# Talk:Molality

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## mass balance equation

I don't understand this new equation which supposedly describes the relation between molality and the mass of the solvent:

${\displaystyle m=\sum _{i}n_{i}M_{i}+m_{s}\,}$

The sum describes the mass of all solutes, and ${\displaystyle m_{s}}$ is probably the mass of the solvent. Then ${\displaystyle m}$ on the left hand side is the mass of the solution. There is no molality in the equation. RolfSander (talk) 21:47, 14 April 2011 (UTC)

From this mass balance the final form derived contains the molality denoted with tilde above m after making the necessary algebraic operations (division by mass of the sovent and other rearrangements).
${\displaystyle {\frac {1}{w_{s}}}-1=\sum _{i}M_{i}{\tilde {m}}_{i}\,}$

Mi molar mass of the component --MagnInd (talk) 23:00, 14 April 2011 (UTC)

According to wikipedia policy, controversial additions should only be made after a consensus has been reached. I suggest that we work on the new text here in a "sandbox" until we are both happy with it. In your revised equation, the molality does indeed appear, and the equations are all correct, AFAICS. However, what is the practical use of them? Your final equation describes how to calculate the mass ratio of all salts to the solvent when you only know the mass fraction of the solvent. I cannot see any use for this equation. Much more interesting would be to show how molality can be converted to molar concentration. This is not easy, especially if there is more than one solute. However, it would be very useful. RolfSander (talk) 10:58, 15 April 2011 (UTC)
I agree to the temporary sandbox.

The equation derived is useful especially for binary solutions where the molality of the solute can be expressed from the mass fraction of the solvent.

The conversion to and from molar concentration(s) will be derived.--MagnInd (talk) 12:52, 15 April 2011 (UTC)

Okay, I see. Maybe we can add a section "Related Quantities" similar to what we have on the molar concentration page. There you can show how the mass fraction of the solute can be expressed from the molality. Conversion to molar concentration could be shown there as well. My first attempts are in the sandbox below. RolfSander (talk) 13:21, 15 April 2011 (UTC)
Of course the section "Related Quantities" must be included for similarity to the other concentration pages. The derivation of the expressions could have a show/hide button, for those who want the see the derivation and to not overlengthen the article.--MagnInd (talk) 18:10, 15 April 2011 (UTC)
I think the text about the related quantity mass fraction is ready for moving it from the sandbox to the real article. For conversion to molar concentration, we of course need to find the correct equations first. Introducing show/hide buttons for the derivations is a good idea if the default is set to "hide". RolfSander (talk) 19:34, 15 April 2011 (UTC)
Of course, I′l move it. Surely the default should be "hide".--MagnInd (talk) 20:17, 15 April 2011 (UTC)

It seems that starting with ternary solutions, there isn't an explicit algebraic relation between the molality and the mass fraction of a solute.--MagnInd (talk) 10:01, 17 July 2011 (UTC)

I agree. At least nothing useful. You can probably come up with a complicated equation that includes all other solutes but that wouldn't be very useful in reality...RolfSander (talk) 12:01, 18 July 2011 (UTC)

Unless I'm mistaken, it seems the conversion of molality to mass fraction as of december 1, 2014 is missing a factor of 1000 in :

${\displaystyle w=(1+(b\,M)^{-1})^{-1},}$

due to assuming 1kg of solvent while using grams for the molar mass etc. Why is the equation not

${\displaystyle w=(1+1000*(b\,M)^{-1})^{-1},}$

If this is not the case, then it's confusing as to what units are used.--169.234.32.227 (talk) 23:54, 30 November 2014 (UTC)

### Derivation-TEMPORARY SANDBOX

From the following mass balance a relation between molality and the mass of the solvent can be derived by dividing the equality by the mass of the solvent.

