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
3
votes
2answers
126 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 ...
1
vote
0answers
70 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
votes
0answers
61 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 ...
0
votes
1answer
23 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 ...
1
vote
0answers
29 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 ...
0
votes
2answers
31 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 ...
1
vote
2answers
166 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
vote
1answer
39 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
votes
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 ...
1
vote
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:
$$\begin{align*}
3a+8b+d&=12e+4f+2g\\
a&=e\\
4a+4c+3d&=4e+3f+g+3h\\
...
5
votes
1answer
120 views
Symmetric Direct Product Distributive?
This comes from the context of chemical group theory, so I apologize if I'm using terminology incorrectly. For that context, see Determining the symmetry of overtones of degenerate modes on the chemSE....
1
vote
0answers
56 views
Number of compounds with the same chemical formula
Even though this question may not seem apropriate for this site, it is more of a mathematical one than a chemistry one.
Take an example chemical formula C3H4O2. There are many compounds with this ...
5
votes
0answers
127 views
Quantum Chemistry book recommendation. [closed]
I am trying to learn quantum chemistry. I have an extensive background in math and physics, so I'm looking for a book that makes full use of whatever physics and mathematics is relevant to this ...
-1
votes
2answers
68 views
Strange substitution in integral using partial fractions
Let $[A]_0=a$ and $[B]_0=b$, then $[A]=a-x$ and $[B]=b-x$.
$$\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)$$
Evaluating the integral gives ...
12
votes
2answers
116 views
An application of the Inclusion Principle to Chemistry? (Proof Verification)
Background
I’m taking chemistry and one thing they have us do is draw Lewis structures for molecules. Guessing if there are going to be double or triple bonds is kind of annoying. I’d like to be able ...
1
vote
2answers
47 views
Preparation of aqueous solution
In Chemistry class, Samantha finds that she can make a certain solution by mixing $.04\,\rm L$ of chemical $\mathrm{A}$ with $.02\,\rm L$ of water (this gives her $.06\,\rm L$ of the solution). She ...
0
votes
0answers
25 views
Finiding a constant in wave-function so it solves the Schrodinger equation
Vibrations in a diatomic molecule can be approximated as a harmonic oscillator,
$\hat{H}=\hat{T}+\hat{V}=-\frac{\hbar^2}{2\mu}\frac{d^2}{dx^2}+\frac{1}{2}kx^2$
where x is the displacement from ...
1
vote
1answer
40 views
How Would the Left Side of this Limit be Solved?
I have two equations which represent the ratio of concentration to initial concentration in a chemical reactor, and I need to know what the limit of the left side would be, where when $t$ becomes ...
1
vote
1answer
87 views
How to calculate the average molar mass of the atmosphere? [closed]
The task: Determine the average molar mass of the atmosphere - each for the moist air and the dry air. One example that I have calculated is this one: I have the gas Nitrogen and the percentage for ...
3
votes
3answers
499 views
Differential equations for chemical reaction $\mathrm{A + 2B \to 3C}$
In a chemical reaction $\mathrm{A + 2B \to 3C}$, the concentrations $a(t)$, $b(t)$ and $c(t)$ of the three substances A, B and C measure up to the differential equations
$$
\begin{align}
\frac{da}{...
0
votes
1answer
64 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
51 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
votes
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
vote
1answer
37 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
377 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
156 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
vote
1answer
34 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 ...
1
vote
0answers
126 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
votes
1answer
324 views
Time reversal in Robertson's chemical reaction
I am studying the behavior of the Robertson chemical reaction,
$$\begin{array}{rl} \dot{x} &= -0.04 x + 10^4 y z\\ \dot{y} &= 0.04 x - 10^4 y z - 3 \times 10^7 y^2\\ \dot{z} &= 3 \times ...
2
votes
2answers
63 views
Minimizing Double Values in Combinatorial Chemistry Mixtures
I am a chemist working on a project where I synthesize Mixture Libraries.
Using different starting materials in solution mixtures, all possible combinations can theoretically form as products.
To ...
1
vote
1answer
86 views
Mathematical Problems of Climate Science?
Are there any interesting research-level mathematics problems that have come out of climate science specifically or that are abstractions of some of the issues and models pertaining to climate science?...
0
votes
1answer
45 views
Determining Mass of Lithium [closed]
What is the mass of 1.3 x 10^(23) atoms of lithium.
Lithium has a mass of 6.94, so I assumed that it'd be 6.94 x 1.3 x 10^(23), but that wasn't the case. I wasn't given much practice and I'm not sure ...
2
votes
0answers
118 views
Calculating a “max support flux vector sequence”
Tl;dr: what is a max support flux vector sequence?
In a paper (arXiv link; full citation below) on continuous chemical reaction networks (CCRNs)$^1$ it discusses an algorithm for reaching different ...
0
votes
1answer
15 views
Determining sufficiency of concentrated solutions
I am trying to make a function to calculate whether a given supply of reagents is sufficient to create a list of products at a given solution.
So for a list of products
$$
(a_1, b_1), (a_2, b_2) ... (...
-1
votes
1answer
183 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
votes
1answer
52 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
votes
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:
$$\begin{bmatrix}
4 & 1 & 0 \\
10 & ...
0
votes
2answers
85 views
Linear Algebra Problem (Chemistry) [closed]
$$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
votes
0answers
35 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
votes
1answer
541 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 ...
-1
votes
2answers
235 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....
0
votes
3answers
620 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 (...
1
vote
1answer
54 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{...
1
vote
0answers
73 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
vote
1answer
226 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
votes
2answers
48 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 $\dfrac 14$ ...
17
votes
9answers
4k views
Why can't we remove the sqrt from rms?
In chemistry, we define the root-mean-square speed as
$\sqrt{\bar{u^2}}$ = $\sqrt{\frac{3\text{RT}}{\text{M}}}$
A student asked me why we can't just remove the square root symbol. And aside from "...
2
votes
2answers
3k views
How to get critical constants from Dieterci's real gas equation?
Please, before closing this question as off-topic, consider that this is completely a calculus problem, no chemistry involved
Dieterci's real gas equation is
$$p = {RTe^{-a/(RTV)}\over V - b}$$
...
1
vote
1answer
52 views
Simplify the expression given
So I've been working on a project, and hope to simplify the expression
by substituting the values
and
To obtain a polynomial in terms of the variable [$H^+$] only. Note that I understand this ...
