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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Fundamental equation (Entropy) using Peng-Robinson EoS

As we know, simple systems can reach equilibrium states defined by just three measurable properties: internal energy (U), Volume (V), and the number of each molecule type (N) which can be defined with ...
roee danan's user avatar
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How to solve an ODE where the rate is directly proportional to two amounts?

Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
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I want to know the behavior of the solution without solving the ordinary differential equation for enzyme-substrate reactions. [closed]

I want to know the behavior of the solution without solving the ordinary differential equation for the following enzyme-substrate reactions. This chemical reaction represents the process by which ...
Blue Various's user avatar
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Probability for collisions in a 2D random walk scenario

I am a chemical engineer working on an algorithm for the simulation of catalytic processes in a particle based simulation framework and unfortunately, I am struggling with a math problem and I'm not ...
FritzPeppone's user avatar
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Hard Question on Math Homework concerning chemical Mass of Molecules (Problem explained in Body)

A chemist wants to make a solution of 0.05mg of MgCl2 in 52.51mL of H2O; however, he only has MgCl2 * 6H2O to make his solution. How much water should he add if he has to make the correct ...
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Solving Logarithmic Expression

In the context of the thermodynamics of mixing two separate gases at the same temperature and pressure, one has the generic equation, \begin{gather*} -\frac{\Delta S_{mix}}{nR} = X_A \ln(X_A) + X_B \...
Matt Hanson's user avatar
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Determining the product ratio in a chemical reaction

There is a chemical reaction called Wurtz reaction in which the product forms when two reactant particles collide means there is no worry that if they collide then they will make bond on basis of the ...
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How do I find a set of unit vectors with a given angle between each other?

I am coming from a biology/chemistry background and trying to make some math connections. How would I go about solving for $n$ unit vectors (same magnitude) which are all equally spaced from each-...
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How can I Find the stoichiometric coefficient of a complex chemical reaction??

I'm trying to balance a complex chemical reaction of decomposition of an organic material. I tried using Matlab to sole the set of equations I got, But the problem I get and where I think I'm missing ...
Ahmed Esaa's user avatar
2 votes
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Fourier Transform for IR spectroscopy: integral doesn't converge

From Cozzi-Protti-Ruaro - Elementi di Chimica Analitica Strumentale, page 244: However, since the IR sources are of the continuous type, i.e. they emit over the entire spectral range, the ...
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Fast Fourier Transform from interferogram

Fourier transform spectrometers use a device called Michelson interferometer. To understand how this device works, we first consider a monochromatic radiation. This radiation strikes the beam splitter,...
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Symmetry group of an hourglass shape, the molecule Ferrocene.

I am starting to learn (Visual) Group Theory and I saw this hourglass shaped molecule Ferrocene: I am wondering what group is described by its symmetries. On top of the five rotations I think there ...
Pierrick Leroy's user avatar
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Mass action law and conservation of mass

I am starting to learn about the use of mass action law in chemistry. I am doing some exercises to practice. In particular, I am considering the reaction $$2 X \underset{3}{\stackrel{4}{\...
mejopa's user avatar
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Closed-form expression of $\int_ 0^{\pi/2} (1-x \cot x)^2 \csc^2 x \log (1-x \cot x) dx$

I have been trying, with no luck, to find the closed-form expression of the following integral $$\int_ 0^{\pi/2} (1-x \cot x)^2 \csc^2 x \log (1-x \cot x) dx \approx -0....
Pierre-Francois Loos's user avatar
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The Coffin-Manson is an extension of the Arrhenius equation

Given the following problem: Each TV goes through 10,000 on/off cycles in its field life. The temperature change from these on/off cycles is from 20°C to 60°C. We can perform thermal cycle testing ...
Martinho Luterinho's user avatar
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1 answer
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Need help solving difficult equation [closed]

Need help solving for $X_{\text{ave}}$: $$X_{\text{ave}} = \left(\frac{a_1 f_1^2} {F_0 + F_r\, f_{\text{carb}}\, f_{\text{calc}} \, (1-f_1)} +\frac{a_2 f_2^2} {F_0 + F_r \, f_{\text{carb}} \, f_{\text{...
satansdisciple's user avatar
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Applications (Power Series)

(Hooke's Law for Biomolecules) The entropy of conformation of a protein, considering it to be a freely jointed chain that contains a total of N segments, each of Length L, is given by the expression: $...
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Applications of Vectors in Chemistry: Dot Product

The H-O-H bond angle of H2O is 104.48 °. The Overall dipole moment of the H2O molecule is 1.855D. Calculate the dipole moment of each individual O-H bond. $\theta = 104.48 = 52.24 °$ And I let ...
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Balancing a chemical equation involving ethanol and hydrogen peroxide by setting up a vector equation

