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Chapter 4: Problem 110

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

Expert verified
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

01

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 = \( \frac{0.160 \mathrm{~g}}{95.21 \mathrm{~g/mol}} \)
02

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
03

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
04

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.

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