Question

A mixture contains \(76.5 \% \mathrm{NaCl}, 6.5 \% \mathrm{MgCl}_{2}\), and \(17.0 \% \mathrm{Na}_{2} \mathrm{SO}_{4}\) by mass. What is the molarity of \(\mathrm{Cl}^{-}\) ions in a solution formed by dissolving \(7.50 \mathrm{~g}\) of the mixture in enough water to form \(500.0 \mathrm{~mL}\) of solution?

Short answer

The molarity of Cl⁻ ions in the solution formed by dissolving 7.50 g of the mixture in enough water to form 500.0 mL of solution is \(0.216 \text{ M}\).

Step-by-step solution

Calculate the mass of the components in the mixture

Find the mass of each component in the mixture: - Mass of NaCl: \((7.5\text{ g})\times 0.765 = 5.7375\text{ g}\) - Mass of MgCl₂: \((7.5\text{ g})\times 0.065 = 0.4875\text{ g}\) - Mass of Na₂SO₄: \((7.5\text{ g})\times 0.170 = 1.275\text{ g}\)

Calculate the mass of Cl⁻ from each component

Determine the mass of chloride ions (Cl⁻) from NaCl and MgCl₂: - Mass of Cl⁻ from NaCl: \(\frac{5.7375\text{ g NaCl}}{1} \times \frac{35.45 \text{ g Cl⁻}}{58.44 \text{ g NaCl}} = 3.4074\text{ g Cl⁻}\) - Mass of Cl⁻ from MgCl₂: \(\frac{0.4875\text{ g MgCl₂}}{1} \times \frac{2 \times 35.45 \text{ g Cl⁻}}{95.21 \text{ g MgCl₂}} = 0.4424\text{ g Cl⁻}\)

Calculate the total mass of Cl⁻

Add the mass of Cl⁻ from NaCl and MgCl₂ to get the total mass of Cl⁻ in the mixture: - Total mass of Cl⁻: \(3.4074\text{ g Cl⁻} + 0.4424\text{ g Cl⁻} = 3.8498\text{ g Cl⁻}\)

Calculate the molarity of Cl⁻

Use the mass of Cl⁻ and the volume of the solution (500.0 mL = 0.5 L) to calculate the molarity: - Molarity of Cl⁻: \(\frac{3.8498\text{ g Cl⁻}}{0.5\text{ L}} \times \frac{1 \text{ mol Cl⁻}}{35.45 \text{ g Cl⁻}} = 0.216\text{ M}\) So, the molarity of Cl⁻ ions in the solution is 0.216 M.

Key concepts

Chloride ions

Chloride ions, often denoted as \(\text{Cl}^-\), are negatively charged ions that are a common component of salts such as sodium chloride (\(\text{NaCl}\)) and magnesium chloride (\(\text{MgCl}_2\)). In solutions, chloride ions play a critical role as electrolytes, helping to conduct electricity. The concept of molarity when it comes to chloride ions involves determining how many moles of \(\text{Cl}^-\) are present in a particular volume of solution. It is essential when you need to understand the concentration of chloride in various chemical processes or solutions. When calculating the molarity of \(\text{Cl}^-\) ions in a solution, you must first determine the total mass of chloride ions derived from all compounds in the mixture. Then, you convert this mass into moles using the molar mass of chloride, which is approximately 35.45 g/mol. Finally, divide by the volume of the solution in liters to find the molarity.

NaCl

Sodium chloride, known chemically as \(\text{NaCl}\), is a salt composed of sodium ions (\(\text{Na}^+\)) and chloride ions (\(\text{Cl}^-\)). It's most commonly recognized as table salt and is widely used in food and various industrial applications.NaCl is a critical component when calculating the molarity of chloride ions in a mixture. Each \(\text{NaCl}\) formula unit contains one chloride ion. To find the mass of chloride ions from sodium chloride in a mixture, you multiply the mass of \(\text{NaCl}\) by the proportion of chloride's molar mass over the total molar mass of \(\text{NaCl}\), which is 58.44 g/mol. This tells you how much of that compound's mass contributes to the chloride content in the solution.Knowing the specific mass of \(\text{NaCl}\) in a mixture allows you to calculate how much chloride is being contributed by sodium chloride, aiding in finding the overall concentration of chloride ions.

MgCl₂

Magnesium chloride, chemically represented by \(\text{MgCl}_2\), is made up of one magnesium ion (\(\text{Mg}^{2+}\)) and two chloride ions (\(\text{Cl}^-\)). It's commonly used for dust control, in food additives, and as a source of magnesium in supplements.In terms of calculating solution concentration, \(\text{MgCl}_2\) is significant because each molecule provides two moles of chloride ions. When determining the chloride ion contribution from magnesium chloride, you take the mass of \(\text{MgCl}_2\) in the solution and utilize the compound's molar mass (95.21 g/mol) to find the equivalent mass of chloride ions. You multiply by two since there are two chloride ions per molecule of magnesium chloride.This step is crucial to correctly assess the total amount of chloride ions from all sources in the mixture, particularly when magnesium chloride is a constituent part, ensuring an accurate calculation of overall chloride concentration.

Solution concentration

Solution concentration is a key concept in chemistry, representing the amount of a substance, typically solute, per unit volume of solution. It is most often expressed in terms of molarity (M), which is defined as moles of solute per liter of solution. In the context of our problem, calculating the solution concentration for chloride ions involves accounting for both sodium chloride and magnesium chloride. This requires:

• Determining the mass contribution of chloride ions from each compound in the solution.
• Converting these masses to moles using their respective molar masses.
• Summing these values to find total moles of chloride ions.
• Using the solution volume (in liters) to find molarity by dividing total moles of chloride ions by the volume of the solution in liters.

Understanding solution concentration and how to manipulate it is essential in various scientific and industrial fields, from chemical manufacturing to environmental science.