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A chemical reaction is a process where substances, known as reactants, transform into different substances called products. This change is caused by the breaking and forming of chemical bonds, resulting in new materials with different properties.

For example, in the reaction where chlorine gas reacts with fluorine gas, the chlorine and fluorine atoms bond differently to form chlorine trifluoride. The atoms in the reactants (Chlorine \textbf{Cl} and Fluorine \textbf{F}) rearrange during the reaction to produce the compound chlorine trifluoride (\textbf{ClF}\(_3\)).

It's critical to remember when observing reactions like this, that during a chemical reaction, matter is not created or destroyed. This is known as the law of conservation of mass, which is the cornerstone for balancing chemical equations.

Stoichiometry is essentially the mathematics behind chemistry. It involves calculations that relate the quantities of reactants and products in a chemical reaction. This concept is pivotal in making sure that equations are balanced in terms of atoms and mass.

In our example, stoichiometry lets us find the appropriate coefficients to ensure that the number of atoms of each element is the same on both sides of the equation. It also helps to determine how much reactant is needed to produce a certain amount of product and vice versa, which is particularly useful in industrial applications and chemistry lab settings.

Importance in Balancing Equations

Without stoichiometry, we couldn't precisely predict the outcomes of reactions, as we wouldn't know the exact quantities to experiment with. It provides a quantitative relationship critical not only for the lab but also for real-world applications like pharmaceuticals, engineering, and environmental science.

A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols and numerical subscripts.

In the provided exercise, the reactant chemicals were chlorine gas (\textbf{Cl}\(_2\)) and fluorine gas (\textbf{F}\(_2\)), and the product was chlorine trifluoride (\textbf{ClF}\(_3\)). The subscripts in the formula represent the number of atoms of each element in the molecule. For example, \textbf{Cl}\(_2\) indicates that there are two atoms of chlorine bonded together.

Understanding chemical formulas is essential when balancing chemical equations because it gives us the information required to ensure that atoms are conserved in a reaction. It's the language that allows chemists to convert from the microscopic world of atoms and molecules to the macroscopic world of grams and liters.