Suppose you are making ammonia \(\left(\mathrm{NH}_{3}\right)\) by the Haber reaction, at \(472{ }^{\circ} \mathrm{C}\) : \(3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g) K_{\mathrm{eq}}=0.105\) (a) Describe qualitatively where the equilibrium lies for this reaction. (b) On the face of it, would this reaction be a good one for isolating pure ammonia? (c) What would happen if you could keep feeding \(\mathrm{H}_{2}\) and \(\mathrm{N}_{2}\) into the reaction vessel while at the same time removing \(\mathrm{NH}_{3}\) ?

The founding principle that explains the behavior of equilibrium in response to external changes is known as Le Chatelier's principle. This principle is fundamental in understanding various chemical reactions, including industrial processes such as the Haber reaction for ammonia synthesis.

Le Chatelier's principle asserts that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract that change, attempting to re-establish equilibrium. It's almost like the chemical reaction's method of 'pushing back' against external forces to maintain balance.

For instance, if the pressure is increased in a gas reaction, the equilibrium will shift towards the side with fewer gas molecules to reduce the pressure. Likewise, if the temperature is changed, it will favor the endothermic or exothermic direction to absorb or release heat, respectively - in the Haber reaction, increasing temperature shifts the equilibrium towards the reactants due to the exothermic nature of ammonia synthesis.

When we consider removing a product, like ammonia, from the reaction mixture, according to Le Chatelier's principle, the equilibrium will shift to produce more ammonia to replenish what was removed. This can be envisioned as pulling on a spring—the more you pull, the greater the force that springs back upon release.

The equilibrium constant, symbolized as K_eq, is a quantifiable expression that gives us insight into the balance of reactants and products in a chemical equilibrium.

In the context of the Haber reaction, the equilibrium constant is a measure of how much nitrogen (N₂) and hydrogen (H₂) are converted into ammonia (NH₃) at a particular temperature. A low K_eq value, like the 0.105 figure mentioned in the exercise, indicates a reaction favoring the reactants. Conversely, a high K_eq value signifies a product-favored reaction.

The equilibrium constant is rooted in the ratio of the concentrations of the products to reactants, raised to the power of their stoichiometric coefficients. In mathematical terms, for the reaction 3H₂(g) + N₂(g) ⇌ 2NH₃(g), K_eq is calculated as: \[K_{eq} = \frac{[NH_3]^2}{[H_2]^3[N_2]}\] The [] brackets denote concentrations, and exponents reflect the numbers of moles of each substance represented in the balanced equation.

This value allows chemists to determine the extent to which a reaction will proceed under given conditions and thus how much product can be expected from a set amount of reactants.

The synthesis of ammonia is a cornerstone of industrial chemistry, heavily utilized in the production of fertilizers and other important compounds. At the heart of this synthesis is the Haber-Bosch process, which combines nitrogen and hydrogen gases over a catalyst at high temperatures and pressures to produce ammonia.

Ammonia synthesis is an exothermic reaction, meaning it releases heat. It is represented by the balanced equation: \[3H_2(g) + N_2(g) \rightleftarrows 2NH_3(g)\] Despite its simplicity, ammonia's production on an industrial scale relies on a keen understanding of equilibrium and reaction conditions. The Haber reaction equilibrium is dynamic and reversible, and achieving a high yield of ammonia depends on manipulating factors such as temperature, pressure, and the removal of ammonia from the system as it forms.

As suggested in the exercise, to improve the yield of ammonia, one could continuously supply fresh reactants (H₂ and N₂) and remove NH₃ from the reaction environment. This ongoing process takes advantage of Le Chatelier's principle, maximizing the production of ammonia from nitrogen and hydrogen. Such an understanding and application of chemical equilibria and Le Chatelier's principle are crucial to enhance the efficiency and output of ammonia synthesis.