Talk:Molality

mass balance equation

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

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

The sum describes the mass of all solutes, and $m_{s}$ is probably the mass of the solvent. Then $m$ 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).

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

M_i 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)

Derivation-TEMPORARY SANDBOX

Extended content

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. $m=\sum _{i}n_{i}M_{i}+m_{s}\,$ gives ${\frac {m}{m_{s}}}={\frac {\sum _{i}n_{i}M_{i}+m_{s}}{m_{s}}}\,$ or ${\frac {m}{m_{s}}}={\frac {\sum _{i}n_{i}M_{i}}{m_{s}}}+1\,$ equivalent to ${\frac {1}{w_{s}}}={\frac {\sum _{i}n_{i}M_{i}}{m_{s}}}+1\,$ where ws is the mass fraction of the solvent and nj the amounts of solutes. ${\frac {1}{w_{s}}}-1={\frac {\sum _{i}n_{i}M_{i}}{m_{s}}}\,$ ${\frac {1}{w_{s}}}-1=\sum _{i}M_{j}{\tilde {m}}_{j}\,$ Substuting w_i from $w_{i}={\frac {1}{1+1/(m_{i}\cdot M_{i})}}$ equivalently $w_{i}={\frac {(m_{i}\cdot M_{i})}{1+(m_{i}\cdot M_{i})}}to:<math>\rho \cdot w_{i}=c_{i}\cdot M_{i}$ gives the searched relation for binary mixtures $c_{i}=\rho \cdot {\frac {m_{i}}{1+m_{i}\cdot M_{i}}}$ For n-ary mixtures the conversion is: $c_{i}=\rho \cdot {\frac {m_{i}}{1+\sum m_{i}\cdot M_{i}}}$ where the denominator represents the reciprocal of the mass fraction of the solvent. n-ary mixtures $m_{i}={\frac {c_{i}}{\rho -\sum c_{i}\cdot M_{i}}}\,$ the denominator represents the mass concentration of the solvent substituted in the rearranged definition $m_{i}={\frac {amount_{i}}{mass-of-solvent}}={\frac {molar-concentration_{i}}{density-of-solvent}}\,$ obtained from definition by amplifying with volume of the solution.

Intentionally vague definitions?

This article is terrible - the definitions almost appear intentionally vague. — Preceding unsigned comment added by 67.238.101.3 (talk) 00:32, 27 July 2011 (UTC)

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 $\rho _{0}{*}$ 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:

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

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

(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 "$\rho$(H$_{2}$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 ${\tilde {\rho _{i}}}$ 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 ${\tilde {\rho _{i}}}$ 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 $\gamma$ 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 (talk • contribs)

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)

You're asking 2 questions:

1) Is molality used at all? Yes it is, very often in relation to activity coefficients but also in other areas. Simply try a google scholar search:[3]

2) Which of the components is the solvent? Good question. For binary aqueous solutions it is obvious, in other cases it is necessary to define it when you use molalities. This is already mentioned in the "Problem areas" section of the article. --RolfSander (talk) 10:35, 2 July 2012 (UTC)

Factor of 1000 missing

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 :

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

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

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

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)

I see from the history of this article a recent edit involving the 1000 factor and its presence when some units are used. Perhaps this factor of 1000 can appear in the general formula but in paranthesis like (1000). Thoughts?--185.53.197.247 (talk) 11:34, 16 April 2019 (UTC)

Please do not use a factor of 1000 in these formulas! If you use SI units, the factor is not necessary. If you use non-SI units, there are a zillion of possible units you could insert into any formula, depending whatever units you prefer. -- RolfSander (talk) 12:01, 16 April 2019 (UTC)

It seems that a discrepancy between the use of multiples and submultiples of SI units is involved here re the factor of 1000, namely the use of (1000) gram(s) vs kilogram of solvent, the SI unit mole for amount of substance being usually associated with gram rather than kilogram, the SI unit for mass.--185.53.197.247 (talk) 12:41, 16 April 2019 (UTC)

I removed the 1000 for the formula. Instead the text (now) says the unit should be kg/mol (which isn't normal at least for chemists). Christian75 (talk) 16:25, 30 April 2019 (UTC)

I think that in this context a section in article re Multiples and submultiples is needed. I'll open a section below.--109.166.129.142 (talk) 00:18, 20 July 2019 (UTC)

Usage considerations/Advantage

The advantage mentioned is an advantage, but not at all extent. Even mass changes; which is given by _{$M={\frac {m}{\sqrt {1-v^{2}/c^{2}}}}$} ; 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.
aGastya  ✉ Dicere Aliquid :) 02:01, 7 May 2015 (UTC)

Molality fraction(s)

I notice that there are some objections to the term molality fraction, recently inserted in article and used in some sources to calculate an apparent molar mass for a pseudocomponent from a ternary solution considered pseudo-binary mixture in order to define an apparent molar property for a (pseudo)component as volume just like for the case of usual binary mixtures.--82.137.9.23 (talk) 20:03, 19 October 2017 (UTC)

I put here the removed formula:

