A 3.5-L sample of a \(5.8 \mathrm{M} \mathrm{NaCl}\) solution is diluted to \(55 \mathrm{~L}\). What is the molarity of the diluted solution?

Molarity, often represented by the symbol M, is a measure of the concentration of a solute in a solution. In chemistry, it is one of the most commonly used units to express the concentration. Specifically, molarity is defined as the number of moles of solute divided by the volume of the solution in liters. The formula to calculate molarity is:
\[ M = \frac{moles}{volume} \]
Where 'M' stands for molarity, 'moles' represents the amount of solute in moles, and 'volume' is the total volume of solution in liters. Understanding this concept allows students to grasp how much of a substance is present in a given volume of liquid, which is crucial in many chemical reactions and processes.

In chemistry, the concentration of a solution is a description of how much solute is dissolved in a given amount of solvent. Concentration can be expressed in several ways, such as molarity, molality, percent composition by mass, or parts per million, depending on the precision or context required. Concentration is a critical factor in reactions because it influences the rate and direction of reactions. A high concentration means there is more solute available to react, while a low concentration reduces the chances of collision between reactant molecules, thus affecting the reaction rate.

The concept of moles is fundamental to quantifying matter in chemistry. A mole is the amount of substance that contains as many elementary entities, like atoms or molecules, as there are atoms in 12 grams of carbon-12. This number is known as Avogadro's number and is approximately \(6.022 \times 10^{23}\). To calculate the number of moles of a substance, we generally use the formula:
\[ moles = \frac{mass}{molar~mass} \]
However, in the context of a solution, where molarity (M) is given, the formula for moles calculation becomes:
\[ moles = molarity \times volume \]
This equation establishes a direct relationship between the molarity of a solution, its volume, and the number of moles of solute present.

Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. This process doesn't change the amount of solute present, just its concentration. In practical terms, when you dilute a solution, you are spreading the solute out over a larger volume. The key concept in dilution is the conservation of moles of solute: the number of moles before dilution is equal to the number of moles after dilution. Using the formula:
\[ M_1 V_1 = M_2 V_2 \]
where \(M_1\) and \(V_1\) are the molarity and volume of the initial, more concentrated solution, and \(M_2\) and \(V_2\) are the molarity and volume of the final, diluted solution, students can calculate the new concentration after dilution. This formula encapsulates the dilution process in a simple mathematical expression and is particularly helpful for solving related chemistry problems.