Give precise instructions to your laboratory assistant as to how to prepare \(0.500 \mathrm{~L}\) of a \(1.50 \mathrm{M}\) aqueous solution of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\). Remember that she will be measuring out the sucrose in grams. She has available a 0.50-L volumetric flask.

When working in a lab, understanding how to calculate molarity is crucial for creating precise chemical solutions. Molarity, often denoted as M, is a way of expressing the concentration of a solution. It is defined as the number of moles of solute present in one liter of solution.

To calculate molarity, you use the formula:
\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]
Let's break this down using our exercise as an example. We need to prepare 0.500 liters of a 1.50 M sucrose solution. We first identify that we're dealing with sucrose, \(C_{12}H_{22}O_{11}\), as our solute. To find the moles of sucrose required, we simply multiply the molarity (1.50 M) by the volume of the solution (0.500 L). Effectively, this tells us how many moles of sucrose are needed to achieve the desired concentration in half a liter of water.

After calculating the moles required for our solution, we need to convert that amount into a weight in grams since our laboratory measurements are more conveniently taken in mass rather than moles. We do this conversion using the molar mass of the solute.

The equation for this conversion is simple:
\[\text{Weight of solute (g)} = \text{Moles of solute} \times \text{Molar Mass (g/mol)}\]
The molar mass, which is the weight of one mole of a substance, is unique to each compound and is calculated by adding together the atomic masses of the elements that comprise it. In our sucrose example, the molar mass is 342.30 g/mol. So, if we have already determined that we need 0.75 moles of sucrose for our solution, we multiply this number by the molar mass to convert it to grams.

A volumetric flask is a type of laboratory glassware that is specifically designed to prepare solutions of a precise volume. It has a flat bottom, a long neck, and a single etched mark that indicates a specific volume when filled to that point.

Here's the proper usage: Place the dry flask on a balance, tare it, add the required weight of the solid solute, which you've already calculated, and then add solvent – typically distilled or deionized water – up to the mark on the neck. By carefully adding water until the bottom of the meniscus (the curve seen at the top of the liquid) touches the mark, you'll ensure the correct final volume of the solution.

The final step in preparing an aqueous solution is to ensure that it is completely homogeneous, meaning that the solute has been evenly dispersed throughout the solvent. This is critical for the accuracy of experiments using the solution.

Once the solute is added to the solvent in the volumetric flask and filled to the mark, placing the stopper on the flask and inverting it multiple times is an effective way to mix it. The process must be gentle to avoid creating bubbles or splashing, which could lead to an incorrect volume or concentration. As we noted in the exercise improvement advice, this step helps to achieve a uniform concentration throughout the solution, ensuring that it's ready for use in experiments.