${\displaystyle m=\sum _{i}n_{i}M_{i}+m_{s}\,}$

gives

${\displaystyle {\frac {m}{m_{s}}}={\frac {\sum _{i}n_{i}M_{i}+m_{s}}{m_{s}}}\,}$

or

${\displaystyle {\frac {m}{m_{s}}}={\frac {\sum _{i}n_{i}M_{i}}{m_{s}}}+1\,}$

equivalent to

${\displaystyle {\frac {1}{w_{s}}}={\frac {\sum _{i}n_{i}M_{i}}{m_{s}}}+1\,}$

where ws is the mass fraction of the solvent and nj the amounts of solutes.

${\displaystyle {\frac {1}{w_{s}}}-1={\frac {\sum _{i}n_{i}M_{i}}{m_{s}}}\,}$
${\displaystyle {\frac {1}{w_{s}}}-1=\sum _{i}M_{j}{\tilde {m}}_{j}\,}$

Substuting w_i from

${\displaystyle w_{i}={\frac {1}{1+1/(m_{i}\cdot M_{i})}}}$ equivalently
${\displaystyle w_{i}={\frac {(m_{i}\cdot M_{i})}{1+(m_{i}\cdot M_{i})}}to:[itex]\rho \cdot w_{i}=c_{i}\cdot M_{i}}$

gives the searched relation for binary mixtures

${\displaystyle c_{i}=\rho \cdot {\frac {m_{i}}{1+m_{i}\cdot M_{i}}}}$

For n-ary mixtures the conversion is:

${\displaystyle c_{i}=\rho \cdot {\frac {m_{i}}{1+\sum m_{i}\cdot M_{i}}}}$

where the denominator represents the reciprocal of the mass fraction of the solvent.

n-ary mixtures

${\displaystyle m_{i}={\frac {c_{i}}{\rho -\sum c_{i}\cdot M_{i}}}\,}$

the denominator represents the mass concentration of the solvent substituted in the rearranged definition

${\displaystyle m_{i}={\frac {amount_{i}}{mass-of-solvent}}={\frac {molar-concentration_{i}}{density-of-solvent}}\,}$

obtained from definition by amplifying with volume of the solution.

## Name

It would be interesting to add some details about who defined the concept and gave the name molality.--MagnInd (talk) 21:58, 28 August 2011 (UTC)

## Symbol

Thanks, Toolnut, for all your edits here. I support your change from m to b as the symbol for molality because it avoids the confusion with m for mass. However, I would like to see a general consensus here for the change. Do others agree as well?

If we now keep the symbol b, we will also have to check and if necessary adjust all pages that may refer to molality, e.g.: Molar concentration · Mass concentration · Number concentration · Volume concentration · Normality · Percentage solution · Mole fraction · Mass fraction · Mixing ratio RolfSander (talk) 21:27, 11 November 2011 (UTC)

Perhaps l would be more sugestive as notation by beeing next to m in the alphabet and coming from molality.--MagnInd (talk) 14:35, 20 November 2011 (UTC)
If we could choose from scratch, l might not be a bad idea. However, IUPAC only suggests the two possibilities m and b. I don't think we should invent something new here.--RolfSander (talk) 15:24, 20 November 2011 (UTC)
From where does b come?--MagnInd (talk) 17:41, 20 November 2011 (UTC)s
No idea. Maybe they just wanted something that cannot be confused with mass.--RolfSander (talk) 09:07, 21 November 2011 (UTC)
Perhaps because it's the letter next to c for molar concentration :-)Toolnut (talk) 16:31, 21 November 2011 (UTC)
FYI, I have only deduced the defintion of molality for multi-solute solutions from what the prior contributions were attempting to express, a little awkwardly, which definition is not found in any of the sources quoted for this article, nor is it in my first-year college-chemistry book. However, with a little logic and derivations, I have attempted to make it consistent with the formulas previously given for multi-solute solutions by other contributors.Toolnut (talk) 21:09, 13 November 2011 (UTC)

Thanks again, Toolnut, for completing the derivation of relations to other compositional quantities.--MagnInd (talk) 12:34, 20 November 2011 (UTC)

