The Chemistry Book

Algebra is one of the main branches of mathematics. In order to succeed in high school chemistry, students must have good skills in elementary algebra, the most basic form of algebra. The distinction between algebra and arithmetic (math) is that numbers in algebra are often denoted by symbols. For example, instead of saying there are 32 students in the room, an observer might state there are Q students in the room, where Q is equal to the actual number of students.

Why is the use of symbols (or letters) important in chemistry? Let's consider a simple density problem. Density is mass divided by volume. This is shown as m/v, in which m is equal to mass and v is equal to volume. Scientists find it easier to say m/v than mass divided by volume. Now, let's consider some example problems.

Examples

Example 1

What is the density of a substance when mass is 12 grams and it has a volume of 6 milliliters (mL)?

The easiest way to solve this problem is to write out the problem using symbols. Next, substitute the numbers and units for where the symbols are placed:

D = m/v

D = 12 g / 6 mL

D = 2 g/mL

This means density (D) is equal to two grams per milliliter (2 g / mL). Now, that is easy!

Example 2

Sometimes chemists need to consider more complex problems - with many variables (symbols or letters). Consider the following gas law problem:

What is the pressure of one mole of a gas when the volume is 2 liters and sits at 298 Kelvin?

To solve this problem, a chemist uses the ideal gas law: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature.

This looks complicated, right? Don't panic. It's easy to solve.

First, write out the problem using symbols. Next, substitute the numbers and units for where the symbols are placed (Hey! That looks familiar):

PV = nRT

P (2 liters) = (1 mole) (0.083 L atm K⁻¹ mol⁻¹) (298 Kelvin)

P = (1 mole) (0.083 L atm K⁻¹ mol⁻¹) (298 Kelvin) / 2 liters

P = 12 atm (atm is the unit of pressure)

See? That wasn't bad at all.

Common Mistakes

The first common mistake occurs when students fail to write the number with the units. Solving chemistry problems is easiest when units are shown and used as guides to cancel out numbers. This mistake is made worse in dimensional analysis problems. Learn to follow the units - and chemistry is really easy.

A second common mistake is over-reliance on a calculator. The calculator is only as good as the numbers put into it. If you place the numbers in the wrong sequence then you will get the wrong answer.

For example:

Six divided by two is three. In your calculator, place 6 hit the division symbol followed by the number 2. If you do this out of sequence then you'll get the wrong answer.

References

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