Video Transcript
50 grams of a 26 percent mass by mass solution was mixed together with 130 grams of a 17 percent mass by mass solution. What is the percentage concentration by mass of the new solution?
Let’s draw a diagram to help us understand this question. 50 grams of a 26 percent mass by mass solution, what we will call solution A, was mixed together with 130 grams of a 17 percent mass by mass solution, what we will call solution B. The combination of these two solutions produces a third solution, solution C. We want to determine the percentage concentration by mass of solution C. To do so, we must first recognize the equation for percent concentration. Percent concentration equals the mass of the solute divided by the mass of the solution times 100 percent.
We can find the mass of the solute in solution C by summing together the mass of the solute in solutions A and B. Likewise, we can find the mass of solution C by adding the mass of solution A to the mass of solution B. We already know the mass of solution A to be 50 grams and the mass of solution B to be 130 grams. This means that the mass of solution C must be 180 grams. We don’t know the mass of the solute in solution A or B. We can calculate the mass of the solute by rearranging the percent concentration equation. The mass of the solute equals the percent concentration divided by 100 percent times the mass of solution.
Let’s calculate the mass of the solute in solution A. We can substitute solution A’s percent concentration and mass of solution into the equation and determine the mass of the solute in solution A to be 13 grams. We’ll repeat this process for solution B. We can substitute solution B’s percent concentration and mass of solution into the equation and determine that the mass of the solute in solution B is 22.1 grams. Now, we can add together the mass of the solute in solution A and the mass of the solute in solution B to determine that the mass of the solute in solution C is 35.1 grams.
Finally, we can return to the percent concentration equation and substitute the mass of the solute in solution C and the mass of solution C. Before solving, always make sure that the mass units match. We perform the calculation and determine that the percentage concentration by mass of solution C is 19.5 percent mass by mass.
