### Video Transcript

A one-molar solution of CuSO4 is prepared by dissolving 159.5 grams of CuSO4 in water to produce one liter of solution, where the molar mass of oxygen is 16 grams per mole; sulfur, 32 grams per mole; and copper, 63.5 grams per mole. What would happen to the concentration if the amount of water was increased so that the total volume of solution is doubled? (A) The concentration would stay the same. (B) The concentration would double. Or (C) the concentration would halve.

CuSO4 is copper sulfate. One molar is the concentration of the copper sulfate. It can also be written as one mole per liter. So we know that the initial concentration is one mole per liter. But the question asks us, what would happen to the concentration if the amount of water was increased so that the total volume of solution is doubled? To help us answer this, we can use this equation. This equation tells us that the molar concentration in moles per liter is equivalent to the number of moles of solute divided by the total volume of solution in liters. A solute is the minor component of a solution. It is the substance that is described as dissolving. The question tells us that copper sulfate is dissolved, so copper sulfate is the solute.

A solution, on the other hand, is defined as a mixture in which one or more solutes are distributed uniformly within the solvent. We’ve already established that the solute is copper sulfate. A solvent is the major component of a solution into which other substances dissolve. We are told in the question that this is water, so the solution is composed of copper sulfate dissolved in water. We know from the question that the concentration is one mole per liter, so we can replace 𝑛, the number of moles of solute, with one mole and can replace 𝑣, the total volume of solution, with one liter. So all we have done is rearrange the concentration given.

Now that the initial concentration is in this format, we can find out what would happen if the volume was doubled. The question tells us that the amount of water is increased, not the number of moles of solute, so this will still be one mole. The volume of solution, however, has been doubled, so we can multiply the one liter in the initial fraction by two. This would give one mole over two liters, which is equivalent to 0.5 moles per liter. As the initial concentration was one molar, or one mole per liter, and the final concentration was 0.5 moles per liter, we can come to the conclusion that adding that amount of water would halve the concentration.

So the answer to the question “What would happen to the concentration if the amount of water was increased so that the total volume of solution is doubled?” is (C), the concentration would halve.

What would happen to the concentration if the amount of CuSO4 used to prepare the solution was doubled? (A) The concentration would stay the same. (B) The concentration would halve. Or (C) the concentration would double.

We’ve already established that the concentration of the copper sulfate solution can be written as one mole divided by one liter, where the one mole refers to how many moles of copper sulfate there are and the one liter refers to the total volume of the solution, the major component of which is water. The question asks, what would happen to the concentration if the amount of copper sulfate used to prepare the solution was doubled? If the amount of copper sulfate used was doubled, then the number of moles of copper sulfate will double. So we can multiply the number of moles of copper sulfate by two.

Although the amount of copper sulfate used was doubled, the rest of the preparation would remain the same. So the copper sulfate solution would be dissolved in water to produce one liter of solution, so the total volume of solution would still be one liter. We can write the concentration after the amount of copper sulfate has doubled as two moles divided by one liter, or two moles per liter. The concentration has changed from one mole per liter to two moles per liter, so it has doubled.

Therefore, the answer to the question “What would happen to the concentration if the amount of copper sulfate used to prepare the solution was doubled?” is (C), the concentration would double.