Since we seem to have a consensus here to use the symbol b for molality, I have now adjusted the pages Molar concentration and Mass concentration.--RolfSander (talk) 23:04, 2 December 2011 (UTC)

### Density of solvent notation

The density of solvent , if appears in the conversion formulae, should have the symbol ${\displaystyle \rho _{0}{*}}$ to avoid confusion with the mass concentration of solvent having the subscript zero.--MagnInd (talk) 20:53, 29 November 2011 (UTC)

Huh? The density of the solvent (mass of solvent over volume of solvent) does not come up: it cannot be derived, at least not exactly; I guess you meant the "mass concentration of the solvent" (mass of solvent over volume of solution, with subscript "0"). The only density that is known is that of the solution, unsubscripted ρ.Toolnut (talk) 20:35, 30 November 2011 (UTC)
Thanks for catching my mistake in the article: "mass density of solvent" was indeed incorrect. I see now that someone unnamed had correctly changed it, but RolfSander had undone his changes immediately after. Toolnut (talk) 02:52, 7 December 2011 (UTC)
Can you please show me where I undid a correct change? I cannot find it. Regarding the difference between "mass concentration of the solvent" and "mass density of the solvent": We wouldn't have this problem if we used the usual "gamma" as the symbol for mass concentration. I never liked to have the symbol rho for both mass concentration and density as well.--RolfSander (talk) 08:15, 7 December 2011 (UTC)
Find it here. Good idea about renaming the symbol: I'm for it if there's consensus.Toolnut (talk) 12:06, 7 December 2011 (UTC)
Oh, I see it now. Sorry for the undo. Regarding gamma instead of rho: I hope that MagnInd agrees with us. If yes, let's wait another week to see if anyone else wants to comment on it. Then, if there's consensus, let's change it here and also on other pages that refer to mass concentration.--RolfSander (talk) 19:33, 7 December 2011 (UTC)
The question is that rho is not an arbitrary chosen symbol. It is a unified/self-consistent notation which underlies the intrinsic connection between the two quantities (being the same for a pure component). The use of different symbols would obscure the intrinsic connection, especially when they appear in the same formula, like:

${\displaystyle \rho =\sum _{i}\rho _{i}^{*}{\frac {V_{i}}{V}}\,=\sum _{i}\rho _{i}^{*}{\frac {n_{i}V_{i}^{*}}{V}}\,}$ sum symbol forgotten--MagnInd (talk) 23:19, 14 December 2011 (UTC)

${\displaystyle \rho _{i}=\rho _{i}^{*}{\frac {V_{i}}{V}}\,=\rho _{i}^{*}{\frac {n_{i}V_{i}^{*}}{V}}\,}$

(relation to volume concentration)

The distinction is done by the star superscript.--MagnInd (talk) 20:12, 9 December 2011 (UTC)

The quantities "density" and "mass concentration" are similar but not identical. To distinguish them, I think it is important to have different symbols for them. If I see "${\displaystyle \rho }$(H${\displaystyle _{2}}$O)" somewhere in a formula, I will immediately assume that this is the density of water (and not the mass concentration of water in an aqueous solution). You are right that the use of different symbols might obscure the intrinsic connection between the two quantities. However, I think it is even worse that the use of the same symbol would obscure the difference between them!--RolfSander (talk) 19:43, 10 December 2011 (UTC)

A solution to this dilemma could be the the assigning the symbol rho with say tilde above ${\displaystyle {\tilde {\rho _{i}}}}$ to mass concentration and leaving rho unsuperscripted to densities of components. This minimize the potential for confusion while keeping the intrinsic connection between the two.--MagnInd (talk) 10:23, 15 December 2011 (UTC)

