solution Definition and 24 Threads

In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. These surrounded solute particles then move away from the solid solute and out into the solution. The mixing process of a solution happens at a scale where the effects of chemical polarity are involved, resulting in interactions that are specific to solvation. The solution usually has the state of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. One important parameter of a solution is the concentration, which is a measure of the amount of solute in a given amount of solution or solvent. The term "aqueous solution" is used when one of the solvents is water.

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  1. I

    A Numerical solution of the Poisson equation

    In my case, there is proton radiation acting on the material. Consequently, the protons get stuck in the sample and create an electrostatic field. I would like to solve the Poisson equation inside the sample. I assume that the medium is infinite and homogeneous, that is, the potential at...
  2. M

    A A part in a solution for exercise 1.24 from Atiyah-MacDonald

    In the part below where the author of this solution, wants to show that: ##a\vee (b\wedge c)=(a\vee b)\wedge (a\vee c)##, in the third equality he adds ##2ac+2ab+2abc=2a\wedge(b\vee c)##; can someone explain to me why can we do this here? Thanks!
  3. M

    A Deduce that the spectrum of a local ring is always connected

    Iv'e got this proof from some claim: Any Pure maths doctors out there who can explain to me why since ##V\ne \emptyset## that ##1\notin \mathfrak{b}##? Thanks!
  4. mishima

    How to predict the volume of a solution?

    I've never had a good understanding of this. Say I am dissolving 20g sodium chloride into 1L of water. Is the only way to theoretically predict the final volume of solution to consult density tables? edit: I realize this isn't a practical situation, and that typically you are making a solution...
  5. A

    Finding Non-Trivial Solution(s) For 3x3 Matrix

    I didn't have any good way to put this in the homework statement, but this is what the question is asking: For what c-value(s) will there be a non-trivial solution: ## x_1 - x_2 + x_3 = 0 ## ## 2x_1 + x_2 + x_3 = 0 ## ##-x_1 + (c)x_2 + 2x_3 = 0 ## I have spent a good couple hours looking at...
  6. M

    Morin 3.7 -- Block sliding sideways on an inclined plane

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  7. tellmesomething

    Please explain this suggested solution for the field inside a charged hollow sphere

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  8. M

    Finding general solution to linear system

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  9. chwala

    Find the particular solution of the second order differential equation

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  10. chwala

    Find the solution to the given differential equation

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  11. chwala

    Show that the system of equations has no unique solution

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  12. V

    I Detailed solution of an envelopes example in a math book

    Can someone please show me the steps from circled equation 1 to 2? Thank you.
  13. D

    B What is a closed form solution?

    Hi friends, I was wondering if you could give the definition of 'closed form', with examples of closed form solutions and open? form solutions. Foe example, is this a closed form solution? $$\sum_{k=1}^\infty \frac{1}{2^k}$$ Or this? $$\sum_{k=1}^5 \frac{1}{2^k}$$ Thanks.
  14. D

    Solving a separable matrix ODE.

    I have never solved a matrix ODE before, and am wondering if solving it is similar to solving ##y'=ay## where ##a## is a constant and ##y:\mathbb{R} \longrightarrow \mathbb{R}## is a function. The solution is right according to wikipedia, and I am just looking for your inputs. Thanks...
  15. Spikey

    Seeking Innovative Attachment Solutions for a Biochemistry Project

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  16. R

    I Lentz superluminial solution, anything new on it?

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  17. SCHROEDERFPM

    I H2O/gold solution will not boil

    This is my solution and it remained still and did not bubble once while the pot boiled . I realise salt and oil impurities may increase the boiling point but I wouldn't imagine to this extent, and when I filtered the solution the oil seemed to collect the copper and other dissolved metals...
  18. chwala

    Show that ##f(x,y)=u(x+cy)+v(x-cy)## is a solution of the given PDE

    Looks pretty straightforward, i approached it as follows, ##f_x = u(x+cy) + v(x-cy)## ##f_{xx}=u(x+cy) + v(x-cy)## ##f_y= cu(x+cy) -cv(x-cy)## ##f_{yy}=c^2u(x+cy)+c^2v(x-cy)## Therefore, ##f_{xx} -\dfrac{1}{c^2} f_{yy} = u(x+cy) + v(x-cy) - \dfrac{1}{c^2}⋅ c^2 \left[u(x+cy)+v(x-cy)...
  19. mido hoss

    Optimizing Null Space Solutions: How to Remove Zeros in Rank Deficient Matrices

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  20. jamesbrazil

    Maple Finding the solution of this long equation using Maple

    I need help solving an equation. I started using Maple, but had no success. Could someone explain to me which command to use? I need to find a very small value of ##x##, that is, ##x \ll 1##. The equation is $$434972871000000000.0+{\frac {\sqrt {6} \left( { 1.488388992\times 10^ {-36}}\,\ln...
  21. G

    Does anyone know how to put an equation tag in $$ line?

    This has bothered me for a while and I have not found a good solution, it's convenient to write math equations using the \$\$ on the fly and occasionally we want to put a tag for an equation. tag works for the equation environment but not for \$\$. For example I would like to have [1] displayed...
  22. mcastillo356

    B I need to check if I am right solving this integral

    Hi, PF 1-The elementary integral is ##\displaystyle\int{\displaystyle\frac{1}{a^2+x^2}dx}=\displaystyle\frac{1}{a}\tan^{-1}\displaystyle\frac{x}{a}+C## 2-The example is...
  23. L

    Solve these two coupled first-order differential equations and sketch the flow

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  24. H

    Ingenious Algorithm Riddle: Imposs. Even w/Answer

    Hardly anyone would think of this solution. I even wonder how anyone would come up with the question. And it is even more amazing that the questioner and solver were not the same person.
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