In this example problem, we will calculate the final sulfate ion concentration in a dilute solution given an initial concentrated solution. Our problem reads: "A concentrated solution of aqueous aluminum sulfate is made by dissolving 274 grams of solid aluminum sulfate in enough water to make 975 milliliters of solution. Then, 7.5 milliliters of this concentrated solution is added to 60 milliliters of water. Calculate the sulfate ion concentration in the final dilute solution." Our first step is to calculate the sulfate ion concentration in the concentrated solution. We'll do this using our equation for molarity: Molarity equals moles of solute divided by liters of solution. To calculate the moles of our solute, which is sulfate, we'll start with 274 grams of aluminum sulfate. In our dimensional analysis, we'll convert from grams of aluminum sulfate to moles of aluminum sulfate using the molar mass of aluminum sulfate. Then, we can convert from moles of aluminum sulfate to moles of just sulfate using the number of sulfate ions in the formula unit. There are three sulfates in aluminum sulfate. Performing this calculation, we get 2.4 moles of sulfate. Next, we'll calculate our liters of solution. We're told that we add enough water to make 975 milliliters of solution, and we can convert this into liters of solution using dimensional analysis. We'll get 0.975 liters of solution. Next, we can plug both of these numbers into our equation at the top, so that we have 2.4 moles of sulfate divided by 0.975 liters of solution. We'll get 2.46 molar sulfate in our concentrated solution. Our next step is a solution dilution problem. We're going to dilute 7.5 milliliters of this concentrated solution with 60 milliliters of water. For solution dilution, we can use the equation M1V1 = M2V2. Solving for M2, or the concentration of our dilute solution, it equals (M1V1) / V2. The concentration of sulfate in our concentrated solution is 2.46 molar sulfate, and we're using 7.5 milliliters of this concentrated solution. The volume of our dilute solution is 60 milliliters of water plus 7.5 milliliters of the concentrated solution (assuming a linear addition of volumes). Performing this calculation, we should get 0.273 molar sulfate in the dilute solution.