Chemical formulas and equations are a precise language used by chemists to describe matter and its transformations. These symbolic representations use letters for elements and numbers to convey quantitative information. A large number often appears directly in front of a chemical formula, and its meaning is fundamental to understanding the entire equation.
Defining the Big Number
The large number placed directly before a chemical formula is called a coefficient. It indicates the quantity of the entire chemical substance being considered, representing how many individual molecules or formula units are involved. For instance, in \(2\text{H}_2\text{O}\), the coefficient two means there are two separate molecules of water. The coefficient can also represent the number of moles of a substance, a standard unit used to measure large quantities. If no number is written, a coefficient of one is implied. The coefficient applies to every atom contained within the formula that immediately follows it.
How Coefficients Differ from Subscripts
A common point of confusion is the difference between the coefficient and the subscript. Coefficients are the large numbers positioned in front of the formula, affecting the entire compound. Subscripts are the small, lowered numbers written within the formula, such as the ‘2’ in \(\text{H}_2\text{O}\).
The subscript specifies the composition of the molecule, indicating how many atoms of a particular element are bonded together to form one unit. For example, the subscript ‘2’ in water shows that one molecule contains two hydrogen atoms bonded to one oxygen atom. Changing a coefficient only alters the amount of the substance, similar to multiplying a recipe. If the subscript is changed, the identity of the substance changes completely. Changing \(\text{H}_2\text{O}\) to \(\text{H}_2\text{O}_2\) transforms water into hydrogen peroxide, a different compound. Coefficients can be adjusted when manipulating an equation, but subscripts must remain constant to preserve the chemical integrity of the substance.
Using Coefficients to Balance Equations
The primary application of coefficients is to satisfy the Law of Conservation of Mass when writing chemical equations. This fundamental law states that matter cannot be created or destroyed during a chemical reaction, meaning the total mass of the reactants must equal the total mass of the products. Consequently, the number of atoms for each element must be identical on both sides of the reaction arrow. A chemical equation that does not yet adhere to this law is considered unbalanced. To balance the equation, chemists systematically adjust the coefficients in front of the reactants and products until the atom count for every element is equal. This process ensures that the equation accurately reflects the transformation.
Consider the formation of water from hydrogen gas (\(\text{H}_2\)) and oxygen gas (\(\text{O}_2\)), which initially appears as \(\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}\). On the reactant side, there are two oxygen atoms, but the product side only shows one, violating the conservation of mass. To fix this, a coefficient of two is placed in front of the water molecule, resulting in \(\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}\). This new coefficient of two means there are now two oxygen atoms and four hydrogen atoms on the product side. To balance the hydrogen, a coefficient of two is then placed in front of the hydrogen gas reactant, yielding the final balanced equation: \(2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}\). The coefficients provide the correct stoichiometric ratio, representing the relative number of molecules that must combine and form.