Question

Calculate the number of particles in each of the following: (a) 0.100 mol zinc atoms, \(Z n\) (b) 0.200 mol chlorine molecules, \(C l_{2}\) (c) 0.300 mol zinc chloride formula units, \(Z \mathrm{nCl}_{2}\)

Short answer

(a) \(6.022 \times 10^{22}\) zinc atoms; (b) \(1.2044 \times 10^{23}\) chlorine molecules; (c) \(1.8066 \times 10^{23}\) zinc chloride formula units.

Step-by-step solution

Understanding the Mole Concept

The mole is a standard unit in chemistry that denotes a specific number of particles (atoms, molecules, or formula units). Avogadro's number, which is approximately \(6.022 \times 10^{23}\), is the number of particles in one mole.

Calculating Particles in Zinc Atoms

For 0.100 mol of zinc atoms:Use the formula: \[\text{Number of atoms} = \text{moles} \times \text{Avogadro's number} = 0.100 \times 6.022 \times 10^{23}\]Calculate the result:\[\text{Number of zinc atoms} = 6.022 \times 10^{22}\]

Calculating Particles in Chlorine Molecules

For 0.200 mol of chlorine molecules:Use the same method: \[\text{Number of molecules} = \text{moles} \times \text{Avogadro's number} = 0.200 \times 6.022 \times 10^{23}\]Calculate the result:\[\text{Number of chlorine molecules} = 1.2044 \times 10^{23}\]

Calculating Particles in Zinc Chloride Formula Units

For 0.300 mol of zinc chloride formula units:Apply the formula: \[\text{Number of formula units} = \text{moles} \times \text{Avogadro's number} = 0.300 \times 6.022 \times 10^{23}\]Calculate the result:\[\text{Number of zinc chloride formula units} = 1.8066 \times 10^{23}\]

Key concepts

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry that helps bridge the atomic scale to quantities we can measure and understand. It is approximately \(6.022 \times 10^{23}\). This large number represents the amount of atoms, molecules, or formula units present in one mole of any substance.

• By using Avogadro's number, we can convert moles into any of these tiny entities like atoms and molecules.
• Every time we talk about a mole, we inherently consider Avogadro’s number to quantify actual particles.

Avogadro's number is crucial because it allows us to work with macroscopic amounts of material, while still understanding the individual particles at the molecular level. Learning to use Avogadro's number effectively is key in solving many types of chemical calculations, such as finding how many molecules exist in a teaspoon of sugar or determining the number of atoms in a piece of copper wire.

Chemical Calculations

Chemical calculations are at the heart of understanding how chemical reactions occur and how substances are quantified. A basic aspect of these calculations is using moles and Avogadro's number to determine the number of particles in a given sample. Here's a breakdown:

• Identify the amount of substance in moles you have, which might come from a given mass or a molar concentration.
• Use Avogadro’s number to calculate the number of particles from the moles of the substance. This step involves simple multiplication.

In the problem, you calculated the number of particles for zinc atoms, chlorine molecules, and zinc chloride formula units. Each involved taking the known number of moles:- Zinc atoms: 0.100 mol- Chlorine molecules: 0.200 mol- Zinc chloride: 0.300 mol
And multiplying by Avogadro’s number to find the number of these tiny particles:- Zinc atoms result from \(0.100 \times 6.022 \times 10^{23} = 6.022 \times 10^{22}\).- Chlorine molecules give \(0.200 \times 6.022 \times 10^{23} = 1.2044 \times 10^{23}\).- Zinc chloride formula units compute to \(0.300 \times 6.022 \times 10^{23} = 1.8066 \times 10^{23}\).These calculations form a basis for advanced chemical problem-solving, ensuring the accurate preparation and reaction understanding in lab work and industrial applications.

Zinc Chloride

Zinc chloride, represented chemically as \(ZnCl_2\), is a compound formed when zinc and chlorine combine in precise stoichiometric ratios. Understanding its formula unit allows us to perform various calculations, which is essential in both lab settings and industrial uses.

• Each formula unit of zinc chloride contains one atom of zinc and two atoms of chlorine.
• This compound is often used as a catalyst, in tinning fluxes, or to manufacture other zinc-based compounds.

The concept of formula units is crucial as they help quantify how many complete sets of a compound exist in a sample, similar to how molecules work for molecular compounds.
For calculating the number of formula units in zinc chloride, you need to know:- Total moles you have (e.g., 0.300 mol in the problem).
Using Avogadro’s number, you then find the number of formula units by multiplying it with the moles. This gives you insight into the scale of particles involved in reactions. Knowing these values can help predict how much product will form in a reaction or how much of a reactant is needed for a full reaction.