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Chapter 4: Problem 46

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

Expert verified
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

01

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
02

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
03

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
04

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.

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