(a) What is the molar mass of ribose \(\left(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}\right)\) ? (b) What is the mass of \(3.87\) moles of ribose? (c) How many ribose molecules are there in \(3.87\) moles? (d) How many oxygen atoms are there in \(3.87\) moles of ribose? (e) What is the mass in grams of the oxygen atoms in part (d)?

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. In essence, it's the calculation of reactants and products in chemical processes and is fundamental to ensuring reactions are conducted safely, efficiently, and economically.

When dealing with stoichiometry, we need to comprehend the concept of the mole, which is a unit for expressing amounts of a chemical substance. One mole of any substance contains Avogadro's number of particles, be they atoms, molecules, ions, or others. This means that stoichiometry often requires the conversion between moles and mass using the molar mass, as illustrated in the calculation of the mass of ribose given its number of moles.

Molar mass acts as a conversion factor between the mass of a substance and the amount in moles. By multiplying the amount in moles by the molar mass, you can determine the mass of substance present, which is a common stoichiometric calculation in chemistry.

Avogadro's number, denoted as \(6.022 \times 10^{23}\), is a fundamental constant in chemistry representing the number of constituent particles, generally atoms or molecules, that are contained in one mole of a substance. It allows chemists to count particles by weighing them and is essential in converting between atomic scale masses and human-scale masses.

Understanding Avogadro's number is crucial when computing the number of particles in a given sample. For instance, as seen in the ribose example above, multiplying the number of moles by Avogadro's number gives the total number of molecules. Similarly, dividing the total number of atoms by Avogadro's number gives you the number of moles of a substance, facilitating various calculations in stoichiometry, including determining the mass of a specific number of atoms of an element.

The molecular formula provides the exact number of each type of atom in a molecule, which directly impacts the molar mass calculation. For ribose, with the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}\), we see that there are 5 carbon atoms, 10 hydrogen atoms, and 5 oxygen atoms.

Using the molar masses of the individual elements, the molecular formula enables the calculation of the compound's molar mass, which is the sum of the molar masses of all atoms in the formula, in grams per mole. The molecular formula is vital for not only finding out the molar mass but also to understand the proportion of elements within a compound. This ratio is crucial when analyzing chemical reactions and performing stoichiometric calculations, such as determining the number of oxygen atoms in a certain mass of ribose, as demonstrated in the textbook problem.