Why must a balanced chemical equation be used when determining \(K_{e q} ?\)

When learning about chemical reactions, one of the fundamental concepts is the balanced chemical equation. It represents a reaction where the number of atoms of each element is conserved across reactants and products, complying with the law of conservation of mass. Consider the reaction where hydrogen gas combines with oxygen to form water:

\[\begin{equation}2H_2 + O_2 \rightarrow 2H_2O\text{,}\end{equation}\]

In this balanced equation, there are four hydrogen atoms and two oxygen atoms on each side of the arrow. Balancing chemical equations ensures that all atoms present before the reaction are accounted for afterward, which is crucial not only for experimental chemistry but also for understanding concepts like the equilibrium constant (\(K_{eq}\)). By maintaining a balance, chemists can quantify and predict the outcomes of reactions.

The law of conservation of mass is a cornerstone of chemical science, stating that in a closed system not subjected to any external exchange of matter, the mass of the system remains constant over time. This implies that during a chemical reaction, the mass of reactants must equal the mass of products. If you start with a gram of substance A and it reacts to form a gram of substance B, nothing is lost or gained in the transformation; it is merely rearranged. This law underpins the need for balanced chemical equations, ensuring that stoichiometry calculates precisely how much of each reactant is needed and how much product will be formed. It affirms the principle that matter is neither created nor destroyed during a chemical reaction, a concept first established by Antoine Lavoisier in the 18th century.

Stoichiometry is the aspect of chemistry that pertains to the quantitative relationships between the substances involved in a chemical reaction. Derived from the Greek words \(\text{'stoicheion'}\) (element) and \(\text{'metron'}\) (measure), stoichiometry allows chemists to calculate the amounts of reactants needed and products formed in a chemical reaction. These calculations are based on the balanced chemical equation, where the coefficients represent the mole ratio of the substances. For instance, in the synthesis of ammonia:

\[\begin{equation}N_2 + 3H_2 \rightarrow 2NH_3\text{,}\end{equation}\]

stoichiometry tells us that one mole of nitrogen gas reacts with three moles of hydrogen gas to produce two moles of ammonia. Without a correctly balanced equation, stoichiometry would not provide accurate or meaningful data, thereby affecting our understanding of reaction processes and yields.