The symbol ${\displaystyle {\tilde {\rho _{i}}}}$ would be okay if it was commonly used in science. However, wikipedia should only document what is already there and not invent new things (even if they would make sense, like your suggestion with the tilde). Therefore, instead of inventing a new symbol, I would prefer if we keep the established symbol ${\displaystyle \gamma }$ and explain the intrinsic connection of density to mass concentration in the "Related Quantities" section of the mass concentration page.--RolfSander (talk) 09:28, 23 December 2011 (UTC)
A tilded or bolded letter does not constitute a new symbol, just a means of disambiguation in a formula. As for the gamma letter, it could be confused with another quantity namely the activity factor which is needed in formulas for thermal expansion.— Preceding unsigned comment added by MagnInd (talkcontribs)

The density of the solvent appears in the relation between molality and apparent molar property.--5.15.57.134 (talk) 09:21, 4 September 2014 (UTC)

## Non-dimensionless (mixed) ratio

A mixed ratio is dimensional, unlike ratio of quantities with the same dimension such as mass, amount.--MagnInd (talk) 20:37, 6 December 2011 (UTC)

It seems that mass ratio or amount ratio are not covered on en.wp unlike in de.wp: [1]--MagnInd (talk) 20:44, 6 December 2011 (UTC)

They can both be found here: mixing ratio.--RolfSander (talk) 21:35, 6 December 2011 (UTC)
It seems that the two mixing ratios (mass and molar) are different than those described on de.wp. A NIST document contains reference to the ratios described on de.wp [2].--MagnInd (talk) 18:38, 9 December 2011 (UTC)
Can a ratio be non-dimensionless? The wikipedia page about ratio says that those are really proportions, see: Ratio#Different_units. I'm not sure about the term "proportions" but I also think that "ratio" is not correct for non-dimensionless quantities. --RolfSander (talk) 10:36, 21 June 2012 (UTC)
Perhaps quotient would be more appropiate?--MagnInd (talk) 21:39, 21 June 2012 (UTC)
Quotient would be fine for me.--RolfSander (talk) 18:59, 22 June 2012 (UTC)

## Obscure and esoteric?

As an industrial chemist for 35 years I virtually never encounter this in the literature. The only place I've seen this is in textbooks. I am wondering whether it is actually used, and if so where? Perhaps pharmaceutical chemistry? Some examples from the literature (NOT textbooks) would be appropriate. The concept is a lot more of a problem than is claimed here. A solution of NaCl, for instance, will solvate certain compounds that water alone will not. What is the solvent in the cases where while there may be only one liquid, but the solvent is a mixture? What if two solids when combined form a liquid mixture? In industrial chemistry it is VERY common that the appropriate combination of two (occasionally three) solvents makes a better solvent than any of the components. I *HIGHLY* question the (not clearly articulated) assertion made here that only one (liquid) chemical can be "the" solvent. Actually, this concept breaks down as you move away from ideal binary solute-solvent systems. Given any system {A,B} with interactions A-A, B-B, and A-B, the solvency can be defined as the A-B interactions. As soon as you move to a trinary system {A,B,C} determination of whether A-B, A-C, and B-C interactions are "solvent-like" (compared to some vague alternative) borders on the absurd. Seems to me that molality is more a subject of mixology than chemical science. That is, it aids the technician making up solutions, rather than having any intrinsic theoretical value. Another example of the problem how does molality fair when water is replaced with heavy water? Suddenly "b" changes by 20% ?? Is there ANY area of study that it is regularly used? Other than to waste the student's time in learning esoterica? If so, cite it, if not I suggest the article state that it has not been widely accepted and because of its limited applicability (unless it can be defined for multicomponent solutions) its use is usually depreciated.Define it or state that there is no clear definition for other than binary mixtures.71.31.149.224 (talk) 20:30, 1 July 2012 (UTC)

The advantage mentioned is an advantage, but not at all extent. Even mass changes; which is given by ${\displaystyle M={\frac {m}{\sqrt {1-v^{2}/c^{2}}}}}$ ; m is rest mass. Should this to be mentioned in appropriate language, even though it doesn't affect much, and not a big difference is possible in everyday life.