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

When 0.160 g of MgCl₂ is dissolved in 100.0 mL of solution, the concentration of Mg²⁺ ions is 0.0168 M, and the concentration of Cl⁻ ions is 0.0336 M.

Step-by-step solution

Convert grams of MgCl₂ to moles.

To find the moles of MgCl₂ dissolved, we must first convert the 0.160 g of MgCl₂ to moles. Using the molar mass of MgCl₂, which can be found by adding the molar masses of Mg (24.31 g/mol) and two Cl atoms (2 x 35.45 g/mol): Molar mass of MgCl₂ = 24.31 g/mol + (2 x 35.45 g/mol) = 95.21 g/mol Now, convert the mass of MgCl₂ to moles using the molar mass: Moles of MgCl₂ = (0.160 g) / (95.21 g/mol) = 0.00168 mol

Calculate the moles of Mg²⁺ and Cl⁻ ions produced.

When MgCl₂ dissolves, it produces one mole of Mg²⁺ ions and two moles of Cl⁻ ions for each mole of MgCl₂. Therefore, we can find the moles of Mg²⁺ and Cl⁻ ions produced as follows: Moles of Mg²⁺ = Moles of MgCl₂ = 0.00168 mol Moles of Cl⁻ = 2 x Moles of MgCl₂ = 2 x 0.00168 mol = 0.00336 mol

Convert the volume of the solution to liters.

The volume of the solution is given in milliliters (mL), and we need to convert it to liters (L) to calculate the molar concentration. To do this, divide the volume in milliliters by 1000: Volume in liters = 100.0 mL / 1000 = 0.100 L

Calculate the concentration of Mg²⁺ and Cl⁻ ions.

Now we can find the concentration of Mg²⁺ and Cl⁻ ions in the solution by dividing the moles of each ion by the volume of the solution in liters: Concentration of Mg²⁺ = Moles of Mg²⁺ / Volume in liters = 0.00168 mol / 0.100 L = 0.0168 M Concentration of Cl⁻ = Moles of Cl⁻ / Volume in liters = 0.00336 mol / 0.100 L = 0.0336 M Therefore, when 0.160 g of MgCl₂ is dissolved in 100.0 mL of solution, the concentration of Mg²⁺ ions is 0.0168 M, and the concentration of Cl⁻ ions is 0.0336 M.

Key concepts

Understanding Molarity

When dealing with solutions in chemistry, a common way to express the concentration is through molarity. Molarity is defined as the number of moles of solute (the substance being dissolved) per liter of solution.
In formula terms, it's represented as:\( M = \frac{n}{V} \)where \( n \) is the number of moles of solute, and \( V \) is the volume of solution in liters.

• Molarity helps us understand how concentrated a solution is.
• Higher molarity means a more concentrated solution with more solute particles per unit volume.
• It is expressed in units of moles per liter (M).

For example, the earlier problem resulted in a molarity calculation:
Concentration of Mg²⁺ is 0.0168 M.
This directly tells us how many moles of magnesium ions are present per litre of the solution.

Ion Dissolution Process

Ion dissolution is the process where ionic compounds, like \( \text{MgCl}_2 \), separate into their respective ions in a solution.
This is a critical concept in understanding how ions interact in water and influence the solution's properties.When \( \text{MgCl}_2 \) dissolves in water:- It dissociates into one \( \text{Mg}^{2+} \) ion and two \( \text{Cl}^- \) ions.- The dissolution equation is represented as:\[ \text{MgCl}_2 (s) \rightarrow \text{Mg}^{2+} (aq) + 2 \text{Cl}^- (aq) \]

• Ionic compounds dissolve to form a solution with free ions capable of conducting electricity, often known as an electrolytic solution.
• The molar relationships in dissolution help in calculating the resulting ion concentrations, as seen by multiplying the moles of compound by the number of ions produced.

The earlier problem highlighted that 0.00168 moles of \( \text{MgCl}_2 \) leads to 0.00168 moles of \( \text{Mg}^{2+} \) and 0.00336 moles of \( \text{Cl}^- \). This straightforward stoichiometry helps understand precisely what happens at a molecular level during dissolution.

Chemical Calculations in Solutions

Chemical calculations are essential to comprehend solutions and their specific characteristics.
Calculations typically involve converting mass to moles, determining volume in liters, and understanding reaction stoichiometry.Here's how the process plays out step by step:

• Mass to Moles: Use the molar mass to convert the mass of a compound to moles, as seen in the conversion of 0.160 g of \( \text{MgCl}_2 \) to 0.00168 mol.
• Volume Conversion: Convert the volume of solution from mL to liters for use in molarity calculations. For example, 100.0 mL equals 0.100 L.
• Moles of Ions: Based on the stoichiometry of dissolution, calculate the amount of each ion present.

These calculations form the bedrock of many solution-based problems in chemistry. By understanding each small step, you'll be empowered to unravel complex chemistry problems efficiently.