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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9 views

Chemical Reaction Networks: Applications

I have recently read a bit on chemical reaction network theory. I was wondering whether the mathematical concepts have cross field applications like neural networks. For example, can I apply chemical ...
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0answers
23 views

Building a tetrahedron from two defined vectors?

I am currently writing a program that computes specific molecular bond angles for one of my research projects but am running into some trouble. Suppose I want a tetrahedron with vertices A, B, C, D. ...
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2answers
111 views

How many different isomers of $C_3 H_4 Cl_2 F_2$ exist?

I was on my high school chemistry class when I came across this problem, which, I think, belongs to group theory. The problem is that it is not possible to label the carbons as reflection should not ...
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1answer
160 views

Application of Combinatorics/Graph Theory to Organic Chemistry?

Recently, I have been self-teaching graph theory and having an organic chemistry course at school. When I was learning isomer enumeration I found great resemblance between organic molecules and ...
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1answer
38 views

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 ...
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1answer
31 views

How to convert kJ/kmole to kJ/kg? [closed]

So say I have CO2 and a value of 50 000 kJ/kmole. This is how ive converted just want to check if im right. so.. kJ/kmole = J/mole 1 mole of CO2 = 12 +16x2 = 44g J/.044 Kg then what would I do? ...
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31 views

Non-linear systems: Modelling the behavior of an oscillatory system when adding a perturbation.

I have a non-linear system of equations that describes an oscillatory system. the oscillations is generated by the interplay of two chemical species $A$ and $B$ Equation 1 \begin{align} \frac{d[B]}{...
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1answer
31 views

applications of (topological and algebraic) commutative diagrams in organic synthesis

In algebraic topology, there are a lot of commutative diagrams and commutative diagrams up to homotopy. Different ways of compositions of maps in a commutative diagram are equal or homotopy equivalent....
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44 views

Solving two electron integral

During one of my practical courses we had to do the Hartree-Fock-method "by hand". Part of that was to calculate the occurring two electron integrals. With $$\chi_i(r) = 2 \cdot \alpha_i^{3/2} e^{-\...
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1answer
29 views

Solving for numerator in equation with logarithms (Activation Energy Equation)

I'm having trouble solving for k1 in this equation: ln(0.286/k1) = (100000/8.314)(1/500 - 1/490) The right side should equal 0.491, which I can calculate just fine, but then the left side gives me ...
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1answer
20 views

What is the amount of non-isomorphic trees of order n with a maximum incidence of 4?

It's a graph-theory model of the theoretical amount of possible non-cyclic alkanes isomers. I can't find a way to compute it? Any hints appreciated.
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1answer
46 views

Finding a group of Complex numbers That is Isomorphic to this Group

So, I'm reading Introduction to Symmetry and Group Theory for Chemists to prepare for a project in Modern Algebra (and out of pure interest) and I've come across a problem that I thought would be ...
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1answer
86 views

Cannot solve this integral used in quantum chemistry

I am writing computer code for an implementation of the Hartree Fock algorithm and I am stuck on a certain integral. This is a great walkthrough to get some background : HFTheory Anyway, the set-up ...
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1answer
61 views

How to reduce the chemical reaction system $A+B \rightleftharpoons^{k_+}_{k_-} C$ with transfer using the quasi steady state assumption

Suppose we have the reaction $$A+B \rightleftharpoons^{k_+}_{k_-} C$$ within some reaction $\Omega\subset\mathbb{R}^3$, we assume this region to be well mixed and we denote the concentration of $A$ as ...
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3answers
89 views

What is the meaning of delta squared?