$y_{i}={\frac {b_{i}}{b_{T}}}$, y_i the molality fraction of solute i,

which can be similar to the name ionic strength fraction encountered in other sources.--82.137.9.23 (talk) 20:11, 19 October 2017 (UTC)

Therefore, when ionic strength is expressed as molality, the name molality fraction is nearby as an immediate consequence.--82.137.9.23 (talk) 20:23, 19 October 2017 (UTC)

The name molality fraction has been removed on the ground of insufficient reference for it. What would be the sufficient number of references?--82.137.9.166 (talk) 20:51, 23 October 2017 (UTC)

I've checked another source in another journal (Food Science) which uses the same formula for an mean apparent molar mass of the 2 solutes and the same ratios of molalities but this time just not naming in any way the two ratios involving molalities. The ratios of molalities leads to a complex fraction which finally simplifies and gives a ratio of molar amounts.

Is this a better solution not to name the two ratios?--82.137.9.114 (talk) 09:04, 24 October 2017 (UTC)

In general, topics worth mentioning are described here: [4]. For the case of "molality fraction", I think it would be notable if it is used in more than just one or a few specific articles. However, it is neither mentioned in the IUPAC gold book [5] nor in any chemistry text book, AFAIK. I think the reason why the term "molality fraction" is hardly used is because it is not really related to molality. The mass of the solvent cancels out. You could just as well define a "molarity fraction" (note the letter "r" here) and get the same value because the volume of the solution cancels out here as well. Both would be identical to a simple mole fraction. -- RolfSander (talk) 09:11, 24 October 2017 (UTC)

Of course the phrase "molality fraction" can be avoided by using a simple descriptive or explanatory joining of words such as "ratio involving molalities" for the above ratio. On the other hand in the field of mixed electrolytes solution I've encountered the phrase "ionic strength fraction" in the same context of mean apparent molar mass of ionic solutes, possibly in books by Robinson and Stokes.--82.137.9.114 (talk) 10:30, 24 October 2017 (UTC)

About ratios and fractions, one can also define and encounter a phrase like "mole fraction fraction" (sic!), or equivalently "mole fraction ratio" which equals indeed the binary mole ratio of components (in a at least ternary system when mixing binary subsystems with a common constituent). This defining occurs when applying Gibbs or Gibbs-Duhem equation to ternary and multicomponent mixtures. This requires groupings of components in binary mole or mole fraction ratios which can be held constant, as shown by papers authored by L.S. Darken (J. Am. Chem. Soc. 72, 2909, 1950), C. Wagner (Thermodynamics of Alloys), R. Schuhmann, jr (Acta Met. 3, 219, 1955), H.A.C. McKay (Nature, 169, 464, 1952), Nev A. Gokcen (Journal of Physical Chemistry, 64, 401, 1960). This mole(mole fractions) ratios occur in (isothermal-isobaric) phase diagram representations like ternary plot, quaternary plot, n-ary plot, etc.--82.137.9.114 (talk) 11:28, 24 October 2017 (UTC)

Relation to activity coefficient (of an electrolyte)

Some aspects concerning this mentioned relation will be introduced in article.--82.137.13.190 (talk) 14:14, 25 October 2017 (UTC)

The following block of text will be introduced which underlies the mentioned relation:--82.137.13.190 (talk) 14:24, 25 October 2017 (UTC)

For concentrated ionic solutions the activity coefficient of the electrolyte is split into electric and statistical components.

The statistical part includes hydration index number h , the number of ions from the dissociation and the ratio r between the apparent molar volume of the electrolyte and the molar volume of water and molality b of the electrolyte.

Concentrated solution statistical part of the activity coefficient is: $\ln \gamma _{s}={\frac {h-\nu }{\nu }}\ln(1+{\frac {br}{55.5}})-{\frac {h}{\nu }}\ln(1-{\frac {br}{55.5}})+{\frac {br(r+h-\nu )}{55.5(1+{\frac {br}{55.5}})}}$,

Relation to apparent molar volume

I think the relation to apparent molar volume would need further details about intermediate steps in derivation.--5.2.200.163 (talk) 13:41, 3 August 2018 (UTC)

See the talk:Apparent molar property#Relation to molality for comparison of equations.--5.2.200.163 (talk) 14:23, 3 August 2018 (UTC)

Multiples and submultiples for molality units

I think that this article needs a section with multiples and submultiples for the main molality unit, in connection to the factor of 1000, mentioned above. Amy suggestions?--109.166.129.142 (talk) 00:29, 20 July 2019 (UTC)

Molality is NOT a concentration!

By IUPAC definition a concentration is defined exclusively with respect to volume. Accordingly, "molal concentration" is not even listed among the possibilities and the definition of molality does not use the term "concentration". --Geon79 (talk) 23:37, 23 September 2019 (UTC)

Yes, you're absolutely right: Molality is NOT a concentration. (BTW: I've moved your comment to the bottom of the page. This is where you normally find new items)--RolfSander (talk) 11:07, 24 September 2019 (UTC)

Factor of 1000 and the unit for molar mass

The above discused factor of 1000 enters the unit for molar mass when not present explicitly.--178.138.99.40 (talk) 18:59, 24 May 2021 (UTC)