The formula \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) is a source of many conversion factors. (a) Write at least three of them. (b) Suppose you have a sample of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and it contains a total of 72,000 hydrogen atoms. How many carbon atoms does this sample contain? (c) Suppose you have a sample of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and it contains a total of 72,000 hydrogen atoms. What is the mass in grams of the entire sample?

Understanding molar mass is critical in converting between grams and moles of a substance, which can be essential in various chemical calculations. The molar mass is calculated by summing the atomic masses of all the atoms in a molecule.

For instance, let's consider the compound glucose with the chemical formula \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\). Each carbon (C) atom has an atomic mass of approximately 12 g/mol, each hydrogen (H) atom has an atomic mass of about 1 g/mol, and each oxygen (O) atom carries an atomic mass of around 16 g/mol. Thus, the molar mass of glucose is calculated by multiplying the number of each type of atom by its atomic mass and summing the totals: \[\text{Molar Mass of Glucose} = (6 \times 12\,\text{g/mol}) + (12 \times 1\,\text{g/mol}) + (6 \times 16\,\text{g/mol}) = 180\,\text{g/mol}.\]

Knowing the molar mass allows chemists to convert moles to grams and vice versa, facilitating quantitative analysis and reaction predictions. This serves as a foundation for more complex stoichiometric calculations.

The mole ratio is a key concept in stoichiometry that relates the amounts of reactants and products in a chemical reaction. It is derived from the coefficients of a balanced chemical equation or by comparing the number of atoms of each element in a formula.

Take glucose again as an example, where the mole ratio of carbon to hydrogen (\(C:H\)) can be determined directly from its formula; for every 1 mole of carbon, there are 2 moles of hydrogen. Similarly, the ratio of carbon to oxygen (\(C:O\)) is 1:1. These ratios allow us to convert between amounts of different elements or compounds. For instance, if a glucose sample contains 72,000 hydrogen atoms, the mole ratio would indicate that there must be half as many carbon atoms, or 36,000, which directly corresponds to the stoichiometry of the formula.

Atomic mass, expressed in atomic mass units (amu) or grams per mole (g/mol), is the weight of a single atom of an element. It is roughly equivalent to the sum of the numbers of protons and neutrons in the atom's nucleus. In a chemical formula, these individual atomic masses combine to give the total molar mass.

For example, hydrogen has an atomic mass of approximately 1 amu, hence when we calculate the molar mass of glucose, the mass contributed by hydrogen is computed by multiplying this by the number of hydrogen atoms in the molecule. Similarly, carbon's atomic mass is about 12 amu, a crucial factor in summing up the glucose's overall molar mass. Familiarity with the atomic masses of elements enables chemists to perform various calculations regarding molecular compounds and reactions.

A chemical formula represents the types and numbers of atoms in a molecule. It provides a wealth of information, including the types of elements present, their ratios, and the potential for forming conversion factors based on these ratios.

In the case of glucose (\(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\)), the subscripts indicate six carbon atoms, twelve hydrogen atoms, and six oxygen atoms. This data not only allows us to compute the molar mass but to also instantly infer the 1:2 and 1:1 mole ratios of carbon to hydrogen and carbon to oxygen, respectively. The ability to read and interpret chemical formulas is fundamental for predicting physical properties, reactivity, and outcome of chemical reactions.

Stoichiometry is the study of the quantitative relationships or ratios between reactants and products in chemical reactions. It relies on the law of conservation of mass and the concept of moles to ensure balanced chemical equations. The stoichiometry of a reaction indicates the proportions of reactants needed and products formed.

In practice, stoichiometry can predict the amount of reactants necessary to form a desired quantity of product, as demonstrated in the glucose example. If we have 72,000 hydrogen atoms in a glucose sample, stoichiometry helps us calculate both the number of glucose molecules present and the corresponding mass of the sample. By understanding stoichiometric principles, students can better grasp how chemical reactions proceed and are quantified, which is fundamental in many fields, from pharmaceuticals to environmental sciences.