Galileo said – “Mathematics is the language with which God wrote the universe” .
I don’t know how true is that , but I do know that Mathematics is of paramount importance in study of any science. Personally, I get freaked out at the sight of integers,logs and calculus but I also know that these are an indispensable part of our study .So, in the next few posts let us try to understand some basics concepts in Mathematics, which are needed for understanding Chemistry. And trust me, without a general idea of these concepts, it is very difficult to properly understand what we are about to discuss in future posts. So let’s get started 🙂
Why do we need Mathematics in any science?
A Scientist conducts experiments only finite number of times. Based on the observations of the experimental data, one needs to find a general relationship between quantities being studied.This is where mathematics comes into picture. Mathematical modeling helps us to generalize the relationship between the variables under study and later use it for any value whenever required. So if we are studying the dependency of one variable y on another variable x ,we can keep changing x and see how y changes with x. We can later find a relation between x and y from the data obtained from our experiment.
e.g. Suppose the value of y obtained from our experiment where we are varying x is as follows –
x |
y |
1 |
1 |
2 |
4 |
3 |
9 |
4 |
16 |
If we study the above experimental data, we can find a relationship between the values of x and y.We can thus formulate a mathematical expression relating both values. In this case the equation would be , y= x^{2 }. So now if we need to know what is the value of y for x=9 we don’t have to conduct the experiment again.We just need to plug-in the value of x in the above equation and we would get y=9×9=81.
If ‘x’ is time and ‘y’ is concentration of the products ,then the above equation would be the rate (reaction rate) equation for the reaction under study.
Here ‘x’ and ‘y’ are called variables i.e quantities which vary through the course of the experiment i.e they are not constant.
The variable which is in our control ‘x’ is called the independent variable. e.g. time.We decide for how long to conduct the experiment and what should be the time intervals between two observations. We could run the experiment for 1 hour(x) and study the concentration of the products (y) after every 10 mins or we could run the reaction for 30 mins and observe the concentration after every 5 mins.
The variable which changes with x , which is under our study is called the dependent variable’y’. This is not in our control.’y’ changes as we change ‘x’ and it is the change of ‘y’ that we are observing in our experiment. e.g. studying how concentration changes with time.
We can later plot the graph of x vs y and see the pictorial representation of our data.(We shall discuss more about graphs in the subsequent posts.)
Mathematical concepts like slopes,tangents,graphs, calculus(derivatives and integration) and statistical interpretations are important to study,simplify, generalize and arrange data systematically and thus get a quantitative sense of concepts we are studying. So, let us clear our understanding about these mathematical concepts and comprehend chemistry in a better way. We shall start our discussion on graphs,slopes , logarithms in the next few posts. Till then,
Be a perpetual student of life and keep learning …
Good day!