Question

Calculate the concentration of all ions present when \(0.160 \mathrm{~g}\) of \(\mathrm{MgCl}_{2}\) is dissolved in \(100.0 \mathrm{~mL}\) of solution.

Short answer

To calculate the concentration of all ions present: 1. Find the moles of MgCl₂: Moles of MgCl₂ = \( \frac{0.160 \mathrm{~g}}{95.21 \mathrm{~g/mol}} \) 2. Determine the moles of Mg²⁺ and Cl⁻ ions: Moles of Mg²⁺ = moles of MgCl₂ × 1 Moles of Cl⁻ = moles of MgCl₂ × 2 3. Convert the volume of the solution to liters: 0.1 L = 100.0 mL × \( \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}} \) 4. Calculate the concentration of each ion: Concentration of Mg²⁺ = \( \frac{\text{moles of Mg}^{2+}}{0.1 \mathrm{~L}} \) Concentration of Cl⁻ = \( \frac{\text{moles of Cl}^-}{0.1 \mathrm{~L}} \)

Step-by-step solution

Calculate the moles of MgCl2

To begin, we need to know the molar mass of MgCl2. Mg has a molar mass of 24.31 g/mol, and Cl has a molar mass of 35.45 g/mol. So, the molar mass of MgCl2 is 24.31 + 2(35.45) = 95.21 g/mol. Now, we can calculate the moles of MgCl2: moles of MgCl2 = mass ÷ molar mass moles of MgCl2 = \( \frac{0.160 \mathrm{~g}}{95.21 \mathrm{~g/mol}} \)

Determine the moles of Mg^2+ and Cl- ions

For every 1 mole of MgCl2, we have 1 mole of Mg^2+ ions and 2 moles of Cl- ions as MgCl2 dissociates in water into ions: MgCl₂ → Mg^2+ + 2Cl^- So, to find the moles of each ion, multiply the moles of MgCl2 by the stoichiometric coefficient of each ion: moles of Mg^2+ = moles of MgCl2 × 1 moles of Cl- = moles of MgCl2 × 2

Convert the volume of solution to liters

As the concentration is usually expressed in mol/L, we need to convert the volume of the solution from mL to L: 100.0 mL × \( \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}} \) = 0.1 L

Calculate the concentration of each ion

To find the concentration of each ion, divide the moles of the ion by the volume of the solution in liters: Concentration of Mg^2+ = \( \frac{\text{moles of Mg}^{2+}}{0.1 \mathrm{~L}} \) Concentration of Cl- = \( \frac{\text{moles of Cl}^-}{0.1 \mathrm{~L}} \) Now, substituting the values from steps 1-3, you can calculate the concentration of both Mg^2+ and Cl- ions.

Key concepts

Molar Mass

The concept of molar mass is crucial in chemistry as it helps convert between the mass of a compound and the number of moles it contains. Molar mass is defined as the mass of one mole of a substance, typically expressed in units of grams per mole (g/mol). For any element, the molar mass in grams is numerically equivalent to the atomic mass in atomic mass units (amu) found on the periodic table. Let's consider an example with magnesium chloride (\(\mathrm{MgCl}_2\)). Magnesium (\(\mathrm{Mg}\)) has a molar mass of 24.31 g/mol, and chlorine (\(\mathrm{Cl}\)) has a molar mass of 35.45 g/mol. Since \(\mathrm{MgCl}_2\) contains one magnesium atom and two chlorine atoms, its molar mass is calculated by summing these values:

• Mg: 24.31 g/mol
• Cl: 2 × 35.45 g/mol = 70.90 g/mol

Adding these, \(\mathrm{MgCl}_2\) has a molar mass of 95.21 g/mol. Understanding molar mass is the first step in converting grams to moles, which is necessary for determining concentrations in solutions.

Dissociation in Water

Dissociation refers to the process where ionic compounds separate into their constituent ions upon dissolving in water. This process is essential in forming a solution because it allows the ions to be free and evenly distributed.When \(\mathrm{MgCl}_2\) is dissolved in water, it separates into magnesium ions (\(\mathrm{Mg}^{2+}\)) and chloride ions (\(\mathrm{Cl}^-\)) as represented by the equation:\[\mathrm{MgCl}_2 (s) \rightarrow \mathrm{Mg}^{2+} (aq) + 2\mathrm{Cl}^- (aq)\]So, for every mole of \(\mathrm{MgCl}_2\) that dissociates, one mole of \(\mathrm{Mg}^{2+}\) ions and two moles of \(\mathrm{Cl}^-\) ions are produced. This knowledge is crucial when calculating the concentration of each ion in a solution.

Mole Concept

The mole is a basic unit of measurement in chemistry that expresses amounts of a chemical substance. One mole contains exactly \(6.022 \times 10^{23}\) entities, such as atoms, molecules, or ions, which is known as Avogadro's number.Using the mole concept, we can connect the mass of a substance to the amount of substance in terms of moles. For example, the formula used is:\[\text{moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}\]Consider the task of dissolving 0.160 g of \(\mathrm{MgCl}_2\). With a known molar mass of 95.21 g/mol, the number of moles of \(\mathrm{MgCl}_2\) is calculated as:\[\text{moles of } \mathrm{MgCl}_2 = \frac{0.160\,\mathrm{g}}{95.21\,\mathrm{g/mol}} = 0.00168\,\text{moles}\]Understanding the mole concept allows us to transform a given mass into a usable form for further calculations, such as determining ion concentrations in solutions.

Solution Concentration

Solution concentration denotes how much of a given substance is present in a certain volume of liquid, and is often expressed in terms of molarity (M), which is moles of solute per liter of solution.The formula to find the concentration of ions in solution is:\[\text{Concentration (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]Given the exercise, once we've calculated the moles of \(\mathrm{MgCl}_2\), and then the ions \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cl}^-\), this formula helps us find their concentrations. Using a solution volume of 0.1 L:

• \(\text{Concentration of } \mathrm{Mg}^{2+} = \frac{0.00168\,\text{moles of } \mathrm{Mg}^{2+}}{0.1\,\mathrm{L}} = 0.0168\,\mathrm{M}\)
• \(\text{Concentration of } \mathrm{Cl}^{-} = \frac{2 \cdot 0.00168\,\text{moles of } \mathrm{Cl}^{-}}{0.1\,\mathrm{L}} = 0.0336\,\mathrm{M}\)

Understanding solution concentration is vital for preparing chemical solutions with the desired strength and reactivity.