(a) Is the concentration of a solution an intensive or an extensive property? (b) What is the difference between \(0.50 \mathrm{~mol}\) \(\mathrm{HCl}\) and \(0.50 \mathrm{M} \mathrm{HCl} ?\)

Understanding the difference between intensive and extensive properties is fundamental in chemistry. Intensive properties, such as melting point, boiling point, and density, do not depend on the amount of a substance. They remain the same whether you're analyzing a gram or a kilogram of the substance. For instance, the boiling point of water is always 100°C at standard atmospheric pressure, regardless of how much water you are looking at.

Extensive properties, however, like mass and volume, change with the amount of substance present. When you have more of a substance, these properties increase accordingly. In the textbook exercise, you learned that the concentration of a solution is an intensive property. This means that a saline solution that is 0.9% sodium chloride remains 0.9% whether you have a milliliter or a liter—a very helpful concept when doing dilutions or scaling reactions.

Molarity is a term that frequently pops up in chemistry, particularly when dealing with solutions. It is defined as the number of moles of solute divided by the volume of solution in liters. Represented by the unit M (molar), it’s a way of expressing concentration that tells you how 'strong' or 'concentrated' a solution is. For example, a 1 M solution of sodium chloride means that there is 1 mole of sodium chloride in every liter of solution.

It's crucial to note that molarity can change with temperature because it involves volume, which can expand or contract with heat. When a problem asks for molarity, it's asking for this specific ratio. In the textbook solution, we saw that molarity is distinct from just having moles of a substance because it also accounts for how much space those moles take up in a solution.

A mole is an incredibly important unit in chemistry, serving as a bridge between the microscopic world of atoms and molecules and the macroscopic world we live in. One mole is defined as precisely 6.02214076×10²³ (Avogadro's number) of particles—be that atoms, molecules, ions, or electrons.

When we talk about moles of a substance, we are referring to a certain mass that corresponds to that many particles. It's a bit like saying 'a dozen eggs'—no matter the size of the individual eggs, a dozen is always 12 of them. In chemistry, 'moles of substance' indicates an exact quantity without regard for volume or concentration. As illustrated in the textbook solution, knowing the moles of HCl presents you with the quantity of the substance, while molarity would place that quantity in the context of a volume, providing another layer of information about the solution's composition.