Question

One of the two most important uses of ammonia is as a reagent in the first step of the Osfwald process, a synthetic route for the production of nitric acid. This first step proceeds according to the equation $$ 4 \mathrm{NH}_{3}(\mathrm{~g})+50_{2}(\mathrm{~g}) \rightleftarrows 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ What is the expression for the equilibrium constant of this reaction?

Short answer

The expression for the equilibrium constant of this reaction is: \[ K = \frac{\text{[NO]}^4 \text{[H}_2 \text{O]}^6}{\text{[NH}_3]^4 \text{[O}_2}^5} \]

Step-by-step solution

Identify the products and reactants

In this reaction, the reactants are Ammonia \(\mathrm{NH}_3\) and Oxygen \(\mathrm{O}_2\), and the products are Nitric Oxide \(\mathrm{NO}\) and Water \(\mathrm{H}_2 \mathrm{O}\).

Understand the general formula for the equilibrium constant

The general equation for the equilibrium constant \(K\) for a reaction, represented as \[ aA + bB \longleftrightarrow cC + dD \]. is given by: \[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] where \([A]\), \([B]\), \([C]\), and \([D]\) represent the molar concentrations of the chemicals at equilibrium, and \(a\), \(b\), \(c\), and \(d\) are their coefficients in the balanced chemical equation.

Apply the formula to the given reaction

Now, applying this general formula to the given reaction gives the equilibrium constant expression: \[ K = \frac{\text{[NO]}^4 \text{[H}_2 \text{O]}^6}{\text{[NH}_3]^4 \text{[O}_2}^5} \] where \(\text{[NH}_3\), \(\text{[O}_2\), \(\text{[NO]}\), and \(\text{[H}_2 \text{O]}\) are the molar concentrations of these gases at equilibrium.

Key concepts

Chemical Equilibrium

In chemistry, chemical equilibrium is the state where the concentrations of reactants and products do not change any further over time, indicating that the rate of the forward reaction equals the rate of the reverse reaction. At equilibrium, the reaction has not necessarily stopped, but occurs in such a way that the concentration of reactants and products remains constant.

To illustrate, in a closed system, when a reaction such as
\(aA + bB \longleftrightarrow cC + dD\)
reaches equilibrium, the ratio of the products and reactants' concentrations raised to the power of their respective coefficients in the balanced equation stays the same. This equilibrium can be disturbed by changing conditions like temperature, pressure, or concentration, a concept known as Le Chatelier's principle. Understanding this principle helps in predicting the direction in which the equilibrium will shift when such changes occur.

Ostwald Process

The Ostwald process is a chemical procedure used to produce nitric acid, which is crucial for fertilizers and explosives. It involves a series of reactions, starting with ammonia which is oxidized to form nitric oxide (NO) and water as shown in the exercise. This process is named after Wilhelm Ostwald, who developed it in the early 1900s.

The process involves multiple steps:

• Oxidation of ammonia.
• Oxidation of nitric oxide into nitrogen dioxide.
• Absorption of nitrogen dioxide in water to form nitric acid.

Understanding the reaction stoichiometry and equilibrium of the initial oxidation step sets the foundation for efficiently producing nitric acid on an industrial scale.

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It relies on the balanced chemical equation to determine the amount of each substance involved. The coefficients in a balanced equation provide the ratio of the moles of reactants consumed to the moles of products formed.

For instance, in the Ostwald process example from the exercise, the balanced chemical equation shows that 4 moles of ammonia react with 5 moles of oxygen to produce 4 moles of nitric oxide and 6 moles of water. These stoichiometric coefficients are essential not only for calculating quantities but also for determining the equilibrium constant expression, which is directly related to the proportions of reactants and products.

Equilibrium Constant Formula

The equilibrium constant formula is a mathematical expression that quantifies the position of equilibrium for a reversible chemical reaction. The formula typically represented as
\(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\)
where
\(K\) is the equilibrium constant,\([A]\), \([B]\), \([C]\), and \([D]\) are the concentrations of the reactants and products at equilibrium, and \(a\), \(b\), \(c\), and \(d\) are the stoichiometric coefficients from the balanced chemical equation.

For gas-phase reactions, partial pressures may be used instead of concentrations. It's important to remember that these constants are only truly constant at a specific temperature. If given the task of solving for the equilibrium constant, like the problem statement provided, the values of equilibrium concentrations or pressures must be provided, or else the task involves only writing down the expression in terms of the reaction's stoichiometry.