A \(355-\mathrm{mL}\) can of soda pop contains \(41 \mathrm{~g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\). What is the molarity of the solution with respect to sucrose?

When solving problems involving molarity, an essential step is determining the molar mass of the compound in question. For sucrose, a disaccharide sugar often found in food, calculating molar mass involves summing the atomic masses of all the atoms within a molecule. Sucrose's chemical formula is \( C_{12}H_{22}O_{11} \), which means it consists of 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms.

The atomic mass of carbon is approximately 12.01 g/mol, hydrogen is about 1.01 g/mol, and oxygen is roughly 16.00 g/mol. By multiplying these atomic masses by the number of respective atoms in a molecule of sucrose and summing them up, the molar mass for sucrose can be calculated as follows:

\[ \text{Molar mass of sucrose} = (12 \times 12.01 \text{ g/mol}) + (22 \times 1.01 \text{ g/mol}) + (11 \times 16.00 \text{ g/mol}) \]
\[ \text{Molar mass of sucrose} \approx 342.30 \text{ g/mol} \]
The precision of molarity calculations highly depends on the accurate determination of such molar masses.

Volume conversion is a key component in preparing molarity calculations, and many solutions are measured in milliliters. However, the standard unit for molarity calculations is liters. Therefore, a conversion is necessary if the volume of a solution is given in milliliters. One liter is the equivalent of 1,000 milliliters. To convert milliliters to liters, you must divide the number of milliliters by 1,000.

For instance, in the exercise given, a soda pop can contains 355 milliliters of solution. Converted to liters:

\[ \text{Volume in liters} = \frac{\text{Volume in milliliters}}{1000} \]
\[ \text{Volume in liters} = \frac{355}{1000} \approx 0.355 \text{ L} \]
This straightforward conversion is imperative to ensure that all components in the molarity formula are consistent with SI units, facilitating a correct calculation of the solution's concentration.

The term 'moles of solute' refers to the amount of substance dissolved in a solution. In chemistry, the mole is a fundamental unit in the International System of Units (SI) that measures the amount of a certain substance. One mole corresponds to Avogadro's number (\(~6.022 \times 10^{23}\) entities) of atoms, molecules, ions, or other particles.

To calculate the moles of solute, you divide the mass of the substance by its molar mass, which provides the number of moles present. In our exercise, the can of soda contains 41 grams of sucrose. Given the molar mass of sucrose is 342.30 g/mol, the moles of sucrose in the soda pop can is:

\[ \text{Number of moles} = \frac{\text{Mass of the solute (g)}}{\text{Molar mass (g/mol)}} \]
\[ \text{Number of moles} = \frac{41}{342.30} \approx 0.120 \text{ moles} \]
Understanding how to find the moles of solute is crucial in the study of solutions and is a central concept in quantitative chemistry, as it connects mass (a macroscopic property) with the number of particles (a microscopic property).