. A certain nut crunch cereal contains 11.0 grams of sugar (sucrose, \(C_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) ) per serving size of 60.0 grams. How many servings of this cereal must be eaten to consume 0.0278 moles of sugar?

Understanding molar mass is fundamental to solving a wide array of chemistry problems, including stoichiometry ones like the one in our exercise. The molar mass represents the mass of one mole of a substance, expressed in grams per mole (g/mol). A mole is a standard unit that measures the quantity of a substance in terms of the amount of particles it contains, speaking very simply, one mole is roughly equal to Avogadro's number, which is approximately 6.022 x 10²³ particles.

To calculate the molar mass of sucrose, or any substance, we sum the atomic masses of all the atoms in one molecule of the substance. These atomic masses can typically be found on the periodic table and are measured in atomic mass units (amu). However, conveniently, the atomic mass in amu is numerically identical to the molar mass in g/mol for that element. For sucrose, which has the chemical formula \(C_{12}H_{22}O_{11}\), add the molar masses of 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms.

Calculating Sucrose's Molar Mass:

The molar mass of carbon is about 12.01 g/mol, hydrogen is about 1.01 g/mol, and oxygen is about 16.00 g/mol. Therefore, for sucrose:

• Carbon: \(12 \times 12.01\ g/mol = 144.12\ g/mol\)
• Hydrogen: \(22 \times 1.01\ g/mol = 22.22\ g/mol\)
• Oxygen: \(11 \times 16.00\ g/mol = 176.00\ g/mol\)

Adding these together gives us the molar mass of sucrose, which is an essential value for many stoichiometry problems.

Stoichiometry problems frequently require conversion between moles and grams. As we've noted, the molar mass connects these two units: it tells us the mass of one mole of a substance. To convert moles to grams, we multiply the number of moles by the molar mass of the substance. Conversely, to convert grams to moles, we divide the mass of the substance by its molar mass.

Let's apply this to our cereal problem. Once we've calculated the molar mass of sucrose, we can tackle the conversion:

• To find moles from grams (given in the problem as 11.0 grams of sucrose per serving), you'd divide by the molar mass of sucrose.
• To determine grams from moles (the overall goal, 0.0278 moles of sugar), you'd multiply by the molar mass of sucrose.

It's important to be comfortable with this flip between moles and grams since it's a core concept in chemistry that enables us to quantify and relate the amounts of reactants and products in a chemical reaction.

The chemical formula of a compound is a representation of the elements that make up that compound and the proportion of each element. For sucrose, its chemical formula is \(C_{12}H_{22}O_{11}\). Understanding this formula is vital, as it directly informs the molar mass calculation.

This formula indicates that each molecule of sucrose consists of 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. Recognizing the chemical formula also assists with visualizing the structure of the molecule and predicting how it will interact with other substances in chemical reactions. In the context of the cereal problem, the chemical formula helps us to understand what sugar (in this case, sucrose) is at a molecular level and why its molar mass is calculated as it is. Knowing the formula enables us not just to calculate molar mass, but also to infer properties and behaviors of the molecule in various chemical scenarios, such as energy content, solubility, and reaction outcomes.