Problem 17 - General Chemistry: Principles and Modern Applications

Question

Assuming the volumes are additive, what is the \(\left[\mathrm{Cl}^{-}\right]\) in a solution obtained by mixing \(225 \mathrm{mL}\) of \(0.625 \mathrm{M}\) \(\mathrm{KCl}\) and \(615 \mathrm{mL}\) of \(0.385 \mathrm{M} \mathrm{MgCl}_{2} ?\)

Step-by-Step Solution

Answer

The concentration of Chloride ions [Cl-] in the resulting solution would be approximately 0.7314 M.

Step 1: Understand The Chemical Compounds

The compound KCl dissociates in solution to form K+ and Cl- ions. On the other hand, MgCl2 gives us Mg2+ and two Cl- ions in solution. This means that a mole of KCl will have the same number of moles of Cl- ions while a mole of MgCl2 will have twice the number of moles of Cl- ions.

Step 2: Calculate The Moles

For KCl, the number of moles can be calculated by multiplying the volume of the KCl solution (in liters) by its molar concentration. Thus, moles of Cl- from KCl = 225 mL * (1L/1000 mL) * 0.625 M = 0.140625 moles. We can obtain the moles of chloride ions from MgCl2 in the same way: moles of Cl- from MgCl2 = 615 mL * (1 L/1000 mL) * 0.385 M * 2 = 0.47355 moles. The multiplication by 2 accounts for the fact that each molecular unit of MgCl2 gives 2 ions of Cl-.

Step 3: Add The Moles

Now we need to add the moles of Cl- ions from both solutions to get the total moles. Total moles of Cl- = moles of Cl- from KCl + moles of Cl- from MgCl2 = 0.140625 moles + 0.47355 moles = 0.614175 moles.

Step 4: Calculate The Concentration

Finally, the molar concentration (M) of Cl- ions can be obtained by dividing the total moles by the total volume. The total volume = 225 mL + 615 mL = 840 mL = 0.84 L. Therefore, molar concentration (M) = total moles / total volume in Liters = 0.614175 moles / 0.84 L = 0.7314 M.

Key Concepts

Chloride Ion Concentration

Understanding chloride ion concentration in a solution involves recognizing how different compounds contribute their ions when dissolved. In this exercise, we mix solutions of KCl and MgCl₂. Both compounds dissolve and dissociate in water to release chloride ions (Cl⁻).

• KCl: Each molecule of potassium chloride (KCl) dissociates into one K⁺ ion and one Cl⁻ ion.
• MgCl₂: Magnesium chloride (MgCl₂) behaves differently. It splits into one Mg²⁺ ion and two Cl⁻ ions. Thus, MgCl₂ contributes twice the number of Cl⁻ ions per molecule compared to KCl.

Careful consideration of the dissociation process is key as it influences how many chloride ions are present in the final solution. Knowing the behavior of these molecules upon dissolving helps determine the total chloride ion concentration.

Molarity Calculation

Calculating molarity, which measures concentration, is essential when mixing solutions. Molarity is defined as the number of moles of solute per liter of solution. To find it, we need:

• Total moles of solute (chloride ions in this case)
• Volume of the solution in liters

For example, with KCl's molarity known and its volume converted to liters, we calculate the moles of Cl⁻ ions. The same process applies to MgCl₂, multiplying by 2 for its two chloride ions per formula unit. Finally, total moles of chloride ions are found by adding the moles from both solutions. Dividing this total by the solution's overall volume gives molarity. This calculation underscores how solute and solvent quantities relate to the concentration of the chloride ions.

Chemical Dissociation

Chemical dissociation refers to the process where ionic compounds separate into individual ions in solution. This understanding is vital for predicting the behavior of dissolved substances.

• When KCl dissociates, it directly forms one Cl⁻ ion per molecule.
• However, MgCl₂'s dissociation results in two Cl⁻ ions per molecule, doubling its contribution of chloride ions relative to KCl.

Knowing how compounds dissociate allows for accurate calculation of ion concentrations in solutions. This principle not only helps in chemistry exercises but also in real-world applications like determining pollutant concentrations in water supplies or medication dosages. By grasping the basics of dissociation, we understand the fundamental chemical behaviors necessary for calculating subsequent concentrations such as molarity.