Question

Which of the following solutions contains the great est number of particles? Support your answer. a. \(400.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) sodium chloride b. \(300.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) calcium chloride c. \(200.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) iron(III) chloride d. \(200.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) potassium bromide e. \(800.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) sucrose (table sugar)

Short answer

The solution with the greatest number of particles is b. \(300.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) calcium chloride containing 0.09 moles of particles.

Step-by-step solution

Identify the number of ions produced by each solute when dissolved in water

First, we need to determine how many ions each solute produces: a. Sodium chloride (NaCl) dissociates into 2 ions: Na+ + Cl- b. Calcium chloride (CaCl2) dissociates into 3 ions: Ca2+ + 2Cl- c. Iron(III) chloride (FeCl3) dissociates into 4 ions: Fe3+ + 3Cl- d. Potassium bromide (KBr) dissociates into 2 ions: K+ + Br- e. Sucrose (C12H22O11) does not dissociate into ions, as it is a non-electrolyte.

Calculate moles of particles for each solution

Now, we will calculate the moles of particles in each solution by using the formula: moles of particles = volume (L) * molarity (M) * (number of ions produced by the solute) a. Moles of particles in NaCl solution = (400 mL / 1000) * 0.10 M * 2 = 0.08 moles b. Moles of particles in CaCl2 solution = (300 mL / 1000) * 0.10 M * 3 = 0.09 moles c. Moles of particles in FeCl3 solution = (200 mL / 1000) * 0.10 M * 4 = 0.08 moles d. Moles of particles in KBr solution = (200 mL / 1000) * 0.10 M * 2 = 0.04 moles e. Moles of particles in sucrose solution = (800 mL / 1000) * 0.10 M * 1 = 0.08 moles

Compare the moles of particles in each solution

Now that we've calculated the moles of particles in each solution, compare the values to find the greatest quantity: a. 0.08 moles b. 0.09 moles c. 0.08 moles d. 0.04 moles e. 0.08 moles

Identify the solution with the greatest number of particles

The solution with the greatest number of particles is b. \(300.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) calcium chloride containing 0.09 moles of particles.

Key concepts

Molarity

Molarity is a key concept in chemistry that refers to the concentration of a solution. It describes the number of moles of a solute that are dissolved in one liter of solution. The formula to calculate molarity is given by:
\[ M = \frac{n}{V} \]where

• \( M \) represents molarity,
• \( n \) is the number of moles of solute, and
• \( V \) is the volume of the solution in liters.

Understanding molarity is essential for determining how substances interact in solutions. In the given exercise, all solutions have the same molarity of 0.10 M, which means each liter of these solutions contains 0.10 moles of their respective compounds.
The volume of the solutions varies, leading to different amounts of particles when we consider ionic compounds that dissociate into multiple ions.

Ionic Compounds

Ionic compounds consist of positively charged ions (cations) and negatively charged ions (anions) bonded together through ionic bonds. They typically dissolve in water, dissociating into their constituent ions which allow them to conduct electricity in solution.
In our exercise context, examples of ionic compounds include sodium chloride (NaCl), calcium chloride (CaCl2), iron(III) chloride (FeCl3), and potassium bromide (KBr). When these compounds dissolve in water, they separate into their respective ions:

• NaCl dissociates into Na⁺ and Cl^-, producing 2 ions.
• CaCl2 dissociates into Ca²⁺ and 2 Cl^-, producing 3 ions.
• FeCl3 dissociates into Fe³⁺ and 3 Cl^-, producing 4 ions.
• KBr dissociates into K⁺ and Br^-, producing 2 ions.

Each type of ionic compound can impact the solution's total particle count differently due to their unique dissociation behavior.

Dissociation

Dissociation refers to the process by which an ionic compound separates into individual ions when dissolved in a solvent like water. This is a fundamental process that affects the way solutions conduct electricity and the number of particles present in a solution.
For example, calcium chloride (CaCl2) dissociates into three ions: one Ca²⁺ ion and two Cl^- ions. This means that when one mole of calcium chloride is dissolved, it produces three moles of ions.
In the exercise, comparing the resulting ions from different solutions helps in determining which one contains the most total particles. Although all the solutions have the same molarity, those that dissociate into more ions lead to higher numbers of particles in the solution.

Mole Concept

The mole concept is central to understanding and solving quantitative problems in stoichiometry. It provides a bridge between the atomic world and the macroscopic amounts we work with in the lab. A mole is a unit that quantifies the amount of substance, typically containing Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\) particles.
Using the mole concept allows chemists to count entities at the atomic level conveniently. When calculating the moles of particles in solutions, as demonstrated in the exercise, this concept is indispensable.

• We can determine the number of moles through the formula: \[ \text{moles} = \text{volume (L)} \times \text{molarity (M)} \times \text{number of ions} \]

In our example, calcium chloride, when dissolved, produces more ions per mole compared to sucrose, thereby leading to a higher number of moles of particles despite having the same molarity and volume adjustments. Understanding this principle allows accurate predictions of particle amounts in chemical reactions and processes.