In chemistry, coefficients can change because they represent “how many” molecules are involved, but subscripts cannot change because they define “what substance” you have at all. Changing subscripts turns one compound into a completely different one, so it no longer represents the same reaction.

Coefficients vs subscripts

  • Coefficients are the big numbers in front of formulas, like the 2 in 2H2O2\text{H}_2\text{O}2H2​O; they tell you how many molecules or formula units are reacting or being produced.
  • Subscripts are the small numbers inside a formula, like the 2 in H2O\text{H}_2\text{O}H2​O; they tell you how many atoms of each element are in a single molecule and therefore define its composition and identity.

Why only coefficients are adjusted

  • When balancing equations, the goal is to obey the law of conservation of mass by making the number of each type of atom the same on both sides without changing what substances are present; coefficients let you scale how many particles you have while keeping each substance the same.
  • If subscripts were changed to balance an equation, water H2O\text{H}_2\text{O}H2​O could become H2O2\text{H}_2\text{O}_2H2​O2​, which is hydrogen peroxide, a completely different substance with different properties, so the original reaction would no longer be described.

A quick analogy

  • Subscripts are like the ingredient ratios in a recipe (e.g., 2 cups flour to 1 cup sugar); changing them creates a different dish altogether, not just more or less of the same dessert.
  • Coefficients are like doubling or tripling the entire recipe; you get more of the same dish, which is exactly what is needed to “balance” how much reacts and how much is produced.

What really changes in a reaction

  • In a properly written chemical equation, the formulas (and thus subscripts) are fixed to represent the actual substances that react and form, while coefficients are adjusted until each element has the same total atom count on both sides.
  • So chemists only adjust coefficients and not subscripts because balancing is about matching atom counts for the same chemicals, not inventing new chemicals by rewriting their formulas.

TL;DR: Subscripts are part of the chemical’s identity, so changing them changes the substance; coefficients just change how many units you have, which is exactly what balancing equations is supposed to do.

Information gathered from public forums or data available on the internet and portrayed here.