Calculate the number of moles of solute in each of the following solutions: (a) \(0.75 \mathrm{~L}\) of \(1.50 \mathrm{M} \mathrm{HNO}\) (b) \(10.0 \mathrm{~mL}\) of \(0.75 \mathrm{M} \mathrm{NaClO}\) (c) \(175 \mathrm{~mL}\) of \(0.50 \mathrm{MLiBr}\)

Understanding the concept of 'moles of solute' is fundamental in chemistry because it represents a way to quantify the amount of a substance. A mole is a unit of measurement used to express quantities of a chemical substance and is defined as the number of atoms found in 12 grams of carbon-12, which is approximately 6.022 x 10²³ particles – this number is known as Avogadro's number.

In the context of the textbook exercise, the 'moles of solute' refers to the number of moles of the chemical substance that is dissolved in a particular volume of solution. For example, when we say there are 0.0075 moles of NaCl (table salt) in a solution, this is analogous to stating we have about 4.5 x 10²¹ individual NaCl formula units in that solution.

To improve one's grasp on this topic, visualizing the mole as a large quantity of individual molecules or ions can be helpful. This count of particles is a constant number, just as a dozen refers to a group of twelve items, a mole represents this specific large amount of particles.

The 'molarity formula' is invaluable in the realm of chemistry for calculating concentrations of solutions. Molarity is denoted by 'M' and is defined as the number of moles of solute divided by the volume of the solution in liters. The formula can be written as:
\[ \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
The formula can also be rearranged to find the moles of solute if the molarity and volume are known:
\[ \text{moles of solute} = \text{Molarity} (M) \times \text{Volume in liters} (L) \]

Applying the molarity formula to solve problems can become more intuitive if the student recalls that molarity encapsulates the ratio between the number of moles of a substance and the volume of the solution. Consistent practice with various examples, especially converting between moles, liters, and molarity will strengthen the understanding of how they are interdependent.

Understanding 'volume conversion' is crucial because many laboratory measurements are taken in milliliters (mL), while molarity calculations require volume in liters (L). The conversion is actually quite straightforward because milliliters and liters are part of the metric system; 1000 milliliters equal 1 liter.

To convert milliliters to liters, divide the number of milliliters by 1000:
\[ \text{Volume in liters} = \frac{\text{Volume in milliliters}}{1000} \]
For example, converting 175 mL to liters as shown in the problem's solution (c) results in 0.175 liters.

Students should get accustomed to making this conversion as a preliminary step in solving molarity problems when the volume is given in milliliters. Consistent practice converting different volumes from milliliters to liters and vice versa will yield greater ease and accuracy in chemistry calculations.