9 Common Notation
Mathematical equations can have variables and constants in them, each represented by letters. A variable can change value, while a constant has a fixed value. There is a table of commonly used constants and their values in the text.
Equations may also contain a variety of mathematical symbols. Below is a table of mathematical symbols that you should know.
| Symbol | Definition |
| ° | degree Celsius or Fahrenheit; also used for standard state, which is the state (solid, liquid, or gas) of a substance at room conditions ( 1 atm, 25 °C) |
| ∑ | summation (add the things that follow) |
| ≈ or ≅ | almost or approximately equal to |
| ∝ | proportional to |
| ∞ | infinity |
When two variables are directly proportional to each other, it means when one variable increases the other increases, too. They each might increase by different amounts, so they aren’t equal to each other. While it’s incorrect to put an equals sign between them, we can put a proportionality sign between them, as shown here for the variables V and T.
V ∝ T
When two variables are inversely proportional, it means when one variable increases the other decreases. We can represent this mathematically by using the proportionality sign and taking the reciprocal of one of the variables, such as
V ∝ [latex]\frac{1}{P}[/latex]
Note that in mathematical equations, the proportionality sign can be replaced by an equals sign and a constant.
V ∝ T can be rewritten as
V = cT where c is a constant (called the proportionality constant)
This is useful when turning relationships between quantities discovered in the laboratory into mathematical equations.
Subscripts are used when there exists more than one value of the same variable during a calculation. For example, a gas will have one volume at a specific pressure, but a different volume at a different pressure. The product of the volume and pressure of the gas under each conditions is equal, as shown by the equation
P1V1 = P2V2
While it doesn’t matter which condition is associated with which subscript, both variables for a specific condition must have the same subscript. That is, V1 is the volume of the gas when it has pressure P1.
Equations in chemistry may also contain Greek letters. You should be familiar with the Greek letters in the table below.
| Greek letter | Name | Common Use in Chemistry |
| µ | mu (lower case) | metric prefix for micro (10-6) |
| π | pi (lower case) | 3.14 |
| Δ | delta (upper case) | change, specifically, final – initial |
| λ | lambda (lower case) | wavelength (see Electronic Structure chapter) |
| ν | nu (lower case) | frequency (see Electronic Structure chapter) |
| σ | sigma (lower case) | a type of bonding (see the chapter on Covalent Bonding) |
| π | pi (lower case) | a type of bonding (see the chapter on Covalent Bonding) |
| Ψ | psi (upper case) | wavefunction (see Electronic Structure chapter) |
