What mass of solid NaCl do you need to prepare \(400.0 \mathrm{~mL}\) of a \(2.00 \mathrm{M} \mathrm{NaCl}\) solution from scratch? How much water do you add to the \(\mathrm{NaCl}\) ?

Understanding molarity is crucial for preparing solutions in chemistry. Molarity, denoted as M, is a way of expressing the concentration of a solution. It is defined as the number of moles of solute (the substance being dissolved) present in one liter of solution. The formula is simple: \[\begin{equation} Molarity (M) = \frac{moles \, of \, solute}{volume \, of \, solution \, (L)} \end{equation}\]
When calculating molarity, it is important to note that the volume of the solution must be expressed in liters (L), not milliliters (mL) or any other unit. To convert milliliters to liters, divide the volume in milliliters by 1,000. For example, to prepare a solution, if you start with a volume in milliliters, such as 400.0 mL, you would convert it to 0.400 L before using the molarity formula.
In our exercise, we have a desired molarity of 2.00 M and a final solution volume of 400.0 mL, or 0.400 L. To find the moles of NaCl needed, we multiply the molarity by the volume. Ensuring that students understand this step is instrumental in creating accurate solutions in a laboratory setting.

The bridge between the microscopic world of atoms and the macroscopic realm we can measure is moles to mass conversion. A mole, one of chemistry's central units, represents Avogadro's number (\[\begin{equation} 6.022 \times 10^{23} \end{equation}\]
) of particles—whether they are atoms, molecules, ions, or electrons. The relationship between moles and mass is given by the molar mass of a substance, which is the mass in grams of one mole of that substance.
For example, to convert moles of a substance to mass, you multiply the number of moles by the molar mass. The molar mass of a compound like NaCl is the sum of the molar masses of its constituent elements—around 22.99 g/mol for sodium (Na) and 35.45 g/mol for chlorine (Cl), leading to a molar mass of 58.44 g/mol for NaCl.
To calculate the mass needed for our exercise, we multiply the moles of NaCl (0.800) by NaCl's molar mass (58.44 g/mol) to get 46.75 grams. This moles to mass conversion helps in transforming an abstract number of moles into a tangible quantity of substance that can be weighed and used in experiments.

Dilution is the process of decreasing the concentration of a solute in a solution, usually by adding more solvent. When diluting a solution, it's important to understand that the amount of solute remains constant; only the volume of the solution changes. This concept is often expressed by the equation:\[\begin{equation} C_1V_1 = C_2V_2 \end{equation}\]
where \[\begin{equation}C_1\end{equation}\]
is the initial concentration, \[\begin{equation}V_1\end{equation}\]
is the initial volume, \[\begin{equation}C_2\end{equation}\]
is the final concentration, and \[\begin{equation}V_2\end{equation}\]
is the final volume of the solution. It helps to think of this process as mixing a strong, concentrated drink with water to achieve a milder taste.
In the context of our exercise, dilution involves dissolving a specific mass of NaCl (46.75 g) into water to make a total volume of 400.0 mL of solution. In practical terms, we add enough water to the dissolved NaCl to reach the desired final volume. Remember, in our case, since we're making the solution from scratch, the volume of solid NaCl is negligible, and the final solution volume essentially comes from the added water.