equilibrium, marking processes where reactions proceed in both forward and reverse directions. This means that products can react to form the original reactants, leading to an equilibrium state. In our example of steam reacting with iron filings: \[ 2Fe(s) + 3H_2O(g) \rightleftharpoons Fe_2O_3(s) + 3H_2(g) \],this equilibrium is dynamic. At this point, the rate of the forward reaction (moving towards products) equals the rate of the reverse reaction (forming reactants). Understanding reversible reactions helps in:

• Predicting whether the reaction mixture tends towards product or reactant dominance (through \( K_c \)).
• Manipulating reaction conditions to favor desired products by changing concentration, temperature, and pressure.

Reversible reactions are crucial in industrial applications and biological systems, where balance and efficiency are imperative. Chemists aim to exploit this reversibility to optimize outcomes in chemical processes.