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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 can we calculate the volume of a BCC Wigner-Seitz Cell? (Based on a imaginary cube)

Hello. As you can see in the picture, there’s this shape and shape’s surface consists of 6 square and 8 hexagon parts and I would like to know its volume but I don’t know where to start. The only ...
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3answers
59 views

Pólya Enumeration Theorem and Chemical Compounds

How many different chemical compounds can be made by attaching H, CH3, or OH radicals to each of the carbon atoms in the benzene ring of Figure 1? (Assume that all of the C–C bonds in the ring are ...
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55 views

Are constants from natural science of any importance at all in mathematics as real numbers?

In mathematics, people have discovered constants that are proven to be of great importance mathematically. For example, Archimedes' constant, which is approximately $3.14159265$. Euler's number, ...
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1answer
34 views

Bonds Combinations

Justin runs $CH_4$, a chemical he knows the spectrum of masses of molecules and fragments of molecules it will contain, on a mass-spectrometer. He knows that all, some, or none of the bonds may break ...
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51 views

Example of a toy ODE control problem for chemistry/chemical engineering application?

I work in control theory. I have a student who is interested in chemistry and chemical engineering problems. I thought it would be somewhat easy to find such a problem, but apparently coming up with ...
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68 views

Biological/chemical mathematical modeling - two partners with multiple binding site interactions

I am wondering if there is any reported attempt to mathematically model the interaction of two multiple-sites molecules? I know that there is a lot of literature on how to mathematically model the ...
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57 views

Interactions between mathematics and chemistry

I am supposed to give a 1.5 hour lecture on intersections of mathematics and chemistry. Now I do not at all know how these two can be related. However I know that certain topics in mathematics have ...
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57 views

Proof of the VSEPR shapes.

The VSEPR(Valence Shell Electron Pair Repulsion) predicts that the atoms arrange themselves in such a way that the electron pair repulsion is minimized. Thus the atoms arrange themselves in space in ...
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0answers
25 views

Calculate the confidence interval of $u_x-u_y$

Chemically it is established that the percentage of iron in five samples of ore extracted in a certain mine has an average of $22.3\%$ and a standard deviation of $1.8\%$. In six samples of ore ...
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2answers
62 views

Mixed mathematical chemical problem

How to calculate the concentration of all species present in a solution with $\mathrm{0.3~M}$ $\mathrm{NaH_2PO_4}$? The whole truth is that any time that you add any phosphate ion into an aqueous ...
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90 views

Electron Groups and Platonic Solids

In my Chemistry class, lately I have been learning about Lewis Structures for molecules, and how the arrangements of groups of electrons on each molecule repel each other to form the molecule into a ...
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1answer
96 views

Concentration of $Z$ in the chemical reaction $6Z+B\rightleftharpoons 2Z+A$

Find the differential equation for $z$ the concentration of $Z$ in the chemistry equation $$6Z+B\rightleftharpoons^{k_1}_{k_{-1}} 2Z+A$$ My idea: Let $[Z]=z,\ [A]=a,\ [B]=b$. Then, $$\frac{dz}{dt}=-...
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2answers
164 views

Show that there does not exist a unique stationary distribution.

So I was doing some self study and came across a proposition in one of my chemical engineering course's prescribed textbooks. I can't quite get the proof out. It's to do with a particle moving through ...
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0answers
80 views

Similarity transform with respect to a metric?

Does this type of matrix expression have a name? $$D'S=CDC^{-1}$$ All the matrices are $n\times n$ and $S$ is a matrix consisting of the inner products of the basis vectors of $D'$, so $D'$ is in ...
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0answers
72 views

How to define Chirality and Polarity on a graph?

Is there a concept of Chirality or Polarity defined on graphs? For example, consider a system with spin-$1/2$ (up/down polarity) particles which have also chirality (right/left). I thought to take a ...
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1answer
28 views

Dimensional Analysis Conversion

I am new to learning about dimensional analysis and I am confused with a question. I am supposed to convert 45 km/day to inches/week. I would like to have all work shown. The work I have so far is ...
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0answers
37 views

Stochastic simulation Gillespie algorithm for areas instead of volumes?

I am trying to find resources on the Gillespie stochastic simulation algorithm for my system which happens on a surface. The original algorithm was developed for a reactor of volume $V$, but my system ...
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1answer
23 views

Inuition behind symbolic partial derivative of heat capacity?

