The Problem With Mathematics For A-level Science

A really important topic in science that currently gets overlooked at KS3, KS4 and A-Level is the topic of units and numbers.

Did you know that there are only seven SI Base Units?

• kg, Kilogram (mass).
  
• m, Meter (length).
  
• s, Second (time).
  
• mol, Mole (amount of substance).
• A, Ampere (current).
• K, Kelvin (temperature).
• cd, Candela (luminous intensity).

Further, did you know that all other units are derived from combinations of the base units?

• N, Newton (Force) = kg.m.s^-2, comes from force = mass x acceleration, F = ma.
• J, Joule (Energy) = kg.m².s^-2, comes from kinetic energy = half mass x velocity squared, E_k = 1/2mv².
• Pa, Pascal (Pressure) = kg.m^-1.s^-2, comes from the ideal gas equation, pressure x volume = no. of moles x molar gas constant x temperature, PV = nRT. Rearrange this to P = nRT/V.
• There are many, many other derived units but all are combinations of the SI Base units.

Why is this important?
The equation for a physical quantity is as follows:
Physical quantity = number x unit
This means that all of the rules for mathematical equations also apply to calculations in science such as algebra, indices, standard form, etc. This means that numbers and units can be manipulated in the same way as equations involving x and y terms.

For example:

Calculations involving solutions:
How many moles of substance do I have in 25 cm³ of a 0.5 mol.dm^-3 solution?
(25 cm³ / 1000 cm3.dm^-3) x 0.5 mol.dm^-3 = 1.25x10^-2 mol
N.B. There is no need to use the triangles taught at A-level they are only useful for one particular type of calculation and are based on this system (quantity calculus) anyway. My personal view is that learning a system is much more useful than learning a triangle for one situation!

Calculations involving electricity:
How much power is produced when a current of 6 A with a potential difference of 3 V flows?
3 V x 6 A = 3 J.C^-1 x 6 C.s^-1 = 18 J.s^-1 = 18 W
N.B. Notice here that we did not need to remember the equation Power = voltage x current, P = VI the answer was easily predictable from the units alone using the rules of algebra and indices.

Calculations involving molar mass and Avogadro`s number:
How many molecules of C₂H₆ are there in 6.5 g?
Molar mass of ethane is: 30 g.mol^-1
(6.5 g / 30 g.mol^-1) x 6.02x10²³ molecules.mol^-1 = 1.3x10²³ molecules.
N.B. Notice here that I did not need to use a triangle and that I inserted an arbitrary unit (molecules) to (algebraically) get the answer in the units I wanted.

My view is that this is not a technique that is easy to pick up or intuitive at first but, with some hard work and effort, employing this technique will give you a powerful, intuitive understanding of the mathematical language of science and should lead to a significant improvement in grades, and ultimately, career potential.

Please contact me if you wish to discuss further.

Best of luck in your studies,
Darryl , MChem, MRSC.