Question

A mixture of 3.00 volumes of \(\mathrm{H}_{2}\) and 1.00 volume of \(\mathrm{N}_{2}\) reacts at \(344^{\circ} \mathrm{C}\) to form ammonia. The equilibrium mixture at 110\. atm contains \(41.49 \% \mathrm{NH}_{3}\) by volume. Calculate \(K_{\mathrm{p}}\) for the reaction, assuming that the gases behave ideally.

Short answer

To find the equilibrium constant (K_{pyou have to categorize the formation process and calculate equilibrium amounts Mat table ratios .}

Step-by-step solution

- Write the balanced equation

The balanced chemical equation for the formation of ammonia is:

- Determine the initial moles of each gas with respect to a reference volume

Using the given volumes of hydrogen and nitrogen, if we assume the reference volume is some value V, then:

Key concepts

chemical equilibrium

In a chemical reaction, equilibrium occurs when the rates of the forward and reverse reactions become equal over time. At this point, the concentrations of reactants and products remain constant. For gas-phase reactions like the formation of ammonia, we express the equilibrium state in terms of partial pressures. This leads us to the equilibrium constant, denoted as \( K_p \) for reactions involving gases. The constant \( K_p \) is defined considering the balanced chemical equation and the principle that equilibrium involves no net change in the concentration of participating species.
Understanding the concept of equilibrium is crucial as it allows us to predict the extent of a reaction under given conditions. For example, by knowing \( K_p \), we can determine how much ammonia (H_3\func) is formed when hydrogen (H_2\func) and nitrogen (N_2\func) react at a specific temperature and pressure.

ideal gas law

The Ideal Gas Law is a fundamental equation that relates the pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. It is expressed as \[ PV = nRT \], where R is the universal gas constant. This equation is vital in calculations concerning chemical equilibrium in gaseous reactions since it allows us to convert between the number of moles and gas volume.
In the context of our problem, by assuming that the gases behave ideally, we can use the Ideal Gas Law to find relationships between the initial amounts of hydrogen and nitrogen and their volumes.
Since the reaction occurs at a constant temperature and given initial volumes, this law helps us establish the conditions under which equilibrium will be attained, ultimately aiding in the calculation of \( K_p \).

stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is based on the balanced chemical equation, which provides the ratios in which substances react and form products.
In the ammonia formation reaction, the balanced equation is:\[ 3H_2 (g) + N_2 (g) \rightleftharpoons 2NH_3 (g) \]
This tells us that three moles of hydrogen gas react with one mole of nitrogen gas to produce two moles of ammonia gas. By understanding these ratios, we can calculate the amounts of each substance consumed or produced at equilibrium.
In our example, we deduce the initial moles of hydrogen and nitrogen based on their given initial volumes. This stoichiometric relationship allows us to determine how much of these gases will remain or convert into ammonia at equilibrium.

ammonia formation reaction

One of the most crucial industrial processes is the Haber process, which involves the formation of ammonia (NH_3\func) from nitrogen (N_2\func) and hydrogen (::mathrm{H}_2\func). The balanced reaction is:\[ 3H_2 (g) + N_2 (g) \rightleftharpoons 2NH_3 (g) \]
This reaction is exothermic, meaning it releases heat. The production of ammonia is influenced by pressure, temperature, and the presence of a catalyst. The given problem involves calculating the equilibrium constant \( K_p \) for this reaction under specified conditions.
We start with initial volumes of H_2\func and N_2\func gases. At equilibrium, we apply the percentage volume of H_3\func provided to find the partial pressures of each gas. Understanding this reaction is vitally important, as ammonia is a key component in fertilizers and other industrial processes.