A sample of \(\mathrm{NaOH}\) weighing \(0.38 \mathrm{~g}\) is dissolved in water and the solution is made to \(50.0 \mathrm{~mL}\) in a volumetric flask. What is the molarity of the resulting solution?

Understanding the molar mass of a substance is crucial when it comes to chemical calculations. The molar mass is the weight of one mole of a chemical compound or element and is usually expressed in grams per mole (g/mol). For instance, the molar mass of Sodium Hydroxide (NaOH) is approximately 40.0 g/mol. To find the molar mass, you add the atomic masses of each element in the compound, obtained from the periodic table. Knowing this value allows you to convert between mass and moles of a substance, which is a fundamental step in molarity calculations.

In our exercise example, to determine the number of moles of NaOH, we use its molar mass. You'll often find that the calculation is a simple division: mass of the substance (in grams) divided by the molar mass (in g/mol). Understanding this relationship helps ensure that when we weigh out a substance, we can relate it to the mole concept, which is the foundation for understanding chemical reactions and solution concentrations.

The concept of moles of solute is integral to chemistry. A mole represents a specific number of particles, roughly 6.022 x 10^23, known as Avogadro's number. When we speak of the moles of solute in a solution, we are referring to the amount of that substance present, in moles, before it's dissolved in the solvent.For instance, in our exercise, the task is to determine how much NaOH there is in terms of moles. By defining the molar mass of NaOH, and understanding the mass of NaOH we have, we can calculate the moles of solute using the formula:\[\begin{equation}\text{number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\end{equation}\].This calculation will give us the amount in moles, which is essential in finding out the molarity of the solution.

Since molarity is defined in terms of liters of solution, converting volume measurements is often necessary. This is especially true because laboratory measurements are frequently given in milliliters (mL). Converting milliliters to liters is straightforward:To convert mL to L, you divide by 1000, since there are 1000 mL in one liter.\[\begin{equation}\text{Volume (L)} = \frac{\text{Volume (mL)}}{1000}\end{equation}\].This step is important because failing to convert to the correct units could lead to incorrect calculations of molarity. In our example, the 50.0 mL of solution needs to be converted to 0.050 L before we can use it in the molarity calculation. By standardizing the volume unit to liters, we can apply it universally to calculate the concentration of any solution.

Molarity is a measure of solution concentration, providing valuable information about the ratio of solute to solvent in a solution. Defined as moles of solute per liter of solution, it's symbolized by the capital letter M and mathematically represented as\[\begin{equation}M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}\end{equation}\].Understanding molarity is essential for tasks such as diluting solutions to a desired concentration or combining reagents for a reaction. In the example given, once we have the moles of NaOH and the volume of the solution converted to liters, we find the molarity by dividing the number of moles by the volume in liters. The resulting figure represents the molarity of the NaOH solution, which indicates how concentrated the solution is. The higher the molarity, the more concentrated the solution.