Predict the effect of decreasing the container volume on the amounts of each reactant and product in the following reactions: (a) \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Chemical equilibrium is the state in a reversible reaction where the rates of the forward and backward reactions are equal. At this point, the concentrations of reactants and products remain constant over time. This does not mean that the reactants and products are in equal concentrations, but rather that their concentrations no longer change because the process is balanced.

Equilibrium can be affected by several factors including concentration, temperature, and pressure. Understanding these factors can help predict how a change will shift the equilibrium to favor either the reactants or the products.

Le Chatelier's Principle helps to predict how a change in conditions will affect the position of equilibrium in a reversible reaction. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

For example, when the volume of a gas container is decreased, the pressure inside increases. According to Le Chatelier’s Principle, the equilibrium will shift towards the side with fewer gas moles to reduce this increase in pressure. This concept is crucial for reactions involving gases, where pressure changes can significantly impact the equilibrium position.

Mole counting is an essential part of understanding chemical reactions, especially when predicting how equilibrium will shift. It involves adding up the number of moles of reactants and products in their gaseous states.

In reaction (a), \( C_{3}H_{8}(g) + 5O_{2}(g) \rightleftharpoons 3CO_{2}(g) + 4H_{2}O(l) \), we find that the left side has 1 + 5 = 6 moles of gas, while the right side has 3 moles of gas (note that liquid water does not count towards gas moles). The equilibrium will shift towards the side with fewer gas moles when the volume decreases.

In reaction (b), \( 4NH_{3}(g) + 3O_{2}(g) \rightleftharpoons 2N_{2}(g) + 6H_{2}O(g) \), we count 4 + 3 = 7 moles of gas on the reactants side and 2 + 6 = 8 moles of gas on the products side. Thus, decreasing the volume will shift the equilibrium towards the reactants.

Gas laws describe how gases behave under different conditions of pressure, volume, and temperature. The Ideal Gas Law, \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is number of moles, \( R \) is the gas constant, and \( T \) is temperature, is particularly useful.

When considering chemical equilibria of gases, changes in volume and pressure are critically important. For instance, decreasing the volume of a container holding a gas increases its pressure. According to Le Chatelier's Principle, the system will try to counteract this increase in pressure, often by shifting the equilibrium towards the side with fewer gas moles. Understanding these gas laws allows for better prediction and control of chemical reactions in various industrial and laboratory settings.