Describe how you would make \(500.0 \mathrm{~mL}\) of a \(0.200 \mathrm{M}\) \(\mathrm{NaOH}\) solution from a \(15.0 \mathrm{M}\) stock \(\mathrm{NaOH}\) solution.

The dilution formula is a simple yet powerful tool in chemistry, allowing scientists and students alike to prepare solutions of a desired concentration from a more concentrated stock solution. The key relationship given by the formula is expressed as:
\( C_1V_1 = C_2V_2 \).
Here, \(C_1\) represents the concentration of the original, more concentrated solution, while \(V_1\) is the volume of this stock solution that you need to use. Conversely, \(C_2\) is the concentration of the target, diluted solution, and \(V_2\) is its total volume. The trick in using this formula is in the rearrangement to solve for the unknown quantity, which usually is the volume of stock solution needed—\(V_1\). Through cross multiplication and division, you can isolate this value, leading to a straightforward equation:
\( V_1 = \frac{C_2V_2}{C_1} \).

Molarity, denoted as M, is a unit of concentration in chemistry that specifies the number of moles of a solute per liter of solution. It is one of the most common units used to express concentration because it directly relates to the amount of substance and the volume of the solution, thereby linking stoichiometry with volume measurement.

Calculating Molarity

To calculate molarity, you use the formula:
\( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \).
This equation is essential when preparing solutions of precise concentrations, as well as in stoichiometric calculations which involve reactions in solution. Understanding molarity is especially important when working with reactions that take place in an aqueous medium, where reactions rates and equilibrium states are highly dependent on the concentration of the dissolved substances.

Volume calculation is fundamental when preparing diluted solutions from concentrated stock solutions. The volume of the stock solution required, based on the dilution equation, must be accurately measured to achieve the intended molarity of the diluted solution.

Accurate Measurement Techniques

For optimal results, using precise instruments such as pipettes or volumetric flasks is necessary, which will ensure that the dilution process is as accurate as possible. Additionally, when precision is key, be mindful of the meniscus—the curve seen at the top of a liquid in response to its container. Measurements should always be taken from the bottom of the meniscus at eye level to maintain consistency and accuracy.

Sodium hydroxide (OH) is a commonly used strong base in the laboratory. When working with \(NaOH\) solutions, it's important to recognize that the substance is highly reactive and caustic, requiring careful handling, proper PPE, and consideration of safety protocols.

Preparing \(NaOH\) Solutions

When diluting a stock solution of \(NaOH\), the process should be conducted slowly to control exothermic reactions. The solution should be mixed thoroughly to ensure a homogenous mixture. Additionally, \(NaOH\) solutions have a high affinity for carbon dioxide from the air, forming sodium carbonate, which can affect the concentration of the solution. Therefore, when preparing solutions for sensitive experiments, it's advisable to use freshly prepared \(NaOH\) solutions, avoiding exposure to air for extended periods.