Question

Can the subscripts in a chemical formula be fractions? Explain. Can the coefficients in a balanced chemical equation be fractions? Explain. Changing the subscripts of chemicals can balance the equations mathematically. Why is this unacceptable?

Short answer

In a chemical formula, subscripts must be whole numbers as they represent the number of atoms of each element present in the compound, and atoms are discrete units. Subscripts cannot be fractions. However, in a balanced chemical equation, coefficients can sometimes be fractions, as they indicate the number of molecules or moles needed for the reaction. This represents a ratio, but we often prefer to use whole numbers for simplicity. Changing subscripts to balance a chemical equation is unacceptable because it would alter the identity of the compounds involved, violating the law of conservation of mass. Instead, we adjust the coefficients to balance the equation.

Step-by-step solution

Subscripts as fractions

In a chemical formula, subscripts represent the number of atoms of each element present in the compound. Since atoms are discrete units and cannot be broken down into fractions, it is not possible for subscripts in a chemical formula to be fractions. Each subscript must be a whole number because it represents whole atoms.

Coefficients as fractions

In a balanced chemical equation, coefficients indicate the number of molecules or moles of each compound needed for the reaction to proceed. While it is more common to express coefficients as whole numbers for simplicity, fractions can sometimes be used when balancing equations as long as the coefficients represent a ratio. For example, consider the following unbalanced equation: \[H_2 + O_2 \rightarrow H_2O\] To balance this equation, we can use a fractional coefficient for \(O_2\): \[2H_2 + \frac{1}{2} O_2 \rightarrow 2H_2O\] In this case, the fractional coefficient represents a ratio. However, we often prefer to work with whole numbers and eventually multiply all coefficients by the lowest common multiple to eliminate the fraction: \[2(2H_2 + \frac{1}{2} O_2) \rightarrow 2(2H_2O)\] So, the balanced equation with whole-number coefficients would be: \[4H_2 + 2O_2 \rightarrow 4H_2O\]

Reasons for Unacceptability of Changing Subscripts

Changing the subscripts in a chemical formula to balance the reaction would mean changing the identity of the compounds involved. Since a chemical formula represents a specific compound with a definite composition, altering the subscript would create a new compound with different properties. Balancing a chemical equation is about preserving the law of conservation of mass, so we do not change the actual composition or identity of the compounds in the reaction. That's why we can only adjust the coefficients to balance a chemical equation, as changing the subscripts would violate the basic principles of chemical reactions.

Key concepts

Chemical Formula

A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. It uses the abbreviations of elements from the periodic table. For example, in the chemical formula for water, \(H_2O\), the letters 'H' and 'O' stand for hydrogen and oxygen, respectively. However, it's not just about letters; the numbers, or subscripts, play a key role too.
Subscripts in a chemical formula show how many atoms of each element are present in one molecule of the compound. For example, in \(H_2O\), the subscript '2' after 'H' indicates there are two hydrogen atoms for every one oxygen atom. It is important to use whole numbers because atoms cannot be divided into fractions in this context.
Remember, the composition of a compound is fixed and tinkering with subscripts could alter the compound itself. This is crucial in understanding why changing subscripts to balance an equation is incorrect, as it transforms the compounds involved into entirely different ones.

Coefficients in Chemistry

Coefficients in chemistry are used in balanced chemical equations to indicate the quantity of a substance. These numbers are placed in front of chemical formulas to show how many molecules, moles, or units are involved in the reaction.
The main purpose of using coefficients is to ensure the conservation of mass is maintained, with the same number of atoms for each element on both sides of the equation. While coefficients are typically whole numbers for simplicity, fractional coefficients can sometimes appear in intermediate steps of balancing equations.
Using fractional coefficients helps to express the stoichiometric ratios, notably when dealing with complex chemical equations. However, it's a common practice to convert these fractions into whole numbers by multiplying all coefficients by the smallest common multiple, as it makes interpreting the equation easier and keeps it consistent with the physical nature of the reactants and products.

Subscripts in Chemistry

Subscripts are small numbers written slightly below and to the right of an element symbol in a chemical formula. They indicate the number of atoms of that element in the molecule. For instance, the subscript '2' in \(H_2O\) reveals that there are two hydrogen atoms in each water molecule.
Subscripts are fixed values within formulas because they define the specific chemical entity. Changing a subscript changes the entire compound and its properties.
It's crucial to distinguish that while coefficients can adjust to balance equations, subscripts cannot be altered. Adjusting subscripts might mathematically balance the equation, but it does so at the expense of chemical fidelity. Thus, coefficients, not subscripts, are adjusted to balance chemical reactions, ensuring the integrity of the substance involved.

Conservation of Mass

The principle of conservation of mass is a fundamental concept in chemistry that states that mass is neither created nor destroyed in a chemical reaction. It is the underlying rationale for balancing chemical equations. In any given chemical reaction, the mass of the reactants equals the mass of the products.
When balancing an equation, you use coefficients to make sure the same number of each type of atom appears on both sides of the equation. This reflects the physical reality that atoms are simply rearranged during reactions, not destroyed or created.
This principle imposes constraints on how chemical equations are balanced. Subscripts must remain constant, reflecting the precise makeup of substances, while coefficients can be adjusted to reflect the necessary quantities of each substance to satisfy the conservation of mass. By doing so, the chemical equation remains both balanced and representative of the real-world processes it describes.