Suppose you have two samples. One contains \(1.5\) moles of methane molecules and one contains \(1.5\) moles of carbon tetrachloride molecules. a) Which sample contains a greater number of molecules? Explain your reasoning. b) Which sample weighs more? Explain your reasoning.

Avogadro's law is a fundamental tenet of chemistry that guides us in understanding the relationship between the volume of a gas and the number of moles it contains under constant temperature and pressure. This law can be articulated simply: equal volumes of any ideal gas, at the same temperature and pressure, contain the same number of particles, typically molecules or atoms. This principle leads to the concept of Avogadro's constant, which quantifies these particles—a staggering number of approximately \(6.022 \times 10^{23}\) entities in one mole.

Take for example our exercise question. When comparing samples each containing \(1.5\) moles of different substances, Avogadro's law tells us that, despite the nature of the molecules, the number of entities within each sample is equal. The difference arises not in the quantity of molecules but in their mass and interaction with other physical concepts, like molecular weight—leading to differences in their overall weight.

Molecular weight, an important concept in chemistry, is the sum of the atomic weights of all atoms in a molecule, and it gives us insight into the mass of a molecular specimen. A mole of any substance, as we know, contains Avogadro's number of entities—be these atoms, molecules or ions. The molecular weight then is the mass of one mole of a compound, expressed in grams and it matches the sum of the atomic masses of the elements present in the substance's molecular formula.

Let’s dissect the molecular weights from the exercise. For methane (CH4) with a molecular formula containing one carbon and four hydrogen atoms, its molecular weight is calculated by adding the atomic weights of carbon (approximately 12) and hydrogen (approximately 1 per atom) to reach about 16 grams/mole. Carbon tetrachloride (CCl4), on the other hand, has a significantly higher molecular weight at 154 grams/mole, reflecting its composition of one carbon and four chlorine atoms—where chlorine has a much higher atomic weight than hydrogen.

Stoichiometry is a branch of chemistry that quantifies the relationship between reactants and products in a chemical reaction. It involves calculations that are founded on the conservation of mass and the mole concept. In practice, stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given chemical reaction.

Improving upon the exercise example, stoichiometry isn't directly applied to simply compare masses, but we do use the stoichiometric coefficients (which are in essence the ratios of moles of one substance to moles of another) to determine the proportions of reactants and products. These coefficients tell us, in a balanced chemical equation, how many moles of each reactant are needed and how many moles of each product will be formed. When we multiply the number of moles by the molecular weight, we find the mass of the compounds involved—thereby using stoichiometry to predict the mass of methane and carbon tetrachloride that can be obtained from given quantities of reactants.