I'm having trouble balancing a chemical equation for the combustion of ethanol with hydrogen peroxide to produce carbon dioxide and water. The equation is given as: $$x_4 C _2 H _5 OH +x_3 H _2 O _2 \...
cricket900's user avatar
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Onsager and Stefan-Maxwell Equations

Stefan-Maxwell and Onsager equations are equations which can be used to calculate mole flux of the component due to different types of gradients. It is assumed that driving forces of mass transfer are ...
Dario Mirić's user avatar
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Solving chemical master equation using Kolmogorov system

I am recently studying about chemical reaction networks. And I have problem about application of Kolmogorov system to actual examples. So, here's a chemical reaction $S_1 + S_2 \rightarrow S_3$ with $...
random487510's user avatar
1 vote
1 answer
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Linearized Michaelis-Menten equation for LP

I am attempting to include the Michaelis-Menten equation in (continuous) variables $S$ and $v$ $$v=\frac{V_{\max} S}{K_m + S}$$ where $V_{\max}$ and $K_m$ are given constants, as a linear programming ...
Freiburgermsu's user avatar
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$u''+\cosh u=0$ or $u''+\sinh u=0$

I would like to know a physical or chemical background of the ODE of the second order $u''(x)+\cosh u(x)=0$ or $u''(x)+\sinh u(x)=0$. These two ODEs have beautiful structures. Hence, I am wondering ...
Yasuhito Miyamoto's user avatar
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3 answers
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Is either $\dfrac{A_1}{B_1}=.25$, $\dfrac{A_2}{B_2}=.4$ or $\dfrac{A_1}{B_1} +\dfrac{A_2}{B_2}=.35$?

Solution $A$, containing $25 \%$ oil and $75 \%$ water, is mixed with Solution $B$, containing $40 \%$ oil and $60 \%$ water. If the resulting mixture contains $35 \%$ oil, approximately what ...
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1 vote
1 answer
523 views

What is the underlying mathematics behind law of mass action?

When calculating reaction rates of of a chemical reaction, what is the reason taking product of concentration of chemicals (i. e. V+ = k[A][B]) instead addition (e.g. k[A] + k[B])? Does this related ...
Dendrobium's user avatar
1 vote
1 answer
134 views

Deriving rate equation of a Chemical reaction

I want to derive the rate equation of $x$, concentration of $X$, in the following reaction: $$ aX + bY \rightarrow Z.$$ I know the answer is $$\frac{dx}{dt}=-kx^ay^b$$ for a constant $k$, but I need ...
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First order homogeneous differential equations: comparison between two results

The differential equation to solve is the following $$ -\dfrac{dc_\mathrm{B}}{dt} = k_1\ c_\mathrm{A,0}\ e^{-k_1 t} - k_2\ c_\mathrm{B}$$ This formula expresses the variation in B $(dc_\mathrm{B})$ ...
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Need help in quantitatively modeling solubility of carbon dioxide in beer.

I'm trying to model a 3D surface which reflects the solubility of $CO_2$ in beer. An empirically derived chart is available at this link. Solubility is empirically related to the pressure of $CO_2$ in ...
High Gravity's user avatar
5 votes
1 answer
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How to analytically find the number of unique (simple) hydrocarbon chains, with arbitrary numbers of hydroxyl groups, of $N$ carbon atoms long

I wrote a Python script which already approximates this, however I would like to know how one can arrive at a purely analytical solution (or at least an analytically derived approximation). Let us ...
Alexander Kalian's user avatar
2 votes
1 answer
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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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1 answer
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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) \...
TheLearner's user avatar
1 vote
2 answers
69 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 ...
user avatar
6 votes
1 answer
193 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 ...
Fouad Saffar's user avatar
3 votes
1 answer
358 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 ...
Starlight's user avatar
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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 ...
mamotebang's user avatar
2 votes
1 answer
141 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 ...
Jared Frazier's user avatar
-1 votes
1 answer
108 views

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,...
noob anomaly's user avatar
1 vote
1 answer
88 views

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), ...
user979847's user avatar
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 $$ ...
Joe's user avatar
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1 vote
2 answers
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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 ...
Camilo Vargas's user avatar
2 votes
0 answers
149 views

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 ...
Gromulus_Romulus's user avatar
1 vote
2 answers
176 views

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\\...
auntyellow's user avatar
2 votes
1 answer
229 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)? ...
ProXy's user avatar
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1 vote
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 ...
pstatix's user avatar
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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
149 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 ...
làntèrn's user avatar
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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 ...
Stefano Travaglino's user avatar
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4 answers
200 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=\...
Nickotine's user avatar
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2 votes
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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