If a mixture of 3 moles of \(\mathrm{H}_{2}\) and one mole of \(\mathrm{N}_{2}\) is completely converted into \(\mathrm{NH}_{3}\). What would be the ratio of the initial and final volume at same temperature and pressure?

Balancing chemical equations is fundamental in understanding chemical reactions. It is crucial because the Law of Conservation of Mass dictates that mass is neither created nor destroyed in an isolated system. Consequently, we must have the same number of each type of atom on both sides of the equation.

In the synthesis of ammonia, the balanced equation \[3\mathrm{H}_{2} + \mathrm{N}_{2} \rightarrow 2\mathrm{NH}_{3}\] shows a stoichiometrically correct reaction, where the hydrogen and nitrogen atoms are conserved. Balancing involves making sure that the number of atoms for each element is equal on both sides. In this example, we start with six hydrogen atoms and two nitrogen atoms, resulting in two NH3 molecules, which also contain six hydrogen atoms and two nitrogen atoms in total.

Stoichiometry lies at the heart of chemical reactions, allowing us to calculate relative quantities of reactants and products. Using the balanced equation and the mole concept, stoichiometry enables us to understand the ratios in which chemicals combine and react.

For instance, the ammonia synthesis reaction requires a specific ratio of hydrogen to nitrogen. Our balanced equation shows that for every one mole of nitrogen, we need three moles of hydrogen to make two moles of ammonia. This 1:3 ratio is essential for stoichiometric calculations and helps identify how much reactant is required and how much product can be yielded from a reaction.

Avogadro's Law plays a central role in understanding gas volume ratios in chemical reactions. It tells us that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. Hence, the volume of gas is proportional to the number of moles of that gas under these conditions.

In applying this law to our exercise, we observe that the initial volume of gas (from 3 moles of H2 and 1 mole of N2) is twice as much as the final volume of gas (2 moles of NH3), given that the temperature and pressure remain constant. This demonstrates that the volumes of gases are directly related to their molar amounts, a fact that can greatly simplify calculations involving gaseous reactants or products in chemical reactions.

The mole concept is a fundamental bridge between the atomic scale and the macroscopic world. It provides a means to quantify amounts of substances based on the number of particles. One mole of any substance contains Avogadro's number of particles, approximately \(6.022 \times 10^{23}\) entities.

In the context of our ammonia production exercise, we equate moles of substance with Avogadro's concept to find out that the number of moles initially present is the sum of the moles of hydrogen and nitrogen. This enables us to calculate not just the amounts of substances in moles but also to relate those amounts to observable quantities like volume in the case of gases.