Exercises: Le Chatelier's principle

In the industrial synthesis of ammonia, $\text{N}_2 + 3\ \text{H}_2 \rightleftharpoons 2\ \text{NH}_3$, predict using Le Chatelier's principle what effect increasing the pressure in the reactor has on the ammonia yield. Justify your answer by counting the moles of gas on each side of the equation.

In the Cacahuamilpa caverns (Guerrero), stalactites grow thanks to a natural equilibrium: water dissolves the calcium carbonate in the rock in the presence of $\text{CO}_2$, $\text{CaCO}_3 + \text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{Ca}(\text{HCO}_3)_2$, and when the drop reaches the inside of the cavern some of the $\text{CO}_2$ escapes into the air. Explain, using Le Chatelier's principle, why the escape of $\text{CO}_2$ causes solid $\text{CaCO}_3$ to be deposited (the stalactite).

Nitrogen dioxide, which is brown, is in equilibrium with dinitrogen tetroxide, which is colorless: $2\ \text{NO}_2 \rightleftharpoons \text{N}_2\text{O}_4$, with $\Delta H < 0$ (exothermic). A sealed tube containing this mixture is placed first in hot water and then in crushed ice. Predict in which bath the gas turns darker and in which it turns paler, and justify your answer with Le Chatelier's principle, treating heat as one more participant in the reaction.