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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Proof for relation between a function and its partial molar quantities

A variable, $Y$, depends on $N$ independent variables, $n_1, n_2, n_3, ..., n_N$. This variable is extensive in the sense that: $$Y(\lambda n_1,\lambda n_2,...,\lambda n_N)=\lambda Y(n_1,n_2,...,n_N) \...
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proper dilution for different types of dog medication

I have a concentrated liquid supplement I'm supposed to give my dog that was originally meant to be diluted at 1ml / 24ml of water. Now that liquid is not available but I have the same supplement in ...
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2 votes
2 answers
54 views

Number of spectral lines from $n_2$ to $n_1$ [closed]

When electrons de-excite from higher energy level $\left(n_{2}\right)$ to lower energy level $\left(n_{1}\right)$ in atomic sample, then number of spectral line observed in the spectrum $$ =\frac{\...
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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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6 votes
1 answer
85 views

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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3 votes
1 answer
114 views

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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1 vote
1 answer
98 views

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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-1 votes
1 answer
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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,...
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1 vote
1 answer
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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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1 vote
0 answers
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Finding the outflow density of a steady-state system with constant volume

Consider a steady-state system with constant volume, a single constant inflow, and a single constant outflow, but with spatially varying fluid density within the system. Use the following equation $$ ...
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Compressibility factor (Z) of the Redlich-Kwong Equation

I've been having a problem trying to calculate the compressibility factor of the Redlich-Kwong equation: \begin{equation} P = \frac{RT}{v-b}-\frac{a}{\sqrt{T} \cdot (v^2+vb)} \end{equation} The ...
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2 votes
0 answers
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Modeling Chemical Reactions using a Stochastic Differential Equation

I am working on a simulation project for a biology professor. Per his advice, I need to use a stochastic differential equation to model the kinetic rate of an organism's metabolism. Background to the ...
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How was this matrix equation from literature formulated and how can I customise it?

I've reproduced some results from a research paper which uses a series of matrices to solve a system of feedstock materials for making a particular product. My question is, how did the author of this ...
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0 votes
1 answer
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How to solve chemical equilibrium equations $\bf{N}^T\bf{X}+\bf{C}=\bf{Y}$ and $\bf{N}\ln\bf{Y}=\ln\bf{K}$

Here are chemical equilibrium equations: $\begin{cases} \mathbf{N}^\text{T}\mathbf{X}+\mathbf{C}=\mathbf{Y}\\ \mathbf{N}\ln\mathbf{Y}=\ln\mathbf{K} \end{cases}$ Here $\mathbf{C}=\begin{pmatrix}c_1\\...
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2 votes
1 answer
79 views

Best software for 3D node graphs (graph theory, chemistry, etc.)

What's the best (or at least, easiest-to-use) software for producing graph-theoretical diagrams in 3D space (similar to the pic below, which I found from the Wikipedia article on simple cubic graphs)? ...
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1 answer
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How were these total contained resources calculated?

I'm an investor trying to understand the technical document of a mining resource. If a mining report listed its indicated resources as: 25.59 Mt (meaning Million Tons) 1711 ppm How is the contained ...
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How to find the chemical reaction velocity?

Let me know if this problem should go to Chemistry SE. So I've got a substrate complexing reaction that can be reversed before forming the product: $$2S + E \overset{k_+}{\longrightarrow} C \overset{...
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2 votes
3 answers
100 views

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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1 vote
0 answers
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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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0 votes
4 answers
136 views

Using dimensional analysis to ‘get’ planck’s ${\lambda}$ equation with avogadro’s constant

This is for when you calculate bond energy in: ${j\cdot mol(n)^{-1}}$ and want to use planck’s equation for photon energy to calculate ${\lambda}$ Planck’s equation for photon energy: $${\lambda=\...
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1 answer
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Group symmetries of a trigonal bipyramidal molecule

I am trying to apply what I have just learnt in group theory to find the group symmetries of a trigonal bipyramidal molecule. I know that the atoms forming an equilateral triangle is the dihedral ...
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1 vote
1 answer
457 views

Calculating Wavelength Required To Break Bonds Using The Photon Energy Equation: ${λ = \frac{hc}{E}}$

I'm asking this here because it's a maths type question I seem to get a much warmer response here despite making silly mistakes: My friend told me he is going to use ...
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1 answer
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Is molarity a mathematical measure?

Molarity can simply be defined as $$\text{c} \triangleq \frac{n}{V}$$ where $c$ is the molarity, $n$ is the number of moles of a substance of interest (theoretically a counting measure because a given ...
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3 votes
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219 views

I would like to know why the tangent method, so used in chemistry, works.

I would like to know why the tangent method, so used in chemistry, works. Indeed, the teachers seem to take this method for granted but not a single one has been able to justify it to me. So I leave ...
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0 votes
1 answer
211 views

How to finding the line of best fit for a exponential decay set of data points [closed]

Im having some trouble trying to find a line of best fit that would go through the values of some values for a chemistry experiment. Here is the data: \begin{array}{|c|c|c|c|} \hline Reaction Time(s)&...
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1 vote
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What is the equation for average compound atomic mass?