I am studying thermodynamics. I am trapped at this step. I know it's a chemistry but no one really helped me there. This is a symbolic expression where: $E = f(T, V)$ (or Energy is a function of T ...
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37 views

Transformations commuting in 3D (crystallography)

I'm studying symmetry operations and trying to show that the symmetry operations of a crystal* are closed, so they form a group. A friend of mine said that these operations commute but I can't justify ...
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2answers
320 views

Stable limit cycle

For a system of two differential equations, the eigenvalues determine the stability of the system. When the eigenvalues are positive, the system is unstable. In case of complex eigenvalues, the system ...
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1answer
40 views

Does this averaging function have a name? (“sigma profiles” in chemistry)

I am looking for a mathematical (!!) answer, NOT a chemical one, hence the post to Mathematics. Quick description: Solvation modelling with for example COSMO-SAC uses something called a sigma ...
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1answer
32 views

Understanding an Equation for Pulmonary Diffusion

I've been reviewing some medical documentation in preparation for school and I'm having some trouble understanding how to think of an equation in the paper The physiological basis of pulmonary gas ...
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0answers
64 views

Solve system of equations with no constant terms [duplicate]

I am trying to balance a chemical equation algebraically and have found the resulting system of equations: $$\begin{align*} 3a+8b+d&=12e+4f+2g\\ a&=e\\ 4a+4c+3d&=4e+3f+g+3h\\ ...
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204 views

Symmetric Direct Product Distributive?

This comes from the context of chemical group theory, so I apologize if I'm using terminology incorrectly. For that context, see Determining the symmetry of overtones of degenerate modes on the chemSE....
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59 views

Number of compounds with the same chemical formula

Even though this question may not seem apropriate for this site, it is more of a mathematical one than a chemistry one. Take an example chemical formula C3H4O2. There are many compounds with this ...
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192 views

Quantum Chemistry book recommendation. [closed]

I am trying to learn quantum chemistry. I have an extensive background in math and physics, so I'm looking for a book that makes full use of whatever physics and mathematics is relevant to this ...
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1answer
83 views

Strange substitution in integral using partial fractions [closed]

Let $[A]_0=a$ and $[B]_0=b$, then $[A]=a-x$ and $[B]=b-x$. $$\int_0^x \frac{1}{(a-x)(b-x)}dx = \frac{1}{b-a}\left(\ln\frac{1}{a-x} - \ln\frac{1}{b-x}\right)$$ Evaluating the integral gives ...
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2answers
124 views

An application of the Inclusion Principle to Chemistry? (Proof Verification)

Background I’m taking chemistry and one thing they have us do is draw Lewis structures for molecules. Guessing if there are going to be double or triple bonds is kind of annoying. I’d like to be able ...
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2answers
69 views

Preparation of aqueous solution

In Chemistry class, Samantha finds that she can make a certain solution by mixing $.04\,\rm L$ of chemical $\mathrm{A}$ with $.02\,\rm L$ of water (this gives her $.06\,\rm L$ of the solution). She ...
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1answer
40 views

How Would the Left Side of this Limit be Solved?

I have two equations which represent the ratio of concentration to initial concentration in a chemical reactor, and I need to know what the limit of the left side would be, where when $t$ becomes ...
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1answer
97 views

How to calculate the average molar mass of the atmosphere? [closed]

The task: Determine the average molar mass of the atmosphere - each for the moist air and the dry air. One example that I have calculated is this one: I have the gas Nitrogen and the percentage for ...
3
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3answers
718 views

Differential equations for chemical reaction $\mathrm{A + 2B \to 3C}$

In a chemical reaction $\mathrm{A + 2B \to 3C}$, the concentrations $a(t)$, $b(t)$ and $c(t)$ of the three substances A, B and C measure up to the differential equations $$ \begin{align} \frac{da}{...
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93 views

Incorporating a natural death component into a Monod equation

Hi I have a series of monod equations representing a system with two substrates and two species. Each of the species is producing a substrate that the other species consumes as such the success of ...
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1answer
58 views

Is it true that the maximum length of an alkane branch is $\left\lfloor\frac{3n}7\right\rfloor$?

Suppose we have a tree graph of order n. If we number the chains and branches like we do for alkanes, it seems that the max possible length of a branch is $\left\lfloor\frac{3n}7\right\rfloor$ if we ...
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0answers
81 views

What is the spherical equivalent of splitting a circle into n equal segments and calculating their central angles?

