1.1: The language of measurement in physical chemistry

In order to be good theoreticians, we need tools of our theory. And because this is a physical science, those tools are primarily those of physical measurement. The building blocks of those tools are the same as those that you’ve encountered in physics and chemistry courses before now: the base SI (Système international) units.

Physical quantity	Symbol	SI quantity (mks)	Abbreviation
Length	x (or Δx, or L)	meters	m
Mass	m	kilograms	kg
Time	t (or Δt)	seconds	s
Electric current	I (or J)	Amperes*	A*
Temperature	T	Kelvin	K
Count of substance	n	moles	mol

Table 1: The base SI units, associated with the physical quantities that they measure. Format of table taken from Monk’s Physical Chemistry.
*Depending on the system, either the ampere or the coulomb can be used as the base unit associated with electricity; many definitions are easier to build with the ampere than the coulomb, however. Remember that 1 C = (1 A)•(1 s).

You have studied all of these concepts previously. This is likely the first time you’ve seen all the base SI units assembled in one place, however. In this course, literally all the units we will build are going to be compounds of these units. Some of these compound units will be very straightforward; the units of area and volume, m² and m³, are compounds of a single unit, the length. Others are going to be more sophisticated.

To build these compound units, let's remind ourselves of some key ideas from physics.

Force is one of the first compound units in physics that we get to know well. The SI unit for force is the newton. It is built on the back of the definition of force, which is that interaction necessary to change the velocity of a mass, the definition that’s commonly known as Newton’s second law:

$$F=ma\text{ (single force acting on single object) }{\text{Units: 1 N = (1 kg)(1 m s}}^{-2}\text{)}$$

The symbol a, from classical mechanics, represents acceleration, which is a compound unit in and of itself. For very deliberate reasons I don’t want to consider acceleration too deeply mathematically right now; if you remember that acceleration is synonymous with “rate of change of velocity”, you have what you need to have right now.

The newton is a compound of all three classic base SI units: mass, length, and time. It forms the foundation for other ideas as well, including the idea of work. We will explore many increasingly precise formal definitions of work as we move forward in the course, but the fundamental nature of work is applying a force to an object as that object moves. If that force has a component that is parallel to the motion, the work done is positive; if that force has a component that is antiparallel to the motion, the work is negative.

$$w=F\mathrm{ \Delta }x\mathrm{ cos}\theta \text{ (single force acting on single object) }\text{Units: 1 J = (1 N)(1 m)}$$

(Work may have been symbolized in courses you have taken previously with a capital block or cursive W. In physical chemistry, work is always symbolized with a lower-case w, and as we will find later in the course, the lower-case symbol means as much as the letter.)

There is one other key relationship that comes out of classical mechanics. When work is applied via a constant force to accelerate an object, there is an expression that becomes quite useful - an expression for the mass of that object multiplied by its velocity squared. When framed to fit, we can easily prove that work is equal to the change in this quantity, which we have historically defined as kinetic energy:

$$K=\frac{1}{2}m{v}^2{\text{Units: 1 J = (1 kg)(1 m}}^2{\text{s}}^{-2}\text{)}$$

The most important thing to recognize about these two definitions is the units. They’re exactly identical. We use the name of the man who equated mechanical energy with heat, James Joule, to connect these two ideas; the SI unit of energy is a compound unit, the joule, equivalent to one kilogram times the square of one meter per second, or one newton times one meter.

There are a lot of physical measurements that we can come up with that are specific to one thing or another, and that only have a single application. The joule is a measure that we will apply to a host of phenomena that will connect back in one way or another to energy. That in turn provides us with one of the most important properties of the energy concept; its holistic nature.

We can’t apply force to much of anything outside of specific pushes and pulls; force is not an idea that has much application in chemistry. We will rarely, in classical mechanics, have any occasion to count up enough of anything to constitute the mole; most applications of the mole concept are in chemistry. There are other specific measures (drag, or extinction coefficient, or genetic distance) that apply only in the context of a narrow set of problems in a narrowly defined discipline.

Energy is the one major concept that can describe phenomena in physics, in chemistry, in biology, in engineering, and beyond. All disciplines need to explain work done; all disciplines need to explain heat transfer; all disciplines need to explain stored energy. In studying energy in physical chemistry, we are studying not merely physics or chemistry but principles applicable across the basic and applied sciences.