# Which areas of chemistry require calculus?

I didn't have much chemistry in school/college, and am now building up my knowledge again. I am studying maths in parallel, building up to calculus.

I noticed that the introductory chemistry books (even at the college level) don't use any calculus. However, more advanced books do tend to use calculus.

Can anyone tell me which areas of chemistry require (or make use of) calculus?

• linear combinations of atomic orbitals. – DHMO Oct 7 '16 at 10:32
• Bring me the list of areas, and I'll check those which do. Roughly speaking: quantum chemistry and physical chemistry in general - yes, very much; analytical chemistry - not that much, inorganics - only sporadically, organics - almost none. But remember, in fact there are no areas, everything is connected to everything else. – Ivan Neretin Oct 7 '16 at 10:37
• Frankly, without calculus you don't have a solid grounding in doing chemistry, physics, or engineering. Forty years after taking calculus I still use it and the concepts drilled in taking calculus on a daily basis. – Jon Custer Oct 7 '16 at 12:58
• to add to other answers, understand units, errors, (e.g. standard deviation and how to propagate), significant figures, how to fit data (understand least squares) , and understand molecular symmetry, all of these are just as important in phys chem as in organic chemistry. – porphyrin Oct 7 '16 at 14:08
• In short, in every case where a property varies smoothly when other one does (so, in every area of chemistry). Sometimes you can avoid to use calculus (for example, in cases with very simple linear dependencies), but it would impose serious restrictions. – user1420303 Oct 7 '16 at 23:26

Analytical chemistry : To predict, for example the $\ce{pH}$, for which moieties will complex and also infer statistics thereof.

Electrochemistry : The Nernst-Plank equation is challenging. But just to calculate the concentration of some things, taking care of different kinds of reactants, depending on what you do you'll need to be good in calculus. Nyquist plots are not really difficult to use but the theory to obtain them is quite complex (it's not a pun) if you look at Nyquist stability criterion.

Organometallic Chemistry : To calculate the oxidation degree of a metal for example, or a TOF (turn over frequency), a TON it refers also to catalysis.

Thermodynamics : You need to have good skills in math to do thermodynamics, also in mass transfer or heat transfer, everything which is close to process chemistry, as per the McCabe Thiele model for distillation (for example) this is not hard but you need.

Quantum Chemistry : Here come the hardest thing (as I know it). You need to be very good in linear algebra, able to solve differential equations, have some skills in analysis to calculate integrals, and so on.

Kinetics : Calculus is not really hard but some times really weird. Also have some skills in algebra can help and be able to solve differential equations.

If you're picky, you may find other parts of chemistry in which calculus is used, but the main ones are in this post, especially quantum chemistry and process chemistry.

Finally, it also depends on your education or experience level, as the most you will study at a high level will include some good skills in calculus. You'll need to be critic and also to know what is the theory behind a hypothesis to be able to verify if what the software tells you can be consider as true or false.

For first year college chemistry the only calculus, if there is any at a particular school, would be reaction rate equations.

$\mathrm{d}[A] = -k[A]\mathrm{d}t$ ; $\mathrm{d}[A] =-k[A^2]\mathrm{d}t$ for example

Then second year you take organic chemistry; no calculus.

In the third year, thermodynamics has some multivariable calculus (partial derivatives) and quantum mechanics has partial differential equations.

• What about physical chemistry? – Starlight Oct 7 '16 at 11:34
• @Starlight physical chemistry is thermodynamics, statistical mechanics, and quantum chemistry. Yes, that's where you use calculus. – DavePhD Oct 7 '16 at 11:37

Calculus is the mathematician's or mathematical scientist's divide-and-conquer tool. When a problem is to too complicated to solve, you break it into manageable chunks and then recombine the solved chunks.

In chemistry, there are two main areas for calculus.

Thermodynamics: mainly in the areas of statistical mechanics (where you need to deal with understanding a very large number of particles) and reaction rates (where you need to deal with continuously changing concentrations)

Quantum mechanics: Many of the fundamental concepts are expressed as mathematical relationships, and the relationships are such that they require calculus to compute.

Notice that calculus is used most in the areas of chemistry that overlap with physics.