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. Assume that the volumes are additive.

Short answer

The final concentrations after mixing the solutions are: Co^(2+) is \(0.1667 M\), Ni^(2+) is \(0.1167 M\), and Cl^(-) is \(0.5667 M\).

Step-by-step solution

Calculate the total moles of each ion in the separate solutions

First, we need to figure out the total moles of each ion in their respective solutions. We can use the equation: moles = Molarity × Volume For 50.0 mL of 0.250 M CoCl2 solution: Moles of Co^(2+) = 0.250 mol/L × 0.050 L = 0.0125 mol Since there are two moles of Cl^(-) for each mole of CoCl2, moles of Cl^(-) = 2 × 0.0125 mol = 0.0250 mol For 25.0 mL of 0.350 M NiCl2 solution: Moles of Ni^(2+) = 0.350 mol/L × 0.025 L = 0.00875 mol Again, since there are two moles of Cl^(-) for each mole of NiCl2, moles of Cl^(-) = 2 × 0.00875 mol = 0.0175 mol

Calculate the final volume of the mixture

Now, we need to find the final volume of the mixture. Since the volumes are additive, we can simply add the initial volumes of the two solutions. Final volume = Volume of CoCl2 + Volume of NiCl2 Final volume = 0.050 L + 0.025 L = 0.075 L

Calculate the final concentration of each ion

Now that we have the total moles of each ion and the final volume of the mixture, we can calculate the final concentration by dividing the moles by the total volume. Final concentration of Co^(2+) = Moles of Co^(2+) / Final volume = 0.0125 mol / 0.075 L = 0.1667 M Final concentration of Ni^(2+) = Moles of Ni^(2+) / Final volume = 0.00875 mol / 0.075 L = 0.1167 M Final concentration of Cl^(-) = Total moles of Cl^(-) / Final volume = (0.0250 mol + 0.0175 mol) / 0.075 L = 0.5667 M

Final answer

So, the final concentration of Co^(2+) is 0.1667 M, the final concentration of Ni^(2+) is 0.1167 M, and the final concentration of Cl^(-) is 0.5667 M after mixing the solutions.

Key concepts

Molarity Calculation

Molarity is a measure of the concentration of a solution. It indicates how much of a solute is present in a given volume of solution. To calculate molarity, we use the formula: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]For example, if you have a solution with a known amount of solute, molarity helps you find out how concentrated it is. In the context of the exercise, 50.0 mL of a CoCl\( _{2} \) solution with a molarity of 0.250 M means there are 0.0125 moles of Co\( ^{2+} \) in the solution. This same calculation method applies to any solute in a solution.

• Measure the volume of your solution in liters.
• Know the number of moles of your solute.
• Apply the formula to determine molarity.

Molarity helps chemists understand the strength of a solution and predict how it will react with other substances. It's pivotal in many chemistry calculations.

Ion Concentration

Ion concentration refers to the amount of ions dissolved in a solution. Each salt, like CoCl\( _{2} \) or NiCl\( _{2} \), dissociates into ions when dissolved in water. In this case, CoCl\(_2\) dissociates into one Co\( ^{2+} \) ion and two Cl\( ^{-} \) ions. Similarly, NiCl\(_2\) produces one Ni\( ^{2+} \) ion and two Cl\( ^{-} \) ions.To calculate the concentration of ions after the solutions are mixed:- Calculate the moles of each type of ion.- Consider that for every mole of CoCl\( _{2} \) or NiCl\( _{2} \), two moles of Cl\( ^{-} \) are produced.- Add the moles of the same ions from different solutions together.Finally, divide the total moles of each ion by the final volume of the solution to find the concentration. Understanding ion concentration is crucial for balancing reactions and anticipating how a solution will behave chemically.

Moles Calculation

Calculating moles is essential for determining how many molecules or atoms are present in a solution. "Moles" refers to the count of entities like ions or molecules in chemistry.The equation for calculating moles is:\[ \text{Moles} = \text{Molarity} \times \text{Volume in Liters} \]In the given exercise, for instance, by multiplying the molarity of a solution by its volume, you can find out how many moles of Co\( ^{2+} \) ions and Ni\( ^{2+} \) ions you have. Here are the steps to follow:

• Convert volume from milliliters to liters. For example, 50.0 mL becomes 0.050 L.
• Use the molarity to find moles. For a 0.250 M solution with a 0.050 L volume, you get 0.0125 moles of the solute.

Understanding the concept of moles can help you predict the proportions and amounts of reactants required in chemical reactions.

Chemical Mixture

A chemical mixture occurs when two or more substances are combined in such a way that they remain distinct at the microscopic level. In this exercise, we dealt with mixing two solutions: CoCl\( _{2} \) and NiCl\(_2\). When combining solutions, it is important to consider:- The total number of moles of each component.- The total final volume of the mixture, which is the sum of the individual volumes, assuming they are additive as in this case.- The final concentration of each ion.We assume that after mixing, the volumes are simply added together. This helps in calculating the final concentrations. Calculated concentrations reflect the mixture's behavior in terms of chemical reactions or physical properties. By understanding how different ions interact in a mixed solution, chemists can manipulate the conditions to achieve desired outcomes, such as precipitating a particular ion or adjusting the solution's pH.