Question

Suppose \(50.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{CoCl}_{2}\) solution is added to \(25.0 \mathrm{~mL}\) of \(0.350 \mathrm{M} \mathrm{NiCl}_{2}\) solution. Calculate the concentration, in moles per liter, of each of the ions present after mixing.

Short answer

After mixing the solutions, the concentration of each ion is as follows: \( Co^{2+} = 0.1667 \mathrm{M} \), \( Ni^{2+} = 0.1167 \mathrm{M} \), and \( Cl^- = 0.5667 \mathrm{M} \).

Step-by-step solution

Determine initial moles of ions in each solution

To find the initial moles of ions in each solution, use the following formula: moles = molarity × volume (in liters) - For CoCl2 solution: moles of Co^2+ = 0.250 M × 0.050 L = 0.0125 mol moles of Cl^- = (0.250 M × 0.050 L) × 2 = 0.025 mol (since there are 2 moles of Cl^- for each mole of CoCl2) - For NiCl2 solution: moles of Ni^2+ = 0.350 M × 0.025 L = 0.00875 mol moles of Cl^- = (0.350 M × 0.025 L) × 2 = 0.0175 mol (since there are 2 moles of Cl^- for each mole of NiCl2)

Calculate the final volume of the mixed solution

To find the final volume of the mixed solution, just add the individual volumes: final volume = volume of CoCl2 + volume of NiCl2 final volume = 50.0 mL + 25.0 mL = 75.0 mL Now, convert the final volume to liters: final volume = 75.0 mL × \( \frac{1 L}{1000 mL} \) = 0.075 L

Calculate the final concentration of ions

To find the final concentration of each ion, use the formula: molarity = \( \frac{moles}{final~volume~in~liters} \) - For Co^2+ ion: final concentration of Co^2+ = \( \frac{0.0125~mol}{0.075~L} \) = 0.1667 M - For Ni^2+ ion: final concentration of Ni^2+ = \( \frac{0.00875~mol}{0.075~L} \) = 0.1167 M - For Cl^- ion: final concentration of Cl^- = \( \frac{(0.025 + 0.0175)~mol}{0.075~L} \) = \( \frac{0.0425~mol}{0.075~L} \) = 0.5667 M Therefore, the concentration of each ion after mixing is 0.1667 M for Co^2+, 0.1167 M for Ni^2+, and 0.5667 M for Cl^-.

Key concepts

Molarity Calculation

Molarity is a measure of the concentration of a solute in a solution. It is expressed as moles of solute per liter of solution. Calculating molarity provides insight into how much of a particular substance is present in a given volume of solution. To compute molarity, use the formula:\[\text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]In practice, you begin by determining the number of moles of solute. Then, you divide that by the volume of the solution converted into liters. This will give you the molarity, allowing you to compare concentrations and understand the strength of chemical solutions.

Ions Concentration

In solution chemistry, knowing the concentration of individual ions is crucial for understanding the reaction dynamics. Ions are charged particles that form when a compound dissolves in water. For a compound like \( \text{CoCl}_2 \), it dissociates into \( \text{Co}^{2+} \) and \( \text{Cl}^- \) ions in water. The concentration of each ion can differ based on the number of ions formed per formula unit.To calculate ion concentrations, use the stoichiometry of the compound. For example, every mole of \( \text{CoCl}_2 \) produces 1 mole of \( \text{Co}^{2+} \) and 2 moles of \( \text{Cl}^- \). Therefore, if you know the molarity of \( \text{CoCl}_2 \), you can easily determine the molarity of each ion by considering these ratios.

Chemical Solutions

Chemical solutions are homogeneous mixtures composed of two or more substances. The substance present in the greatest amount is typically the solvent, while the other substances are solutes. In a solution like those encountered in laboratories, it's essential to understand how the solutes (often salts, acids, or bases) impact the solution’s behavior. Studying chemical solutions involves looking at how solutes dissolve in solvents and the resultant ion concentrations. During dissolution, the compound breaks down into constituent ions, which then disperse uniformly throughout the solvent - usually water in aqueous solutions. The properties of the solution can be influenced significantly by these ions, affecting factors like conductivity, boiling point, and reactivity.

Volumes and Moles in Mixtures

Understanding volumes and moles in mixtures is integral for accurate chemical analysis. When solutions are mixed, their volumes are combined, and the moles of individual solutes build up in the mixture. Knowing how to manage these calculations helps in achieving the desired concentration for various experimental or industrial processes. The key is tracking the total moles of each substance by multiplying the initial molarity by the initial volume (converted to liters). When mixing, sum the moles from each solution and adjust the volume to get the new molarity. This technique is useful in creating solutions with specific concentrations or analyzing the possible chemical reactions between mixed solutions.