Question

What is the calcium concentration of a solution formed by adding \(1 \mathrm{~mol}\) of \(\mathrm{CaCl}_2\) to \(1 \mathrm{~L}\) of distilled water at \(298 \mathrm{~K}\) ? 1\. \(1 M\) 2\. \(1 \mathrm{~m}\) 3\. \(2 M\) 4\. \(2 m\)

Short answer

1. \(1 M\)

Step-by-step solution

Writing the dissolution equation for CaCl2

When CaCl2 dissolves in water, it dissociates into its constituent ions. The balanced equation for this process is: \[CaCl_2 (s) \rightarrow Ca^{2+} (aq) + 2Cl^- (aq)\] This means that for every 1 mole of CaCl2, 1 mole of calcium ions (Ca^2+) and 2 moles of chloride ions (Cl^-) are produced in the solution.

Calculating the initial moles and volume of the solution

We are given that 1 mol of CaCl2 is added to 1 L of distilled water. Thus, we have: Initial moles of CaCl2 = 1 mol We also have the volume of the solution: V = 1 L

Calculating moles of calcium ions

As we know from step 1, 1 mole of CaCl2 produces 1 mole of calcium ions (Ca^2+). Therefore, the moles of calcium ions in the solution will be equal to the initial moles of CaCl2. Moles of Ca^2+ = Initial moles of CaCl2 = 1 mol

Calculating the molarity of calcium ions

Molarity (M) is defined as the number of moles of solute per liter of solution. We have the moles of calcium ions and the volume of the solution, so we can calculate the molarity as: M = (Moles of Ca^2+) / V M = (1 mol) / (1 L) M = 1 mol/L So, the calcium concentration in the solution is 1 M. Looking at the given options, our answer is: 1. \(1 M\)

Key concepts

Molarity Calculation

Molarity is a fundamental concept in chemistry. It defines the concentration of a solute in a solution. The molarity (often represented by the symbol M) is calculated using the formula:

• M = \( \frac{\text{moles of solute}}{\text{liters of solution}} \)

To determine the molarity of a solution, you need two pieces of information:

• The number of moles of the solute
• The total volume of the solution in liters

In our original problem, 1 mole of \( \text{CaCl}_2 \) is dissolved in 1 liter of water. The dissolution results in 1 mole of calcium ions \( \text{Ca}^{2+} \) in the solution.
By applying the molarity formula, the molarity of calcium ions is \( 1 \text{ mol/L or 1 M} \). This means that for every liter of the solution, there is 1 mole of calcium ions. It's important to note that the temperature provided (298 K) does not affect molarity unless discussing temperature-dependent reactions.

Ionic Dissolution

Ionic dissolution is the process where ionic compounds, such as \( \text{CaCl}_2 \), dissociate into their respective ions when dissolved in water. This is key to understanding how solutes behave in solutions.

When \( \text{CaCl}_2 \) is added to water, it separates into one mole of calcium ions \( \text{Ca}^{2+} \) and two moles of chloride ions \( \text{Cl}^-\). The dissolution can be expressed through the chemical equation:

• \( \text{CaCl}_2 (s) \rightarrow \text{Ca}^{2+} (aq) + 2\text{Cl}^- (aq) \)

This indicates a complete breakdown of the solid ionic compound into its constituent ions in the solution.

For calculations, remember that the stoichiometry of the dissolution reaction defines the number of ions formed. This understanding is crucial in predicting outcomes in chemical reactions and preparatory steps for laboratory experiments.

Stoichiometry

Stoichiometry involves using balanced chemical equations to calculate the relationships between reactants and products. It lets chemists predict how many moles of products will result from a given amount of reactants, using molar ratios derived from balanced equations.

• The balanced equation for \( \text{CaCl}_2 \) dissolution: \[ \text{CaCl}_2 (s) \rightarrow \text{Ca}^{2+} (aq) + 2\text{Cl}^- (aq) \]

In this reaction, the stoichiometry shows that for every mole of \( \text{CaCl}_2 \) dissociated, 1 mole of \( \text{Ca}^{2+} \) and 2 moles of \( \text{Cl}^- \) are produced.
This stoichiometric relationship is crucial for calculations involving ion concentration and determining product formation in chemical reactions. It ensures accurate chemical and quantitative analysis by maintaining the balance of reactions.

Chemical Equilibrium

Chemical equilibrium refers to the point in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in stable concentration levels of reactants and products. Although \( \text{CaCl}_2 \) dissolution itself is not reversible, understanding equilibrium is important in a broader context where ionic solutions interact with other compounds.

In a solution, ions are constantly moving and can engage in reactions that by themselves may reach equilibrium, influencing the solution's behavior.
Chemical equilibrium concepts, like the equilibrium constant (K), help predict and calculate the extent of reactions, guide solution preparation, and interpret ionic interactions. These principles are vital for understanding reactions in various industrial and research settings, where conditions may trigger new equilibrium states when mixing different solutions or compounds.