Problem 109 - General Chemistry

Question

An aqueous solution contains \(4.50 \mathrm{~g}\) of calcium chloride, \(\mathrm{CaCl}_{2}\), per liter. What is the molarity of \(\mathrm{CaCl}_{2}\) ? When calcium chloride dissolves in water, the calcium ions, \(\mathrm{Ca}^{2+}\), and chloride ions, \(\mathrm{Cl}^{-}\), in the crystal go into the solution. What is the molarity of each ion in the solution?

Step-by-Step Solution

Answer

The molarity of \(\mathrm{CaCl}_2\) is \(0.0405\, \mathrm{mol/L}\), \(\mathrm{Ca}^{2+}\) is \(0.0405\, \mathrm{mol/L}\), and \(\mathrm{Cl}^{-}\) is \(0.0810\, \mathrm{mol/L}\).

Step 1: Calculate Molar Mass of CaCl₂

First, determine the molar mass of \(\mathrm{CaCl}_2\). The atomic mass of \(\mathrm{Ca}\) is approximately \(40.08\,\mathrm{g/mol}\), and the atomic mass of \(\mathrm{Cl}\) is approximately \(35.45\,\mathrm{g/mol}\). Since there are two chloride ions in \(\mathrm{CaCl}_2\), the molar mass is calculated as: \[ \text{Molar Mass of } \mathrm{CaCl}_2 = 40.08 + 2\times 35.45 = 110.98 \, \mathrm{g/mol} \]

Step 2: Calculate Moles of CaCl₂

Using the molar mass, calculate the moles of \(\mathrm{CaCl}_2\) in the solution. You have \(4.50 \, \mathrm{g}\) in 1 liter, so the moles are given by: \[ \text{Moles of } \mathrm{CaCl}_2 = \frac{4.50 \, \mathrm{g}}{110.98 \, \mathrm{g/mol}} \approx 0.0405 \, \mathrm{mol} \]

Step 3: Calculate Molarity of CaCl₂

Molarity is defined as moles of solute per liter of solution. Since the solution is 1 liter, the molarity of \(\mathrm{CaCl}_2\) is: \[ \text{Molarity of } \mathrm{CaCl}_2 = 0.0405 \, \mathrm{mol/L} \]

Step 4: Determine Molarity of Ca²⁺ and Cl⁻ Ions

When \(\mathrm{CaCl}_2\) dissolves, it disassociates into one \(\mathrm{Ca}^{2+}\) ion and two \(\mathrm{Cl}^{-}\) ions. Therefore, the molarity of \(\mathrm{Ca}^{2+}\) ions is the same as \(\mathrm{CaCl}_2\), which is \(0.0405 \, \mathrm{mol/L}\). The molarity of \(\mathrm{Cl}^-\) ions is twice that of \(\mathrm{CaCl}_2\), as each formula unit of \(\mathrm{CaCl}_2\) provides two chloride ions: \[ \text{Molarity of } \mathrm{Cl}^- = 2 \times 0.0405 \, \mathrm{mol/L} = 0.0810 \, \mathrm{mol/L} \]

Key Concepts

Aqueous Solution

An aqueous solution is a mixture where water acts as the solvent. This means water is the component in the largest amount, and other substances dissolve in it. Aqueous solutions are common in many fields like chemistry and biology due to water's excellent solvent properties. - Water can dissolve many substances because it is polar, having a positive and a negative side. - This property allows it to interact and stabilize charged particles, also known as ions, from substances dissolved in it. For example, when you dissolve table salt, \( ext{NaCl}\), in water, the sodium and chloride ions separate, creating an aqueous solution.

Calcium Chloride

Calcium chloride, often represented as \( ext{CaCl}_2\), is a common salt used in various applications such as de-icing roads and in pool maintenance. It consists of one calcium ion and two chloride ions. - When calcium chloride is placed in water, it dissociates, or separates, into individual ions. - This compound is very soluble in water, which makes it ideal for creating concentrated aqueous solutions. Calcium chloride solution's ability to absorb moisture also makes it useful in drying operations.

Calcium Ions

Calcium ions have the chemical symbol \( ext{Ca}^{2+}\). These ions play crucial roles in various biological processes, such as muscle function and bone formation. - In an aqueous solution, calcium ions are completely surrounded by water molecules. - This allows them to move freely, which is critical for their biological activities.In the context of calcium chloride solutions, for every mole of \( ext{CaCl}_2\) that dissolves, one mole of calcium ions is released. This dissociation is straightforward, making calcium ions easily available in the solution.

Chloride Ions

Chloride ions, denoted as \( ext{Cl}^{-}\), are anions, meaning they have a negative charge. These ions are essential in maintaining the electrical neutrality in biological cells and are found abundantly in the human body.- Like calcium ions, chloride ions are well stabilized in aqueous solutions by water molecules.- For each mole of calcium chloride that dissolves, two moles of chloride ions enter the solution.This increase in chloride ion concentration is essential in chemical applications and determines the solution's overall ionic strength.