What is solution: Definition and 13 Discussions

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. 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.
  2. docnet

    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.
  3. docnet

    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...
  4. Spikey

    Seeking Innovative Attachment Solutions for a Biochemistry Project

    I am currently engaged in a local project that requires a unique attachment solution. We need to securely affix a 100g object, coated with cross-linked polyethylene foam, to a board that is covered in synthetic fur. The attachment must be robust enough to endure shaking and bumps. Importantly...
  5. R

    I Lentz superluminial solution, anything new on it?

    I cannot find much on the Lentz solution for superluminal travel since the initial reactions to the paper coming out in 2021. Has more mathematical work been done on this? I have my doubts it would work based on some of the criticisms I have seen but want to see if someone has really evaluated...
  6. 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...
  7. 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)...
  8. mido hoss

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

    During calculating null space from rref matrix some rows are with 1 variable so it give this variable value of zero so the null space of rank deficient matrix be for example {-1,2,0,3,-4,0} my question is how to get rid of zeros in the null space solution and only solve it as basic and free...
  9. jamesbrazil

    Maple Finding the solution of this long equation using Maple

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  10. G

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

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  11. 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...
  12. L

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

    Hi, unfortunately, I have a problem to solve the following task The equation looks like this: $$\left(\begin{array}{c} \frac{d}{dt} x(t) \\ \frac{d}{dt} y(t) \end{array}\right)=\left(\begin{array}{c} -a y(t) \\ x(t) \end{array}\right)$$ Since the following is true ##\frac{d}{dt}...
  13. 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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