Validity of rationale for balancing chemical equations

Question

The reason given for balancing chemical equations is the law of conservation of mass. They say that we balance equations with keeping in mind that atoms of every element included in the reaction must be equal on both sides of equations. And they just add some coefficients for this purpose.

But I apprehend why is the amount of substance not brought under consideration while doing this?

For example when we write,

$$\ce{H2 +O2->H2O}$$

That is; until we don't know how much of $\ce{H2}$ and $\ce{O2}$ was included in the reaction, how can start to balance it? How can we decide that atoms are not equal on both sides? However, the molecular formulas given above are only representing the substances.

Answer 1

When you write the equation

$$\ce{H2 + O2 -> H2O}$$

you are implicitly saying that the stoichiometric coefficient of every substance is $1$. It is like writing the equation $a + b = c$. By not having coefficients in front of $a$, $b$, or $c$, you are implying that $1a + 1b = 1c$ and not $2a + 3b = 4c$ or anything like that.

Obviously that cannot be true for the reaction above because if you react one $\ce{H2}$ molecule and one $\ce{O2}$ molecule, you get one $\ce{H2O}$ molecule and one leftover oxygen atom that doesn't know what to do with itself. The only balanced equation that does not lead to stray atoms is

$$\ce{2H2 + O2 -> 2H2O}$$

or any integer multiple of that, i.e.

$$\ce{$(2n)$H2 + $(n)$O2 -> $(2n)$H2O}$$

Humans prefer to work with small integers or half-integers, so $n$ is usually either chosen to be $1$ or $1/2$.