Calculate the molarity of each solution. (a) \(0.127 \mathrm{~mol}\) of sucrose in \(655 \mathrm{~mL}\) of solution (b) \(0.205 \mathrm{~mol}\) of \(\mathrm{KNO}_{3}\) in \(0.875 \mathrm{~L}\) of solution (c) \(1.1 \mathrm{~mol}\) of \(\mathrm{KCl}\) in \(2.7 \mathrm{~L}\) of solution

Molarity, often denoted by the symbol 'M', is a measure of the concentration of a solute in a solution. It is a way to express how much of a substance (the solute) is dissolved in a certain volume of liquid (the solvent), which together form the solution. The molarity formula is quite simple:

It is given by:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]
To calculate molarity, you need two key pieces of information: the number of moles of the solute and the volume of the solution in liters. The number of moles is a measure of the quantity of a substance based on the number of particles it contains, whereas the volume should be always considered in liters for the molarity calculations. It’s important to ensure that the units are correct when using this formula to obtain accurate results.

Understanding the difference between a solute and a solution is key when discussing molarity. A solute is a substance that is dissolved in a liquid to create a solution. The solute can be a solid, liquid, or gas, but it’s most commonly a solid in chemistry exercises related to molarity.

In our exercise, substances like sucrose, \( \mathrm{KNO}_3\), and \( \mathrm{KCl}\) are the solutes. They are distributed evenly throughout the solvent, which in most chemistry exercises is water, but it can be any other liquid. When the solute dissolves in the solvent, a solution is formed, which is a homogenous mixture where you can no longer distinguish the separate components.

The concentration of a solution refers to how much solute is present in a given quantity of solvent or total solution. There are many units to express concentration, but molarity is one of the most commonly used in chemistry due to its utility in reaction stoichiometry and because it directly relates the volumes and mole quantities of reacting solutions.

Molarity provides a direct measure of this concentration, telling us exactly how many moles of solute are present in one liter of solution. For example, a 1 Molar (\(1 \text{ M}\)) solution has 1 mole of solute per liter of solution. This measurement is also critical in preparing solutions for experiments where the precise amount of a substance is required for a reaction to occur under controlled conditions.

It's also the main reason why we need to make sure we are using the correct volume units when calculating molarity – it directly affects the correctness of the concentration value. If a student neglects to convert milliliters to liters, for instance, the molarity calculated would not be correct and could lead to errors in further calculations or experimental setups.