Question

The number of hydrogen atoms present in \(25.6 \mathrm{~g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) which has a molar mass of \(342.3 \mathrm{~g}\) is : (a) \(22 \times 10^{23}\) (b) \(9.91 \times 10^{23}\) (c) \(11 \times 10^{23}\) (d) \(44 \times 10^{23}\) :

Short answer

The number of hydrogen atoms present in 25.6 g of sucrose is approximately 9.91 × 10^{23}.

Step-by-step solution

Calculate the Moles of Sucrose

To find the number of hydrogen atoms in a given mass of sucrose, first calculate the moles of sucrose using the formula: number of moles = mass / molar mass. For 25.6 g of sucrose with molar mass 342.3 g/mol, the calculation is: number of moles = 25.6 g / 342.3 g/mol.

Calculate the Number of Hydrogen Atoms in Moles of Sucrose

Since the molecular formula of sucrose is C12H22O11, one mole of sucrose contains 22 moles of hydrogen atoms. Use Avogadro's number (approximately 6.022 × 10^23) to convert moles of hydrogen to atoms: number of hydrogen atoms = number of moles of sucrose × 22 moles of H per mole of sucrose × Avogadro's number.

Perform the Calculation

Multiply the number of moles of sucrose by 22 and then by Avogadro's number to find the total number of hydrogen atoms. This will give the answer to the problem.

Key concepts

Understanding Avogadro's Number

When we delve into the microscopic world of chemistry, Avogadro's number becomes a fundamental constant of crucial importance. It's named after the Italian scientist Amedeo Avogadro, and it defines the number of units in one mole of any substance. The mole is a standard unit of measurement in chemistry that provides a bridge between the atoms (or molecules) and the macroscopic amounts we work with in the lab.

Avogadro's number, approximately equal to \(6.022 \times 10^{23}\), denotes the number of atoms or molecules contained in one mole of a substance. This number was derived from the number of atoms in 12 grams of carbon-12, which is an elemental isotope with a relative atomic mass of 12. By understanding Avogadro's number, we can link the microscopic realm where things are measured in atoms or molecules, to the macroscopic realm where we measure substances in grams.

For example, if we want to determine the number of particles in a given sample, we must first find out the number of moles in the substance. With this information, and knowing Avogadro's number, we can calculate the total number of discrete particles, whether they're atoms in an element or molecules in a compound.

The Art of Molar Mass Calculation

Molar mass is a property that chemists use to relate the mass of a substance to the quantity of particles present in the substance. It's typically reported in units of grams per mole (g/mol), and it's calculated by summing the atomic masses of all the atoms in a single molecule of the compound. Each element's atomic mass can be found on the periodic table and is usually expressed in atomic mass units (amu).

For instance, the molar mass of sucrose (\(C_{12}H_{22}O_{11}\)) involves the multiplication of the atomic masses of carbon (C), hydrogen (H), and oxygen (O) by the number of each atom present in the molecule, then adding these results together. The molar mass calculation enables us to transition from the molecular scale (where compounds are a collection of specific atoms) to the scale used in stoichiometric calculations (where we measure masses).

In educational materials, it's helpful to visualize this concept using molecular models or scaled diagrams that represent the weighted contribution of each atom to the overall mass of the molecule.

Stoichiometry: The Balancing Act of Chemistry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's a method based on the conservation of mass, where the mass and the number of atoms are conserved in a reaction, allowing us to calculate how much of a reactant is needed to produce a certain amount of product.

Using the aforementioned molar mass and Avogadro's number, we can perform stoichiometric calculations to find out exactly how much of each substance is involved in a reaction. Stoichiometry also requires us to understand and apply the mole concept to convert between mass, moles, and the number of particles.

The calculation in our exercise is a classic stoichiometric problem in which we determine the number of atoms from a given mass of a compound. We first convert the mass of sucrose to moles (using the molar mass), then translate moles of sucrose to moles of hydrogen atoms (using the chemical formula), and finally, compute the number of hydrogen atoms (using Avogadro's number). It's like a dance between different units and concepts, all beautifully synchronized through stoichiometry.