Write the conversion factor that you would use to convert from moles of \(\mathrm{Cl}_{2}\) to moles of \(\mathrm{NaCl}\) in the reaction: $$ 2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s) $$

Understanding balanced chemical equations is crucial in the study of chemistry. These equations provide a snapshot of a chemical reaction where the number of atoms for each element in the reactants equals the number of atoms in the products. This balancing adheres to the Law of Conservation of Mass which states that mass cannot be created or destroyed in a chemical reaction.

In our example, the equation
\[2 \mathrm{Na}(s) + \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s)\] demonstrates a balanced chemical reaction. The coefficient '2' before sodium (Na) and sodium chloride (NaCl) signifies that two moles of sodium react with one mole of chlorine gas to produce two moles of sodium chloride. If these coefficients were not balanced, it would indicate that the reaction does not align with the Law of Conservation of Mass, which is a fundamental principle in chemistry.

Mole conversion is a pivotal concept in chemistry as it allows for the quantification of substances involved in a chemical reaction. The mole is the unit used to express amounts of a chemical substance, and it is defined by Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities (atoms, molecules, ions, etc.).

The step by step solution provided translates the stoichiometric coefficients into a mole ratio. This ratio is used as a conversion factor that correlates the moles of one substance to the moles of another. In our example, \(2 \text{ moles of NaCl} / 1 \text{ mole of }\text{Cl}_2\) provides this conversion. This tells us that for every mole of chlorine gas used, two moles of sodium chloride are produced. Understanding mole conversion is essential for accurately determining the quantities needed or produced in a given chemical reaction.

A stoichiometric relationship is the heart of quantitative chemistry. It is the link that connects the moles of various substances in a chemical reaction, as defined by the balanced chemical equation. These relationships help to determine how much of each reactant is needed to produce a certain amount of product.

In our example, the stoichiometric relationship is expressed as a ratio derived from the balanced equation: for every 1 mole of \(\mathrm{Cl}_{2}\), 2 moles of \(\mathrm{NaCl}\) are produced. When performing a reaction in the lab, this ratio allows you to predict the amount of sodium chloride that can be obtained from a given amount of chlorine gas. This understanding is essential for the precise calculation and scalability of chemical reactions, which has real-world applications in industries such as pharmaceuticals, manufacturing, and environmental science.