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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Two identical glasses; what percentage; multiple rounds [duplicate]

There are two identical glasses: Glass A contains 99ml of pure cranberry juice (colored red); Glass B contains 99 ml of water (colorless). We take one spoonful (1ml) of liquid from Glass A and mix it ...
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Chemistry math question (not really chemistry)

There are two identical glasses: Glass A contains 99ml of pure cranberry juice (colored red); Glass B contains 99 ml of water (colorless). We take one spoonful (1ml) of liquid from Glass A and mix it ...
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1answer
36 views

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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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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1answer
36 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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38 views

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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112 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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2answers
93 views

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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34 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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33 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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165 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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29 views

Ratio of rates of diffusion of gases.

I stumbled upon a question, A mixture of 50 mL of Hydrogen gas and 50mL of Oxygen gas is allowed to effuse through an effusimeter. After some time it is observed that the residual gas occupies 90mL. ...
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24 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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40 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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1answer
35 views

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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1answer
29 views

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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56 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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1answer
14 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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13 views

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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1answer
102 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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Projecting 3D Data Onto a 2D Plane in Motion

I'm trying to model the rotation of a hydrogen atom about a carbon atom in a chemical reaction. My model consists of a conceptual wheel on an axle that is attached to a car. The axle is described by ...
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16 views

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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1answer
115 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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61 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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34 views

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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1answer
27 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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1answer
59 views

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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63 views

Defining dihedral angles without singularities

I'm a physical chemist by training, so my understanding of any math beyond 4th semester Calculus is quite rusty. I apologize in advance if I use any of the wrong terminology. In computational ...
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1answer
26 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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1answer
39 views

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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1answer
26 views

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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1answer
80 views

How would one calculate percent error between two ratios

Let's say I have a $1:1$ ratio and a $5:1$ ratio which could also be interpreted as a $1:5$ ratio. the fact that both of these ratios are valid but one is $5$ while the other is $0.2$ is the problem, ...
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43 views

Finding the coordinates of an irregular tetrahedron

I am querying about a mathematical problem even though its application is in chemistry. I am trying to find the coordinates for the part of a molecule that forms an irregular tetrahedron. The bond ...
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2answers
53 views

How to write the amount of sodium-iodine?

A chemist working on a flu vaccine needs to mix a 10% sodium-iodine solution with a 60% sodium-iodine solution to obtain a 50-milliliter mixture. Write the amount of sodium iodine in the mixture, S, ...
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1answer
48 views

Why does the mean velocity of gas particles include $\pi$?

In chemistry, we are learning about kinetic molecular theory (KMT) of gasses, and I just couldn't help being surprised when I saw pi in the equation of mean velocity. I know that whenever $\pi$ is ...
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1answer
52 views

Does there exist mathematical background for ultra-slow process control?

I want to ask a question to respected mathematicians and specialists in control theory: Is there a separate direction in nonlinear control theory that develops control of super slow processes? Are ...
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1answer
43 views

Calculate All Possible Combinations to 100%

I have a list of chemicals with percentages composing a certain alloy. I am trying to find a way to see all possible combinations summing to 100%, but am a bit stuck with the maths. For this example,...
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1answer
57 views

Carbon dating using exponential function

Basic carbon dating problems I've seen before, but this seems to take more details into account, both in model and the questions, which I have not seen before, nor understand. Anyone that can help me? ...
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1answer
424 views

Balancing Chemical Reactions using Systems of Equations

I am learning about applications of systems of equations in my applied matrix theory. I am trying out some of the practice exercises around the "balancing chemical equations using systems of equations"...
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1answer
35 views

Applying power to a trapezoid approximation. Is the paper wrong?

So I was reading this paper by a chemist where he used trapezoid approximation to find value of integration of an unknown function $\ f(t) = \int [A]^\alpha dt$. For context: The method presented ...
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1answer
27 views

Euler method for chemical system

I have a simple chemical system $A\rightarrow B$ with $k_1$ and $A_1\rightarrow B$ with $k_2$. I can easily solve it with different packages but I wanted to learn the Euler way. I am solving it in ...
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1answer
26 views

Determining the proportional rate constant for chemical reaction at specific temperature

The main relation one can use to calculate the missing links is the Arrhenius equation: $k=k_0*e^{(-\frac{Ea}{R*T})}$, where $k_0$ is a rate constant of the chemical reaction, $k$ is a proportional ...
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1answer
62 views

Amount of NaHCO3 needed to neutralize HCl [closed]

With the equation: HCl + NaHCO3 --> NaCl + CO2 + H2O Find the number of grams of NaHCO3, to three significant figures, required to neutralize 75 mililitres of 0.110 mol/l HCl. I'm stuck on this ...
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1answer
727 views

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
210 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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64 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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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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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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79 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 ...