I know that $\Delta x = x_2 - x_1$. This is well known Therefore, it follows that $\frac{\Delta a}{\Delta b}$ = $\frac{a_2 - a_1}{b_2 - b_1}$ (Unless I missed an elementary math class!) Now, I found ...
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0answers
21 views

Solving for wavelength when given the uncertainty

The question reads: What wavelength light can be used to determine the speed of an electron with an uncertainty of $7.5 * 10^4$m/s. The equation that I want to use would be $Wavelength = \frac{H ...
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2answers
56 views

Mathematics of chemistry with focus on particular symmetries

A student of mine came with a somewhat unusual request: My question about group theory and if you have a book you could recommend for some foundation: specifically chemical applications of group ...
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1answer
31 views

ODE Oscillation, overdampening response

Below is another version of the creme brulee model. $k_{11}, k_{12},k_{21},k_{22}$ and $A$ are all positive constants. Show the the solutions to these ODEs can never oscillate (proof for $T_1$ is ...
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1answer
65 views

Counting “double bonds” in graphs

Here's an interesting puzzle I've set myself. Consider the set of multigraphs (or, if you prefer, graphs with edges weighted by positive integers), excluding graphs with cycles of length 1. Let the ...
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2answers
115 views

The radioactive gas Radon-222 has a half life of $3.8$ days. Initially, there are $2 · 10^9$ atoms in a sample. How many atoms remain after $10$ days?

I already calculated the number of half lives past: $10/3.8= 2.6$ I don't know if I'm on the right path. I don't know what I'm doing. Please help or at least give me a hint.
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1answer
14 views

Normalizing data to new percentage total?

I have a range of percentage compositions for chemicals in dry air. At the moment they all total to 100%. For example chemical a=35%, b=20%, c=20%, d=10% and e=15%. If I were to alter the percentage ...
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0answers
21 views

Different formulations of chemical kinetics giving different solution trajectories

I am reading a textbook by Keith J. Laidler titled 'Chemical Kinetics' (3rd ed.). Two different differential forms are given for the reaction (pp30, pp38): $ 2A \leftrightarrow B $ with forward rate $...
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0answers
26 views

constrained differential in a chemical reaction model

I have a system of reversible elementary chemical reactions for a catalytic cycle. Each reaction has a forward reaction rate constant $k_{f}$ and a equilibrium reaction constant $k_{eq}$ (we could ...
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1answer
38 views

Uncertainty powers

In class, we are working with powers of uncertainties. The teacher, however, handed me an extremely technical article, and it makes very little sense. Could one please explain to me step by step how ...
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3answers
52 views

Significant Figures in quantity?

I am still having trouble grasping significant figures. How many significant figures would be in this quantity? $01010.0$ I feel like it is 3, but not quite sure.
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22 views

Problem regarding units in Arrhenius equation

The dependency of rate constant of a reaction is given as $$log K=20-\frac {6600}{T}$$ where K is in $min^{-1}$. Now I know Arrhenius equation is $k=Ae^{−E/RT}$. I need to find E on comparing ...
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1answer
83 views

Differential equations, chemical reactions

A chemical substance A changes into substance B at rate $\alpha$ times the amount of A present. Substance B changes into C at rate $\beta$ times the amount of B present. If initially only substance A ...
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1answer
1k views

relating mole fraction to molality

If the mole fraction of water in a HCl solution is 0.78 . calculate the molality of the solution? I don't understand how to relate mole fraction to molality.
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1answer
33 views

Good resources on chemical graph theory

Are there some good resources on chemical graph theory, mainly some covering even the recent results (past 2000)? Tnaks in advance for any help.
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106 views

How to define boundary conditions for a sphere to run reaction-diffusion equations on its surface?

I'm in a Biology lab, and we managed to simulate reaction-diffusion equations on a torus using periodic boundary conditions for a 2D matrix. We want to try doing the same on a sphere, but I'm a ...
1
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1answer
256 views

Chemical kinetics using Laplace transformation

I have a simple chemical reaction $A\leftrightarrow B$ with forward rate $k_1$ and backward rate $k_2$. I can now write the differential equation of this system as following. $ \frac{dA}{dt} = -k_1A +...
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2answers
55 views

N2 diffusion through a vertical fluid column

Trying to figure out the mathematical model that might correlate to laboratory results. I have a cylindrical pressure vessel (picture a can) with height, h, and radius, r. It is filled with distilled ...
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49 views

Why does an infinite Neumann boundary condition become a Dirichlet condition?

