<< Chapter < Page
  Stoichiometry   Page 1 / 1
Chapter >> Page >

Molality (m) is also a measurement of molar concentration like molarity (M). We have seen that molarity(M) is a convenient measurement of the concentration of solution as it allows us to directly compute moles of solute present in the solution. There is, however, a problem in reporting concentration of a solution in terms of molarity. Recall that it is equal to numbers of moles of solute divided by volume of solution in litres. The molar ratio has volume of the solution in the denominator. This means that molarity(M) of a given solution will change with temperature as volume of solution will change with temperature. This is a major handicap as reported concentration needs to be reliable and constant anywhere irrespective of temperature. In this backdrop, molality(m) is measurement of concentration aiming to remove this shortcoming associated with measurement in molarity (M).

Molality(m) also differs to other measurements in yet another important aspect. It involves the ratio of measurement of solute and solvent – not that of solute and solution. This difference is important to be kept in mind while computing quantities and converting measurement units from one to another.

The major objective of this module is to develop skills to convert measurement of concentration from one measurement type to another.

Molality of a solution with respect to solute is defined as :

Molality(m) = Moles of solute (B) Mass of solvent (A) in Kg

m = n B w Akg

Its unit is moles/ kg. In case we consider mass of solvent in gm, then the expression of molality is given as :

m = n B g A X 1000 = Milli-moles of B g A

If mass of solvent of a solution of known molality is known, then number of moles of solute is obtained as :

Moles of solute, B = Molality X Mass of solvent in kg

Similarly,

Milli-moles of B = Molality X Mass of solvent (A) in gm

Problem : 11.7 gm of sodium chloride is dissolved in 400 ml of water. Find molality of the solution.

Solution : Here,

Moles of sodium chloride = 11.7 23 + 35.5 = 11.7 58.5 = 0.2

Mass of the solvent = 400 X 1 = 400 g m = 0.4 k g

Molality, m = 0.2 0.4 = 0.5 m

Molality in terms of molarity and density of solution

Molality and Molarity are linked to each other through density of solution. Beginning with the definition of molarity, a solution of molarity “M” means that 1 litre of solution contains “M” moles of solute. If the density of the solution is “d” in gm/cc, then

Mass of 1 litre solution in gm = 1000 d

Mass of the solute in gm in 1 litre solution = nos of moles X molecular weight = M M O

Mass of the solvent in gm in 1 litre solution = 1000 d M M O

We need to calculate mass of solvent in kg to calculate molality(m) :

Mass of the solvent in kg in 1 litre solution = 1000 d M M O / 1000

Hence, molality,

m = n B W Akg = M 1000 d M M O 1000 = 1000 M 1000 d M M O

We should note that "density of solution (d)" and "strength of solution (S)" differ. Density of solution (d) is ratio of mass of solution (solute + solvent) in gm and volume of solution in cc. It has the unit of gm/cc. On the other hand, strength of solution (S) is ratio of mass of solute in gm and volume of solution in litre. It has the unit of gm/litre.

Problem : The density of 3M sodium thiosulphate (Na2S2O3) solution is 1.25 gm/cc. Calculate molality of Na + and S 2 O 3 ions.

Solution : We can use the formula to calculate molality of the sodium thiosulphate :

m = 1000 M 1000 d M M O = 1000 X 3 1000 X 1.25 3 X 2 X 23 + 2 X 32 + 3 X 16

m = 3000 1250 474 = 3000 776 = 3.866

Alternatively , we can proceed with the basic consideration in place of using formula Since molarity of solution is 3M, it means that 1 litre of solution contains 3 moles of sodium thiosulphate. We can use density to find the mass of the 1 litre solvent.

Mass of solution = 1000 X 1.25 = 1250 g m

Mass of 3 moles of sodium thiosulphate = 3 M N a 2 S 2 O 3 = 3 X 2 X 23 + 2 X 32 + 3 X 16

Mass of 3 moles of sodium thiosulphate = 3 X 46 + 64 + 48 = 3 X 158 = 474 g m

Mass of solvent = 1250 474 = 776 g m = 0.776 k g

Molality of sodium thiosulphate = 3 0.776 = 3.866 m

We are, however, required to calculate molality of ions. We see that one mole is equivalent to 2 moles of sodium ion and 1 mole of thiosulphate ion :

Na 2 S 2 O 3 = 2 N a + + S 2 O 3

Hence,

Molality of Na + = 2 X 3.866 = 7.732 m

Molality of S 2 O 3 = 3.866 m

Density of solution in terms of molarity and molality

Working on the relation of molality developed in previous section :

m = 1000 M 1000 d M M O

1 m = 1000 d M M O 1000 M = d M M O 1000

d = M 1 m + M O 1000

Problem : The molality and molarity of a solution of sulphuric acid are 90 and 10 respectively Determine density of the solution.

Solution : Using relation :

d = M 1 m + M O 1000

d = 10 1 90 + 98 1000 = 10 X 0.011 + 0.98 = 10 X 0.991 = 9.91 g m / c c

Molality in terms of density of solution and strength of solution

We need to know the moles of solute and mass of solvent in kg to determine molality. Now, strength of solution (S) is equal to mass of the solute in gm in 1 litre of solution. Hence,

Mass of the solute in gm in 1 litre of solution = S

Moles of the solute = S M O

Mass of 1 litre solution in gm = 1000 d

Mass of the solvent in gm in 1 litre of solution = 1000 d S

Mass of the solvent in kg in 1 litre of solution = 1000 d S 1000

The molality is :

m = n B W Akg = S M O 1000 d S 1000 = 1000 S M O 1000 d S

Problem : A solution has 392 gm of sulphuric acid per litre of solution. If the density of the solution is 1.25 gm/cc, find molality of the solution.

Solution : Using relation :

m = 1000 S M O 1000 d S = 1000 X 392 98 X 1000 X 1.25 392 = 4.73 m

Molality in terms of mole fraction and molecular weight

Molality is defined as :

m = n B W A k g = n B g A X 1000 = n B n A M A X 1000

n B = m n A M A 1000

On the other hand, mole fraction with respect to solute B is given by :

χ B = n B n A + n B

Substituting for nA, we have :

χ B = m n A M A 1000 n A + m n A M A 1000 = m M A 1000 + m M A

1000 χ B + m M A χ B = m M A

m M A 1 χ B = 1000 χ B

m = 1000 χ B 1 χ B M A

Similarly, we can express molality in terms of mole fraction with respect to solvent (A) as :

m = 1000 1 χ A χ A M A

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Stoichiometry. OpenStax CNX. Jul 05, 2008 Download for free at http://cnx.org/content/col10540/1.7
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Stoichiometry' conversation and receive update notifications?

Ask