# Questions tagged [chemistry]

Questions related to mathematical chemistry which include application of mathematics to problems in chemistry and the development of mathematical methods suitable for such applications and for the formulation of chemical theories

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### How does $\frac{xy}{A}=\frac{1}{bcK}+\frac{x+y}{bc}$ become $\frac{A}{xy} = bcK - \frac{A(x+y)K}{xy}$?

As part of a derivation for a formula I was given the following: $$\frac{xy}{A} = \frac{1}{bcK} + \frac{x+y}{bc} \quad\Rightarrow\quad \frac{A}{xy} = bcK - \frac{A(x+y)K}{xy}$$ Where $b$, $c$, and $K$ ...
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### Approximating the amount of CO2 gas in a balloon from how it changes in water level when placed in water.

Let's say I have a ballon with no CO2 in it and place it in a beaker of 10ml. It rises by 5 ml and the water level is 15ml. (this is the default measurement) Then I fill the balloon with x amount of ...
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### Determining whether or not a system of equations has positive integer solutions

Consider the chemical reaction: $$\mathrm{ClO_3} + \text I_2 \to \mathrm{Cl} + \mathrm {IO_3}$$ When given the reaction in a test, I did not know whether I was meant to balance it by manipulating ...
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### Chemistry Optimization Problems using Calculus I Methods

A standard Calculus I textbook usually has a number of optimization problems in mensuration, physics, biology and economics/finance, crossing a river via canoe and foot, laying a pipeline to an oil ...
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### saturation formula

I have a differential equation $$\frac{dB}{dt}=\epsilon I-\delta B.$$ I want to understand why $B \leq \frac{\epsilon}{\delta}.$ $B$ is the concentration of a virus in the environment, $\epsilon$ is ...
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### Distributing a function into an existing inner-product (math for quantum chemistry)

Question: Can functions outside bra-ket notation be distributed into the bra and ket? Since I am uncertain exactly how to ask this question, I include the problem below. Essentially, I don't know how ...
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### How do I integrate the differential equation?

I have an equation from chemistry: $$\frac{\delta (\frac{\Delta G}{T})}{\delta T}=-\frac{\Delta H}{T^2}$$ This is known as the Gibbs-Helmholtz equation. Now according to Wikipedia, if I integrate this,...
1 vote
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### Help a chemist do some Linear algebra, hydropnics nutrient solution concentration problem.

So I am a chemist, and a hydroponics hobbyist. I am using off the shelf nutrient solutions that come in a three part kit, lets call them M, G, and B. Each bottle has some percent of Nitrogen (N), ...
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### Enumerating chemical graphs

I would like to make and visualize graph library of $n$ vertices that each vertex can only have maximum of four edges. The reason behind this is that the results will be used for designing chemical ...
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### Determining an ODE with monotonically increasing solution and multiple steady states

I am trying to understand what kind of ODE or system of ODE would result in a monotonically increasing solution with multiple steady states. For lack of better terminology, a solution that increases ...
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### Solving the kinetic speed equation of a chemical reaction

DISCLAIMER: This question is divided into two parts, the first is a generalization of the second one, and the majority of the mathematics community in StackExchange will answer it and ignore the ...
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### Taylor expanding in reciprocal monomials?

At 20:19 of this video , The professor writes $Z = \frac{ P \overline{V_{real} } }{RT}$, and he writes, $$\frac{ P \overline{V_{real} } }{RT} = \sum_{i=0}^{n} \frac{ a_i} { V_{real} }$$ But I did ...
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### Given $[D]$ and $\vec p$, can we solve $[D]=\begin{bmatrix}p\\q\end{bmatrix}^{\top}\begin{bmatrix}c\\1...\end{bmatrix}$ for $\vec q$ and $\vec c$?

Given matrix $[D]\in \Bbb R^{m \times n}$ of spectral data composed of $n$ mixtures of two pure component spectra $\vec p$ and $\vec q\in\Bbb R^{m}$, scaled by matrix $[C]\in\Bbb R^{2 \times n}$ ...
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### Value Between $\alpha$ And $\beta$

$dynamic range$ is defined as the lowest concentration at which quantitative measurements can be obtained ($LOQ$) to the concentration at which the calibration curve departs from linearity ($LOL$). ...
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I have a file with the atomic coordinates $(x, y, z)$ of each atom on a two-dimensional sheet. In the case of graphene, the atoms have a distance of approximately 1.42 angstroms. The sheet is usually ...