Calculate the mass of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) in a \(105-\mathrm{mL}\) sample of a \(1.02 \mathrm{M}\) glucose solution.

Understanding molarity is fundamental to solving problems related to solutions in chemistry. Molarity is the measure of concentration of a solution and is expressed as moles of solute per liter of solution. When we say a glucose solution is 1.02 M, it means that every liter of this solution contains 1.02 moles of glucose. To calculate molarity, the formula used is:
\[ \text{{Molarity (M)}} = \frac{{\text{{moles of solute}}}}{{\text{{liters of solution}}}} \].
In practical terms, knowing the molarity allows us to determine how much of a substance is present in a given volume of solution and, from there, calculate the mass of the substance that we are interested in.

The term 'moles of solute' is often brought up when we discuss solutions. A mole is a unit that denotes an exact number of particles, like atoms or molecules, and in chemistry, this number is Avogadro's number (\(6.022 \times 10^{23}\)). To grasp how many moles of a solute are present in a solution, we have to use the molarity. For example, if we have a solution with a molarity of 1.02 M, it means we have 1.02 moles of the solute in 1 liter of that solution. The calculation of the exact number of moles based on the volume of the solution is critical as it sets the stage for finding out the mass, which is the ultimate goal in many stoichiometry problems.

Volume conversion is a straightforward but crucial step in many chemistry calculations, particularly when dealing with solutions. Since molarity is defined in terms of liters, we often need to convert the volume of a given solution into liters before using it in molarity-based calculations. To convert milliliters to liters, remember that there are 1000 milliliters in one liter. So, if you're given a volume in milliliters, you can convert it to liters by dividing by 1000. For example, converting 105 mL of a solution to liters would require you to perform the following calculation:
\[ \text{{Volume in liters}} = \frac{{\text{{Volume in mL}}}}{{1000}} \].
Proper conversion is crucial because using the wrong units can lead to errors, not to mention frustration, as you try to figure out where you went wrong in your calculations.

The molar mass is the weight of one mole of a substance and is usually expressed in grams per mole (g/mol). It is calculated by summing up the atomic masses of all the atoms in a molecule of the substance, as provided by the periodic table. In the context of glucose, whose molecular formula is \( C_6H_{12}O_6 \), the molar mass is the combined atomic masses of 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Molar mass is pivotal in translating between moles of a substance and grams since it tells us what one mole of a particular substance weighs. With the molar mass, you can convert the number of moles of a substance into its mass using the formula:
\[ \text{{Mass}} = \text{{Molar Mass}} \times \text{{Moles of Solute}} \].
Knowing the molar mass of glucose allows us to work out the mass from the moles calculated, giving us the ability to link a volume of glucose solution to the actual amount of glucose it contains in grams.