What is Chemical system, initial and final states?

Example 27.2 (Methane burning in a closed vessel)

A closed vessel contains $2.0\,\mathrm{mol}$ of methane and $3.0\,\mathrm{mol}$ of dioxygen; a spark sets off the combustion $\ce{CH4 + 2O2 -> CO2 + 2H2O}$. In the initial state the system holds $2.0\,\mathrm{mol}$ of $\ce{CH4(g)}$, $3.0\,\mathrm{mol}$ of $\ce{O2(g)}$ and no products. What is in the final state? The rest of the chapter answers.

Example 27.7 (Back to the methane)

Methane would run out at $x = 2.0/1 = 2.0\,\mathrm{mol}$, dioxygen at $x = 3.0/2 = 1.5\,\mathrm{mol}$. The smaller is $1.5\,\mathrm{mol}$: dioxygen is the limiting reactant and $x_{\max} = 1.5\,\mathrm{mol}$. The final state holds $0.5\,\mathrm{mol}$ of methane left over, no dioxygen, $1.5\,\mathrm{mol}$ of carbon dioxide and $3.0\,\mathrm{mol}$ of water.