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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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Mixed Mathematical Chemical problem:

How to calculate the concentration of all species present in a solution with ${ 0.3M}\ {NaH_2PO_4}$? The whole truth is that any time that you add any phosphate ion into an aqueous solution, then ...
1
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0answers
38 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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0answers
29 views

Stochastic chemical kinetics: What's the probability of reaching one state before another?

Say we've got a system of stochastic chemical reactions, in discrete space and continuous time with specified rates, e.g. $x_1 \rightarrow x_1+1$ with rate $f_1(x_1,x_2)$, $x_1 \rightarrow x_1 -1$ ...
3
votes
1answer
89 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}=-...
3
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2answers
139 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
71 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 ...
5
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0answers
65 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
24 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
33 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 ...
0
votes
1answer
21 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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2answers
32 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 ...
2
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2answers
247 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 ...
1
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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 ...
0
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1answer
30 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\\ ...
5
votes
1answer
144 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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0answers
58 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 ...
5
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0answers
147 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 ...
-1
votes
1answer
73 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 ...
12
votes
2answers
117 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
53 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 ...
1
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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 ...
1
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1answer
90 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
votes
3answers
557 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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1answer
69 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 ...
3
votes
1answer
53 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 ...
4
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0answers
79 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 ...
1
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1answer
40 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 ...
5
votes
1answer
412 views

Why are Fokker–Planck equation and Feynman path integral formalism equivalent?

Feynman path integral is equivalent to Fokker–Planck equation. This is mentioned here, but it's not clear why. (This page says Schrodinger equation is also equivalent to Fokker–Planck equation which ...
4
votes
1answer
167 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 $k (k>0)$. $[A]_0$, $[B]_0$, $[C]_0$ ...
1
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1answer
36 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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0answers
141 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 ...
3
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1answer
364 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 ...
2
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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 ...
1
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1answer
88 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?...
0
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1answer
59 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 ...
2
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0answers
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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1answer
15 views

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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votes
1answer
219 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 ...
0
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1answer
57 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 $C = (\Lambda, R)$,...
0
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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
87 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\...
3
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0answers
36 views

Enzymes, Chemical reactions pathways to make a system of differential equations [closed]

Past Paper Question: Consider an enzyme $E$ with four binding sites at which a substrate $S$ can (reversibly) bind to form a complex $C_1$, $C_2$, $C_3$, $C_4$ (with $1$, $2$, $3$ or $4$ binding ...
0
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1answer
599 views

Is pH found using negative log because the scientific notation of the number of hydrogen atoms in a solution is always negative?

I understand subtraction negates addition, and since log and exponents are basically addition and subtraction on steroids, then log must be the way to negate exponents. So from this rationale, is it ...
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2answers
259 views

Determine the density of the liquid in kg/m3.

I got this question on my homework and completed it, however, I would just like to check if my answer is correct or not. I need to convert it to units of cubic meters. Density = 0.81 g/mL 1 gram = 0....
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3answers
743 views

Easy and reliable method for solving four nonlinear equations

I have the following four equations with their four variables: $$4.5*10^{-4}x=yz$$ $$z=\frac{10^{-14}}{t}$$ $$y=0.02-x$$ $$z=t+y$$ I'm going to be solving a lot of equations in a similar manner (...
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1answer
72 views

Partial Derivative Question Relating to Chemistry [closed]

The Ideal Gas Law PV=nrT shows the relationship between pressure P, volume V, and temperature T of a gas, where n is the number of moles of the gas and r is the universal gas constant. Prove \begin{...
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0answers
76 views

Books on Chemical Reaction Theory [closed]

I got interested in Chemical Reaction Theory by studying the lecture notes of Feinberg and related papers for my bachelor thesis and want to dive deeper into that subject. Are there any books you ...
1
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1answer
247 views

Row augmentation to solve for null-space vectors.

I'm looking to understand how a method of balancing chemical equations using the null space vectors of a row augmented matrix works (the method is outlined in detail in the following paper). https://...
0
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2answers
49 views

Adding pure solution to a mixture, what is the resulting concentration?

The antifreeze in my car is a mixture of pure antifreeze and water; the concentration of antifreeze is $50 \%$. Today, I added some pure antifreeze (the volume of liquid I added is about $\dfrac 14$ ...