Question

Calculate the number of particles in each of the following: (a) 0.250 mol calcium atoms, Ca (b) 0.500 mol fluorine molecules, \(\mathrm{F}_{2}\) (c) 0.750 mol calcium fluoride formula units, \(\mathrm{CaF}_{2}\)

Short answer

(a) 1.506 × 10^23 atoms, (b) 3.011 × 10^23 molecules, (c) 4.517 × 10^23 formula units.

Step-by-step solution

Understanding Avogadro's Number

Avogadro's number, \(N_A\), is defined as the number of particles (atoms, molecules, or formula units) in one mole of a substance. It is approximately \(6.022 imes 10^{23}\) particles/mole.

Calculate Particles in Calcium Atoms

For \(0.250\) mol of calcium atoms: \[\text{Number of calcium atoms} = 0.250 \text{ mol} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 1.506 \times 10^{23} \, \text{atoms.}\]

Calculate Particles in Fluorine Molecules

For \(0.500\) mol of fluorine molecules: \[\text{Number of fluorine molecules} = 0.500 \text{ mol} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 3.011 \times 10^{23} \, \text{molecules.}\]

Calculate Particles in Calcium Fluoride Formula Units

For \(0.750\) mol of calcium fluoride formula units: \[\text{Number of \(\mathrm{CaF_2}\) formula units} = 0.750 \text{ mol} \times 6.022 \times 10^{23} \, \text{formula units/mole} = 4.517 \times 10^{23} \, \text{formula units.}\]

Key concepts

Understanding the Mole Concept

The mole is a fundamental concept in chemistry that serves as a bridge between the molecular world and macroscopic measurements. A mole is essentially a counting unit, similar to a dozen, but much larger. One mole of any substance always contains exactly Avogadro's number of particles, which is approximately \( 6.022 \times 10^{23} \).
This number is so large because atoms and molecules are extremely small; therefore, the mole allows chemists to count particles by weighing out amounts in grams. The mole concept is essential for converting between atomic scale (like atoms and molecules) and the laboratory scale (like grams or liters), enabling scientists to conduct experiments and produce reactions in precise quantities.

Performing Particle Calculations

Particle calculations involve determining the number of individual particles contained in a given amount of substance, usually measured in moles. To do this, you multiply the number of moles by Avogadro's Number, since \( N_A \) represents the number of particles in one mole.
For example, if you have 0.250 mol of calcium atoms, you multiply it by Avogadro's Number:

• 0.250 mol \( \times 6.022 \times 10^{23} \) atoms/mol = \( 1.506 \times 10^{23} \) atoms

Similarly, for molecules or formula units:

• 0.500 mol of fluorine molecules \( \times 6.022 \times 10^{23} \) molecules/mol = \( 3.011 \times 10^{23} \) molecules
• 0.750 mol of calcium fluoride formula units \( \times 6.022 \times 10^{23} \) formula units/mol = \( 4.517 \times 10^{23} \) formula units

This procedure is a key skill in chemistry to predict and quantify the outcomes of chemical reactions.

Interpreting Chemical Formulas

Chemical formulas are a succinct way to represent elements within a compound, showing not only which elements are present but also their proportional numbers. Each symbol in a chemical formula represents an element, while subscripts indicate the number of atoms of each element in a molecule.
For example, in \( \mathrm{F_2} \), the 'F' stands for fluorine, and the subscript '2' indicates there are two atoms of fluorine in each molecule. In \( \mathrm{CaF_2} \), 'Ca' represents calcium, while 'F' represents fluorine, with the subscript '2' indicating there are two fluorine atoms for each calcium atom.
Understanding chemical formulas helps chemists understand the composition of compounds and conduct quantitative analyses effectively. Recognizing the relationships between different elements and their proportions is also vital when balancing chemical equations and synthesizing new compounds in the lab.