Question

Which of the following solutions of strong electrolytes contains the largest number of ions: 100.0 \(\mathrm{mL}\) of 0.100\(M \mathrm{NaOH}\) , 50.0 \(\mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{BaCl}_{2},\) or 75.0 \(\mathrm{mL}\) of 0.150 \(\mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4} ?\)

Short answer

The solution containing the largest number of ions is 75.0 mL of 0.150 M Na3PO4, with a total of 0.0450 mol of ions.

Step-by-step solution

Determine moles of each electrolyte in the given solution

First, let's find the moles of each electrolyte in the solution. We can use the formula: Moles of electrolyte = Molarity × Volume (in liters) For the NaOH solution: Moles of NaOH = 0.100 M × 100.0 mL × (1L/1000mL) = 0.0100 mol For the BaCl2 solution: Moles of BaCl2 = 0.200 M × 50.0 mL × (1L/1000mL) = 0.0100 mol For the Na3PO4 solution: Moles of Na3PO4 = 0.150 M × 75.0 mL × (1L/1000mL) = 0.01125 mol

Identify ions produced by electrolytes and their corresponding numbers

When the strong electrolytes dissociate in water, they release their respective ions. Let's identify the ions produced by each electrolyte and their corresponding numbers. For NaOH: 1 Na⁺ ion and 1 OH⁻ ion Total ions = 1 + 1 = 2 For BaCl2: 1 Ba²⁺ ion and 2 Cl⁻ ions Total ions = 1 + 2 = 3 For Na3PO4: 3 Na⁺ ions and 1 PO₄³⁻ ion Total ions = 3 + 1 = 4

Calculate the total number of ions produced in each solution

Now that we have the moles of each electrolyte and the total ions produced per mole, we can calculate the total number of ions produced in each solution using the following formula: Total ions in solution = Moles of electrolyte × Total ions produced per mole of electrolyte For the NaOH solution: Total ions = 0.0100 mol × 2 = 0.0200 mol of ions For the BaCl2 solution: Total ions = 0.0100 mol × 3 = 0.0300 mol of ions For the Na3PO4 solution: Total ions = 0.01125 mol × 4 = 0.0450 mol of ions

Compare the total number of ions and determine the solution with the largest number of ions

Now that we have the total number of ions produced in each solution, let's compare them to find out which solution contains the largest number of ions. NaOH solution: 0.0200 mol of ions BaCl2 solution: 0.0300 mol of ions Na3PO4 solution: 0.0450 mol of ions We can see that the Na3PO4 solution contains the largest number of ions (0.0450 mol). Therefore, the solution containing the largest number of ions is 75.0 mL of 0.150 M Na3PO4.

Key concepts

Molarity

Molarity is a fundamental concept that describes the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. Often symbolized as "M", molarity allows us to determine how concentrated a particular solute is within a given volume of solvent.
For example, a molarity of 1 M (molar) implies there is one mole of solute in every liter of solution. To calculate the molarity, you should use the formula:

• Molarity (M) = Moles of solute / Liters of solution

In practical situations, molarity is significant in determining how a solution will behave in different chemical reactions or physical processes. It helps to predict whether reactions will be successful, based on how much of each reactant is present.

Dissociation in Water

Dissociation is a process where ionic compounds separate into ions when dissolved in water. This is particularly notable for strong electrolytes, which dissociate completely.
When an ionic compound like NaOH is dissolved in water, it splits into its constituent ions: Na⁺ and OH⁻. This process increases the number of particles in the solution, which directly affects properties like electrical conductivity and boiling point elevation.
Water, as a solvent, plays a crucial role by allowing these ions to separate. It surrounds each ion, stabilizing them and preventing them from recombining into their neutral compound. This stabilization occurs due to the polar nature of water molecules, which can align themselves with the charged ions.

Ionic Compounds

Ionic compounds are formed from the electrostatic attraction between oppositely charged ions. These ions typically derive from atoms or molecules that have gained or lost electrons.
For example, sodium chloride (NaCl) is comprised of Na⁺ and Cl⁻ ions. In solid form, these ions are tightly held together in a lattice structure due to their ionic bonds. In solution, these bonds are broken, allowing the ions to move freely.
Understanding ionic compounds is essential because it explains many properties of solutions, such as conductivity and reaction mechanisms. With an ionic compound like BaCl₂, when dissolved in water, it dissociates into one Ba²⁺ ion and two Cl⁻ ions, resulting in an increased count of free particles in solution.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. By using stoichiometry, you can calculate how much of each substance is needed or produced in a reaction.
This involves using the balanced chemical equation to find molar ratios. For example, if a reaction between sodium hydroxide (NaOH) and another substance was 1:1, the stoichiometric calculation would tell us equal moles of each reactant are needed.
In electrolyte solutions, stoichiometry helps determine the number of ions produced. For instance, BaCl₂ yields 3 ions per formula unit, which implies that each mole of BaCl₂ will produce a mole of Ba²⁺ and two moles of Cl⁻. Therefore, understanding stoichiometric relationships ensures precise calculations in analytical and synthetic chemistry.