Question

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

Short answer

In summary, when 0.160 g of MgCl₂ is dissolved in 100.0 mL of water, the concentrations of ions present are 0.01681 mol/L for Mg²⁺ and 0.03362 mol/L for Cl⁻.

Step-by-step solution

Calculate the number of moles of MgCl₂

To find the number of moles of MgCl₂, divide the mass of the sample (0.160 g) by its molar mass. The molar mass of MgCl₂ is: \(Mg: 24.305 \mathrm{~g/mol}\) \(Cl: 2 \times 35.453 \mathrm{~g/mol}\) Molar mass of MgCl₂ = 24.305 + 2(35.453) = 95.211 g/mol Now, we can calculate the number of moles: moles of MgCl₂ = \(\frac{0.160 \mathrm{~g}}{95.211 \mathrm{~g/mol}}\)

Determine the moles of MgCl2

moles of MgCl₂ = \(\frac{0.160 \mathrm{~g}}{95.211 \mathrm{~g/mol}}\) = 0.001681 mol

Calculate the concentration of MgCl₂ in the solution

To find the concentration of MgCl₂, we need to divide the moles by the volume of the solution in liters. The volume of the solution is given as 100.0 mL, which is equivalent to 0.1000 L. Concentration of MgCl₂ = \(\frac{0.001681 \mathrm{~mol}}{0.1000 \mathrm{~L}}\) = 0.01681 mol/L

Calculate the concentrations of Mg²⁺ and Cl⁻ ions in the solution

When MgCl₂ dissolves in water, it dissociates into its ions: Mg²⁺ and Cl⁻. Note that for every one mole of MgCl₂, we get one mole of Mg²⁺ ions and two moles of Cl⁻ ions. Concentration of Mg²⁺ = concentration of MgCl₂ = 0.01681 mol/L Concentration of Cl⁻ = 2 × concentration of MgCl₂ = 2 × 0.01681 mol/L = 0.03362 mol/L The concentrations of all ions present in the solution are as follows: Mg²⁺ ions: 0.01681 mol/L Cl⁻ ions: 0.03362 mol/L

Key concepts

Molar Mass Calculation

Calculating the molar mass of a compound is the first vital step in solving many chemistry problems. Each element of a compound contributes to its overall molar mass based on its atomic mass. It's essential to understand this process thoroughly, as it forms the basis for further calculations like moles and concentration.

To find the molar mass, sum up the atomic masses of each element within a compound. For instance, - Magnesium (Mg) has an atomic mass of approximately 24.305 g/mol. - Chlorine (Cl) has an atomic mass of about 35.453 g/mol, but since there are two chlorine atoms in MgCl₂, multiply it by 2.
For MgCl₂: - Calculate: Molar mass = 24.305 + 2(35.453) = 95.211 g/mol.

Using this aggregated molar mass, you can then determine the number of moles of any given mass of the compound. This step is crucial for understanding the composition of the compound at a molecular level.

Ion Dissociation

Ion dissociation is a process in which an ionic compound separates into its individual ions when dissolved in water. This behavior is significant because it directly impacts the concentration of ions in a solution.

In the case of magnesium chloride (MgCl₂), when it dissolves: - It dissociates to form one magnesium ion (Mg²⁺) and two chloride ions (Cl⁻). - MgCl₂ → Mg²⁺ + 2 Cl⁻
This reaction showcases that every one mole of magnesium chloride provides: - 1 mole of Mg²⁺ ions - 2 moles of Cl⁻ ions

Understanding ion dissociation is vital, as it influences the concentration of each ion in the resultant solution. Knowing that each ion forms in different ratios allows you to determine their individual concentrations, which is crucial for many chemical calculations.

Mole Calculation

The concept of moles is central to chemistry, allowing chemists to count particles at an atomic scale. Calculating moles involves converting the mass of a substance to moles using its molar mass.

Here's a simple way to calculate moles:- Use the formula: Number of moles = Mass of the compound (g) / Molar mass (g/mol).
For example, given 0.160 g of MgCl₂ with a molar mass of 95.211 g/mol:- Calculate the moles as follows: \[ \text{moles of MgCl}_2 = \frac{0.160 \, \text{g}}{95.211 \, \text{g/mol}} = 0.001681 \, \text{mol} \]
This calculation provides an estimate of the substance's amount in terms of a number of particles, akin to counting individual atoms or molecules through the mole concept. Understanding how to convert mass to moles using molar mass is foundational in further determining concentrations of solutions.