I am facing a mathematical problem in chemistry: Suppose we have two atoms X and Y , each has two isotopes (forms of the same atom with different masses) (X1) mass = 12 (units) and represents 90% of ...
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5 votes
2 answers
257 views

Balancing chemical equations - Matrix determinant is zero for specific reaction

I am currently working on a program which takes a chemical equation as input and returns the balanced chemical equation instead. It finds the appropiate chemical coefficients with matrix operations, ...
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2 answers
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How should I start answering this chemical substance question? [closed]

Two substances, A and B, are being converted into a single compound C. In the laboratory it has been shown that, for these substances, the following law of conversion holds: ...
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1 vote
0 answers
37 views

Solve the following definite integral

This integral was given in an electrochemistry textbook and I am having trouble with it.$${-RT\over F}\sum_i\int_{c_i(a)}^{c_i(b)}{t_i\over z_i}d ln(c_i)$$Here R, T and F are constants (gas constant, ...
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0 answers
60 views

Laboratory Flask geometrical shape.

https://en.wikipedia.org/wiki/Laboratory_flask How one can classify Geometrical shape of Laboratory flasks especially applied in Chemistry? Is it a Cylinder, Spherical, Oval, Cone shape? How one can ...
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5 votes
3 answers
1k views

What happen to units when we take Ln?

What happens to units when we take the Ln of the both side of the equation? For example for an equation $PV^k = C$ (which becomes $\ln P = -k \ln V + \ln C$), how can we find the units of $k$ and $C$? ...
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1 vote
0 answers
27 views

When can we equate differentials?

If I have the expression as shown below: $$ dq - p_{ext} dV = ( \frac{\partial U}{\partial V})_{T} dV + ( \frac{\partial U}{\partial T})_{V} dT$$ Can I say that: $$ (\frac{ \partial U}{\partial V})_T =...
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0 votes
2 answers
80 views

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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1 answer
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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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1 vote
1 answer
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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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2 votes
1 answer
69 views

Can we decompose an array of algebraic expressions into a product of matrices that separate known variables from unknowns?

Given vectors $\sigma, \tau \in \Bbb R^n \ge0$, and constant $\mu \in \Bbb R^1>0$, let matrix-valued function $C : \Bbb R \to \Bbb R^{2 \times n}$ be defined by $$C (\mu) := \begin{bmatrix} \vec\...
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0 votes
1 answer
15 views

Mixture Problem help

I want to know if what I did is correct. The problem is: "A mixture A has a 2% hydrogen solution and a mixture B has a 1.5% of this same solution. How much Mix B must be added to 6 ounces of Mix ...
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1 vote
0 answers
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Least Squares and producing chemistry substances - ask references

This question came to me after discuss if there are nice examples of applied linear algerba topics in chemistry. A chemical compound is often a bunch of less complex chemical compouds put together to ...
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1 answer
160 views

How to define complexity?

Before Shannon's 1948 paper, most people hadn't realized that entropy, information, and their thermodynamics are closely related. I believe the concept of complexity today is also reducible between ...
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0 answers
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Deriving the formula of number of geometrical isomers in symmetric polyenes [duplicate]

For example, if we take the case of Hexa-2.4-diene we have 3 isomers which will have cis-cis, trans-trans and cis-trans arrangements at the two double bonds present. The aim is to get a formula for ...
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1 vote
1 answer
1k views

Deriving the formula of number of geometrical isomers in symmetric polyenes

For example, if we take the case of Hexa-2.4-diene we have 3 isomers which will have cis-cis, trans-trans and cis-trans arrangements at the two double bonds present. The aim is to get a formula for ...
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  • 213
2 votes
0 answers
71 views

A question on Turing's original reaction-diffusion paper

I am reading the classical reaction-diffusion paper by Alan Turing: The chemical basis of morphogenesis (1952). The paper is in the following: https://www.mit.edu/~kardar/teaching/IITS/lectures/lec8/...
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How many 3 dimensional lattices are possible mathematically?

Recently I was studying solid chemistry (crystal lattices) and there was a line in my text book. A French mathematician, Bravais, showed that there are only 14 possible three-dimensional lattices. ...
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0 votes
1 answer
48 views

Integrating differential form. Integral split with same integration margins.

In my textbook of physical chemistry is example of integration of total differential. I'll paraphrase it as I understood it. By integrating $$1) dU=\delta q-pdV$$ we get $$2) \int_{i,L}^f dU=\...
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-1 votes
1 answer
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Wolfram Alpha is doing something I don't understand, please help

I am using Newton Raphson method to obtain the velocity of a chemical reaction, and I needed to derive the next equation:$$\frac{d}{dk}\left(\left(\frac{0.35}{k}\right)^{\frac{k}{k-0.35}}\right)= -0....
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0 votes
1 answer
32 views

Rearrangement of derivatives

Recently I encountered the Clausius-Clapeyron Equation, which was initially given to me in the form, $$\frac{dP}{dT}=\frac{\Delta H_{vap}}{RT^2}P$$ However I was then told that it could be rearranged ...
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1 answer
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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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1 answer
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2D surface of atoms in an archimedian spiral

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 ...
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