You have a sugar solution (solution \(A\) ) with concentration \(x\) You pour one- fourth of this solution into a beaker, and add an equivalent volume of water (solution \(B\) ). a. What is the ratio of sugar in solutions \(A\) and \(B\) ? b. Compare the volumes of solutions \(A\) and \(B\). c. What is the ratio of the concentrations of sugar in solutions \(A\) and \(B\) ?

Understanding solution concentration is essential when studying chemistry, and sugar solutions provide a practical example. The concentration of a solution tells us how much of a substance is dissolved in a certain amount of solvent. In our given problem, we have a sugar solution with an initial concentration represented by the variable x.

When tackling concentrations, it's helpful to keep in mind that the concentration can be expressed in various ways, such as mass per unit volume, percent composition, or molarity, depending on the context and the requirements of the problem at hand.

For a sugar solution, if the concentration is high, it means that more sugar is dissolved in less water; conversely, a low concentration means less sugar in more water. These concepts come into play when we dilute solution A to create solution B by adding water, which is exactly what the problem presents to us—diluting the original sugar solution.

The volume ratio is a comparison between the amounts of two substances or solutions. It's like a recipe that calls for two parts of one ingredient and one part of another—this is a volume ratio of 2:1. In our textbook problem, we find the volume ratio by comparing the amount of original solution A to the new solution B.

To calculate, we see that one-fourth of solution A's volume is poured into a new beaker and then made up to the same volume with water, creating solution B. Hence, if the entire solution A is represented as V_A, the beaker now contains V_A/4 of solution A and V_A/4 of water, making the total volume of B exactly V_A/4. Thus, the volume ratio of A to B is 4:1; there is four times more solution A than solution B when comparing their total volumes available.

Comparing concentrations helps to understand the effect of dilution or concentration of solutions. When we say we are comparing concentrations, we are essentially examining how the amount of solute varies relative to the solvent's volume. In the exercise, we diluted a sugar solution and needed to find how its concentration changed.

In the process of dilution, we took one-fourth of the sugar solution with concentration x and added an equal volume of water. By adding water, we effectively spread the existing sugar across a greater volume, halving the original concentration for solution B, leading to a new concentration x/2.

Therefore, the concentration comparison ratio of A to B is 2:1. This means solution A is twice as concentrated as solution B. Understanding this change in concentration is fundamental for various applications in chemistry, medicine, and culinary practices, as it determines the chemical potential and behavior of solutions.