So this is easy to calculate in 2 dimensions, if you have a circle represented by 3 points the angle between any two consecutive points and the spheres centre is simply $\frac{2\pi}{n}$. I basically ...
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1answer
46 views

How long would it take the air conditioner to exchange the air in your room that is 11ft by 12ft by 8.5ft?

I have this question in chemistry. It's really just for getting you use to conversions. Here's the question: You have a bedroom that is 11ft wide by 12ft long by 8.5ft high and has an air conditioner ...
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1answer
225 views

Conservation law(s) of chemical reaction $\rm A \longrightarrow B + 2C$

I am trying to find the conservation law for the following chemical reaction: $$\rm A \longrightarrow B + 2C$$ where: A converts into $B$ and $C$ at a rate $k (k>0)$. $[A]_0$, $[B]_0$, $[C]_0$ ...
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1answer
40 views

Compounding errors in order to get a well defined “reasonable” range for the end result.

I'm doing some data migration for a company, and there are some materials that are essentially "some things in aqueous solution." In a specification for this material this is defined as "Solids ...
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224 views

Formula to calculate the average diameter of a mixture of two sizes of marbles.

Im looking to mix two particle sizes of powder metals, and need to calculate the resultant average particle size. O.K. More specifically: I mix 50 pounds of metal powder that has a spherical ...
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0answers
187 views

dimensional analysis question

A high school senior was applying to college and wondered how many applications she needed to send. Her counselor explained that with the excellent grade she received in chemistry she would probably ...
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1answer
451 views

Time reversal in Robertson's chemical reaction

I am studying the behavior of the Robertson chemical reaction, $$\begin{array}{rl} \dot{x} &= -0.04 x + 10^4 y z\\ \dot{y} &= 0.04 x - 10^4 y z - 3 \times 10^7 y^2\\ \dot{z} &= 3 \times ...
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2answers
63 views

Minimizing Double Values in Combinatorial Chemistry Mixtures

I am a chemist working on a project where I synthesize Mixture Libraries. Using different starting materials in solution mixtures, all possible combinations can theoretically form as products. To ...
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1answer
97 views

Mathematical Problems of Climate Science?

Are there any interesting research-level mathematics problems that have come out of climate science specifically or that are abstractions of some of the issues and models pertaining to climate science?...
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1answer
73 views

Determining Mass of Lithium [closed]

What is the mass of 1.3 x 10^(23) atoms of lithium. Lithium has a mass of 6.94, so I assumed that it'd be 6.94 x 1.3 x 10^(23), but that wasn't the case. I wasn't given much practice and I'm not sure ...
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118 views

Calculating a “max support flux vector sequence”

Tl;dr: what is a max support flux vector sequence? In a paper (arXiv link; full citation below) on continuous chemical reaction networks (CCRNs)$^1$ it discusses an algorithm for reaching different ...
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Determining sufficiency of concentrated solutions

I am trying to make a function to calculate whether a given supply of reagents is sufficient to create a list of products at a given solution. So for a list of products $$ (a_1, b_1), (a_2, b_2) ... (...
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1answer
260 views

Chemical Equation Balance [duplicate]

How do i fix this problem without using null space matrix? $$4NH_3 + Cl_2 \rightarrow N_2 H_4 + 2NH_4Cl$$ Also before that, I need to learn how to find vectors. If someome show me it, it would be ...
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1answer
66 views

Calculating/generating reaction stoichiometry matrix with unclear definition

My question comes from section 2.1 of the paper Reachability Problems in Continuous Chemical Reaction Networks - to quote: A continuous chemical reaction network (CCRN) is a pair $C = (\Lambda, R)$,...
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3answers
77 views

Who tells me this reaction?

$$P_4O_{10} + H_2O\rightarrow H_3PO_4$$ I've a solution what I couldn't sense. How did we find this matrix and vectors? as you can see: $$\begin{bmatrix} 4 & 1 & 0 \\ 10 & ...
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2answers
89 views

Linear Algebra Problem (Chemistry) [closed]

$$C_2H_2 + O_2\rightarrow H_2O + CO_2$$ How do I solve this equation problem with linear algebra? How do I take vectors and matrix so what should I do at here? But the answer is: $$2C_2H_6 + 7O_2\...