Articles of chemistry

Significant Figures

I have learned in class that to subtract decimal numbers and keep significant figures, one just lines up the decimal, then rounds the answer according to the operand with the fewest places after the decimal. My question is how to handle an integer subtracted by a decimal. 112 – 12.0 If I add the decimal […]

Michaelis-Menten steady state hypothesis

In part $ii) $the part underlined in green suggests that we substitute an equation we get from when $v’=0$ to garner a solution of $s’$ for all time from the time when $v’=0$. However $v’$ does not remain $0$ for all time from the the time when $v’=0$, so why can we substitute the expression […]

Easiest way to solve system of linear equations involving singular matrix

I am trying to balance an unbalanced chemical equation by using setting up a system of linear equations to solve for the stoichiometric coefficients in the chemical equation. After setting up a matrix, to try and solve the system, i cant because one of the matrices is a singular array. I have taken a look […]

Why is $\arccos(-\frac 13)$ the optimal angle between bonds in a methane ($\rm CH_4$) molecule?

Background: In a CH4 molecule, there are 4 C-H bonds that repel each other. Essentially the mathematical problem is how to distribute 4 points on a unit sphere where the points have maximal mutual distance – or, how to distribute 4 position vectors such that the endpoint distances between them are maximized. This question Angle […]

Calculate half life of esters

I’m trying to calculate the level of testosterone released from different testosterone esters. Here are some graphs of testosterone levels after single injections of 250mg of each ester. Testo U Testo B Each ester have a specific half life. e.g. testo e have an half life of 4.5 days. testo b 29.5 testo […]

Pólya's Enumeration formula and isomers

The hydrocarbon benzene has six carbon atoms arranged at the vertices of a regular hexagon, and six hydrogen atoms, with one bonded to each carbon atom. I know that two molecules are said to be isomers if they are composed of the same number and types of atoms, but have different structure. How many isomers […]

Balance chemical equations without trial and error?

In my AP chemistry class, I often have to balance chemical equations like the following: $$ \mathrm{Al} + \text O_2 \to \mathrm{Al}_2 \mathrm O_3 $$ The goal is to make both side of the arrow have the same amount of atoms by adding compounds in the equation to each side. A solution: $$ 4 \mathrm{Al} […]