Methanol, \(\mathrm{CH}_{3} \mathrm{OH},\) is produced industrially by the following reaction: $$\mathrm{CO}(g)+2 \mathbf{H}_{2}(g) \stackrel{\text { copper catalyst } 300^{\circ} \mathrm{C}, 300 \mathrm{atm}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}(g)$$ Assuming that the gases behave as ideal gases, find the ratio of the total volume of the reactants to the final volume.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships among reactants and products in a chemical reaction. It is anchored in the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, the amount of each element must be the same in both the reactants and the products.

To fully grasp stoichiometry, we must understand the concept of the 'mole', which is a unit that measures the amount of substance. The mole concept allows chemists to count particles (such as atoms and molecules) in terms of mass. When we balance a chemical equation, we ensure that the number of atoms for each element is the same on both sides, which implies that the moles of those elements are also balanced.

By using stoichiometry in the given exercise, we compare the moles of reactants (CO and H2) to the moles of the product (CH3OH). With a balanced chemical equation at hand, we can state that 1 mole of CO reacts with 2 moles of H2 to produce 1 mole of CH3OH. By establishing the mole ratio, we create the foundation for predicting how much reactants are needed to produce a certain amount of product, or vice versa.

A chemical reaction involves the transformation of one or more substances into new substances. The reaction described in the exercise is a synthesis reaction, where carbon monoxide (CO) and hydrogen gas (H2) react to form methanol (CH3OH), a chemical used extensively in industry.

Chemical reactions are typically accompanied by energy changes, visible as light, heat, or electrical energy. The conditions under which a reaction occurs, such as temperature and pressure, often play critical roles in the rate and outcome of the reaction. In this exercise, the presence of a copper catalyst and the specific temperature and pressure conditions (300°C, 300 atm) facilitate the production of methanol.

The balanced chemical equation represents the qualitative and quantitative aspects of the reaction. Qualitatively, it tells us the nature of reactants and products, and quantitatively, it indicates how much of each substance is involved, based on the stoichiometry. In this instance, the reactants and products are all gases, which prompts the use of the ideal gas law to relate their volumes.

The mole concept is a fundamental principle in chemistry that provides a bridge between the microscopic world of atoms and molecules and the macroscopic world that we can observe. One mole is defined as the amount of a substance that contains as many particles, be they atoms, molecules, ions, or others, as there are atoms in 12 grams of carbon-12. This number, Avogadro's number, is approximately 6.022 x 10^23 particles.

In practical terms, the mole allows chemists to work with amounts of substances in a way that can be physically measured. Through the mole concept, you can calculate the mass of a substance needed to obtain a certain number of moles, which is essential for preparing chemical reactions or analyzing reaction yields. In the exercise provided, 1 mole of CO reacted with 2 moles of H2 to produce 1 mole of CH3OH. Each mole represents the same number of molecules of each substance, highlighting the importance of the mole concept in quantifying the substances used in chemical reactions.

Because the exercise assumes ideal gas behavior, and given the equality in conditions before and after the reaction, the mole concept allows us to directly relate the volume of a gas to the number of moles. Hence, the volume ratio of the reactants to the products is established by the stoichiometric mole ratio directly derived from the balanced chemical equation.