(a) How many moles of \(\mathrm{C}\) atoms are in \(1 \mathrm{~mol}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) ?\) (b) How many C atoms are in \(2 \mathrm{~mol}\) of sucrose?

The mole concept is one of the fundamental ideas in chemistry. A mole is a unit that measures quantity and allows chemists to count particles like atoms, molecules, or ions in a substance. It’s similar to a dozen, but instead of 12, one mole contains exactly \(6.022 \times 10^{23}\) entities.
This huge number simplifies calculations involving tiny particles. For sucrose \(C_{12}H_{22}O_{11}\), knowing that one mole has \(6.022 \times 10^{23}\) molecules helps determine how many atoms of each element are present.
Every mole of sucrose has 12 moles of Carbon (C) atoms, 22 moles of Hydrogen (H) atoms, and 11 moles of Oxygen (O) atoms. Understanding this concept simplifies complex chemical calculations.

Avogadro's number is essential in chemistry for measuring large quantities of small particles like atoms. Defined as \(6.022 \times 10^{23}\), it tells us how many units are in one mole of any substance.
For example, in the exercise, we used Avogadro’s number to find the quantity of Carbon atoms in sucrose. We calculated:
\[2 \text{ mol} \times 12 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 1.446 \times 10^{25} \text{ atoms} \]
This approach underscores how Avogadro’s number bridges the gap between the macroscopic world (grams, moles) and the microscopic world (atoms, molecules). It helps chemists translate laboratory quantities into practical measurements.

Understanding chemical composition helps in identifying the elements and their amounts within a compound. For instance, sucrose’s formula \(C_{12}H_{22}O_{11}\) means it’s composed of 12 Carbon, 22 Hydrogen, and 11 Oxygen atoms per molecule.
Knowing the chemical composition allows us to predict a substance’s behavior, reactivity, and properties. This information was critical in solving our problem by determining how many moles of Carbon atoms are in the specified moles of sucrose and eventually calculating the number of atoms using Avogadro’s number.
Chemical composition is foundational in stoichiometry, reaction balancing, and understanding molecular structures, forming the core of many chemical calculations.