A solution is prepared by dissolving 10.8 g ammonium sulfate in enough water to make 100.0 mL of stock solution. A 10.00-mL sample of this stock solution is added to 50.00 mL of water. Calculate the concentration of ammonium ions and sulfate ions in the final solution.

First, we need to find the moles of ammonium sulfate in the stock solution. The formula of ammonium sulfate is (NH4)2SO4, and its molar mass is 132.14 g/mol. The mass given is 10.8 g. To find the moles, we will use the formula: Moles = mass (g) / molar mass (g/mol) Moles of ammonium sulfate = \( \frac{10.8 \,\text{g}}{132.14 \,\text{g/mol}} \)

We are given that the stock solution has a volume of 100.0 mL. To find the concentration of ammonium sulfate in the stock solution, we can use the formula: Concentration = Moles / Volume (L) The volume should be converted to liters: Volume = 100.0 mL * \( \frac{1 \,\text{L}}{1000 \,\text{mL}} \) = 0.100 L Concentration of ammonium sulfate = \( \frac{\text{Moles of ammonium sulfate}}{0.100 \,\text{L}} \)

A 10.00 mL sample of the stock solution is taken. Since the concentration of a solution is uniform, we can use the same process as in step 2 to find the moles of ammonium sulfate in this sample: Moles of ammonium sulfate = Concentration of ammonium sulfate * Volume of the sample (L) Volume of the sample = 10.00 mL * \( \frac{1 \,\text{L}}{1000 \,\text{mL}} \) = 0.010 L Moles of ammonium sulfate in the sample = Concentration of ammonium sulfate * 0.010 L Since there are two ammonium ions (NH4+) and one sulfate ion (SO4^2-) in each ammonium sulfate molecule, the moles of ammonium ions in the sample will be twice the moles of ammonium sulfate, and the moles of sulfate ions will be equal to the moles of ammonium sulfate. Moles of ammonium ions = 2 * Moles of ammonium sulfate in the sample Moles of sulfate ions = Moles of ammonium sulfate in the sample

We are given that the sample is added to 50.00 mL of water. Since the volumes are additive, the total volume of the final solution is 50.00 + 10.00 = 60.00 mL. Since the moles of ammonium and sulfate ions in the final solution are equal to those in the sample, we can move on to step 5.

The final solution has a combined volume of 60.00 mL. To find the concentration of ammonium and sulfate ions in the final solution, we can use the formula: Concentration = Moles / Volume (L) Volume of the final solution = 60.00 mL * \( \frac{1 \,\text{L}}{1000 \,\text{mL}} \) = 0.060 L Concentration of ammonium ions = \( \frac{\text{Moles of ammonium ions}}{0.060 \,\text{L}} \) Concentration of sulfate ions = \( \frac{\text{Moles of sulfate ions}}{0.060 \,\text{L}} \) Now, we can plug in the values from the previous steps to find the final concentrations for ammonium and sulfate ions in the final solution.