Question

Calculate the number of representative particles of each substance. a. 11.5 \(\mathrm{mol} \mathrm{Ag}\) b. 18.0 \(\mathrm{mol} \mathrm{H}_{2} \mathrm{O}\) c. 0.150 mol \(\mathrm{NaCl}\) d. \(1.35 \times 10^{-2} \mathrm{mol} \mathrm{CCH}_{4}\)

Short answer

The number of representative particles for each substance is as follows: a. \(6.9253 \times 10^{24}\) Ag particles b. \(1.08394 \times 10^{25}\) H2O particles c. \(9.033 \times 10^{22}\) NaCl particles d. \(8.1297 \times 10^{21}\) CCH4 particles

Step-by-step solution

Identify the given moles for each substance from the problem

a. 11.5 mol Ag b. 18.0 mol H2O c. 0.150 mol NaCl d. 1.35 x 10^(-2) mol CCH4

Calculate the number of representative particles for each substance using the Avogadro's number

a. Number of Ag particles: \(11.5 \text{ mol} \times 6.022 \times 10^{23} \text{ particles/mol}\) b. Number of H2O particles: \(18.0 \text{ mol} \times 6.022 \times 10^{23} \text{ particles/mol}\) c. Number of NaCl particles: \(0.150 \text{ mol} \times 6.022 \times 10^{23} \text{ particles/mol}\) d. Number of CCH4 particles: \(1.35 \times 10^{-2} \text{ mol} \times 6.022 \times 10^{23} \text{ particles/mol}\)

Find the total number of particles for each substance

a. Number of Ag particles: \(6.9253 \times 10^{24}\) particles b. Number of H2O particles: \(1.08394 \times 10^{25}\) particles c. Number of NaCl particles: \(9.033 \times 10^{22}\) particles d. Number of CCH4 particles: \(8.1297 \times 10^{21}\) particles

Key concepts

Avogadro's Number

Avogadro's number, a fundamental metric in chemistry, is the bridge connecting the microscopic world of atoms and molecules to the macroscopic quantities we can observe and measure. Its value is approximately 6.022 x 10^23, representing the number of atoms, ions, or molecules in one mole of a substance. To visualize the sheer magnitude of this number, imagine a grain of sand. If each grain of sand were one particle, Avogadro's number of grains would cover all beaches on Earth multiple times over.

When converting moles to particles in chemical equations, this number serves as the conversion factor. It was named after Amedeo Avogadro, an Italian scientist who first hypothesized that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles. Understanding Avogadro's number allows students to scale up their stoichiometric calculations to tangible quantities for laboratory work and real-world applications.

Chemical Moles

The chemical mole is a fundamental concept in chemistry, acting like the 'dozen' for chemists. Where a dozen represents 12 items, one mole represents approximately 6.022 x 10^23 representative particles. This could be atoms, ions, molecules, or other specified entities. The use of moles bridges the gap between the atomic scale and the bulk scale, enabling chemists to count atoms by weighing.

When analyzing substances, it's practical to measure amounts in grams or liters rather than counting individual atoms. The mole provides a link between an element's atomic weight in atomic mass units (amu) and its mass in grams. For example, one mole of carbon-12 has a mass of exactly 12 grams, and contains Avogadro's number of carbon atoms. This allows for calculation consistency across various substances and reactions, an essential aspect of stoichiometric analysis.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's like a recipe for chemistry, dictating the proportions of ingredients (reactants) required to create a certain amount of product. These proportions are derived from the balanced chemical equation, which shows the number of moles of each substance involved.

Understanding stoichiometry is essential for predicting the outcomes of chemical reactions and for scaling them up or down. Students often use mole-to-mole conversion factors derived from the coefficients in a balanced equation to determine how much of one substance will react with or produce another. Mastery of stoichiometry is not only fundamental for successful laboratory experiments but also for various applications in industrial chemical processes, environmental science, and pharmaceutical drug development.

Representative Particles

Representative particles are individual entities that makeup substances, and could be atoms, molecules, ions, or formula units depending on the nature of the substance. The term simplifies discussions about chemical amounts, where a particle can represent the smallest unit of a substance with its characteristic properties.

For atomic elements like gold or helium, the representative particle is a single atom. For molecular compounds such as water (H2O) or carbon dioxide (CO2), the representative particle is a molecule. Ionic compounds like sodium chloride (NaCl) are made up of formula units, which is the lowest whole number ratio of ions present in the compound. This terminology streamlines the process of conversion between moles and the actual count of entities, through the use of Avogadro's number. By knowing the type of representative particle and the amount in moles, we can calculate the total number of these particles in a sample with relative ease, enabling precise measurements and predictions in chemical reactions.