Often when I read a paper I see a statement of the type: Our boundary condition at the surface is $\frac{\partial f}{\partial x} = \alpha$. In the limit of $\alpha \to \infty$ this is equivalent ...
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1answer
54 views

Formula for $P\small CO_2$

Not really sure where I was supposed to ask this question. I have no background/knowledge in chemistry or math of this level. This is a follow-up question from my question over at StackOverflow (...
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2answers
53 views

Problem approximating for a chemical problem:

Solve using suitable approximation by hand: $$s(s-\alpha)=5\times10^{-13} \\ \frac{\alpha}{(s-\alpha)(0.4-2\alpha)^2}=10^8$$ Now to solve this I tried assuming $s\approx\alpha\approx0.2$ and then ...
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1answer
65 views

Model a chemical phenomenom

I have a chemical phenomenon to model for my research. I'll try to be clear while explaining my problem. I created little molecules (let's call them "emitters"), which emit a signal. When the ...
1
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1answer
33 views

Modelling an energy profile with/without catalyst

I'm trying to make a data table that can be plot to model the energy profile of a chemical reaction with/without catalyst. example image This is essentially what I want to plot, and I'm at a loss for ...
3
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1answer
237 views

Examples of applications of category theory to chemistry

What is some simple application of category theory to chemistry, namely, something that is much easier to do in chemistry with category theory than without. It does not need to be bleeding edge, or to ...
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2answers
80 views

How would chemical equations be balanced with matrices?

For example, I have this equation: $KMnO_4 + HCl = KCl + MnCl_2 + H_2O + Cl_2$ Then I get this: $a \cdot KMnO_4 + b \cdot HCl = c \cdot KCl + d \cdot MnCl_2 + e \cdot H_2O + f \cdot Cl_2$ ...
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1answer
82 views

Nonlinear Dynamics and Chemical Reactions (Ivanova Reaction System)

I have a homework problem in which I'm given an Ivanova reaction system $X+Y \longrightarrow 2Y$, $Y+Z \longrightarrow 2Z$, $Z+X \longrightarrow 2X$, and I'm asked to write the mass-action ODEs ...
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1answer
342 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
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3answers
80 views

A lab worker needs $5$ litres of $20\%$ alcohol solution.

A lab worker needs $5$ litres of $20\%$ alcohol solution. A $10\%$ solution is mixed with a $60\%$ solution. How many litres of the $60\%$ solution will be required?
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0answers
36 views

Mathematical treatment of mass action kinetics with detailed balance (as opposed to complex balance)

I'm looking for a mathematical treatment of mass action kinetics under the assumption of detailed balance. In particular, I'm interested in the proof that the free energy is a global Lyapunov function....
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2answers
2k views

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,...
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2answers
4k views

How to find the number of atoms of an element in $x$ amount of a compound

Lets say I am given a certain mass of a compound. Additionally, the number of moles of the compound itself are known, as well as its molar mass. How can I, using an equation, find the number of atoms (...
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0answers
454 views

mathematics of chemical stoichiometry

I would like to better understand the mathematical description of chemical stoichiometry and thermodynamic chemical equilibrium. This problem has many features and I know my description might be too ...
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1answer
117 views

What does the $-1$ mean in $2\mu g/L^{-1}$

What does the $-1$ mean in the expression $2\mu g/L^{-1}$? Does it literally mean multiply by $-1$?
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2answers
71 views

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 ...
5
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0answers
67 views

Deconvolution of distribution of diffraction reflexes

I'm a chemist stuck in a mathematical problem. Please bear with me as I'm trying to express myself in Math language. Let me explain in short terms the experimental method I'm using: X-ray diffraction....
2
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1answer
132 views

Differential equation based on chemical kinetics

In chemical equations, rate laws have the following form: $$r=kx^ay^b$$ ...where $r$ is the time derivative of either $x$ or $y$ times a constant: $$r=-\frac{dx}{\beta dt}=-\frac{dy}{\gamma dt}$$ Here'...