Question

@ Moderators
@ Stars
@ Best Users


Define Molarity and Molality Derive the relation between them​

Answer 1

Step-by-step explanation:

Molarity is defined as the no. Of moles of solute in 1ltr of solution and molality is defined as the no. Of solvent in 1kg of solvent. The difference is that molarity is change with temperature but the molality does not depend on temperature.

Answer 2

♣ Definitions :-

♠》 Molarity (M) :-

It is the number of moles of solute dissolved in one litre of solution.

$\bf M = \dfrac{n_2 }{V_{sol.}(in \:L)} \\ \\ \bf M= \dfrac{n_2 }{V_{sol.}(in \:mL)} \times 1000$

♠》 Molality (m) :-

It is the number of moles of solute dissolve in one kg of Solvent.

$\bf m = \dfrac{n_2 }{W_1(in \:kg)} \\ \\ \bf m = \dfrac{n_2 }{ W_1(in \:g)} \times 1000$

-----------------------

♣ Relation b/w Molarity and Molality :-

$\large \purple{ \underline {\boxed{{\bf  \frac{d}{ M }  =  \frac{1}{m} + \frac{M_2}{1000} }}}}$

-----------------------

♣ Derivation :-

We have ,

$\sf m = \dfrac{n_2 }{ W_1(in \:g)} \times 1000 \: \: \:. \: . \: . \: \{i \} \\ \\ \bf and \\ \\ \sf M = \dfrac{n_2 }{V_{sol.}(in \:mL)} \times 1000 \: \: \: .\: . \: . \: \{ii \}$

Dividing {i} by {ii} We Get,

$\sf\dfrac{m}{ M} = \dfrac{V_{sol.}}{W_1} \\ \\ \sf = \frac{W_{sol.}/d}{W_1} \\ \\ \sf = \frac{W_1 + W_2}{d.W_1}$

$\sf = \dfrac{1}{d} \bigg \{ \dfrac{W_2}{W_1} + 1 \bigg \} \\ \\ \sf = \dfrac{1}{d} \bigg \{ \frac{n_2}{n_2} \times \dfrac{W_2}{W_1} + 1\bigg \} \\ \\ \sf = \frac{1}{d} \bigg \{ \dfrac{n_2}{W_2 /M_2} \times \dfrac{W_2}{W_1} + 1 \bigg \} \\ \\ \sf = \frac{1}{d} \bigg \{ \frac{n_2.M_2}{W_1} + 1\bigg \}\\\\ \sf = \dfrac{1}{d} \bigg \{ \dfrac{m. M_2 }{1000} + 1 \bigg \}$

$\large :\longmapsto \purple{ \underline {\boxed{{\bf  \frac{d}{ M }  =  \frac{1}{m} + \frac{M_2}{1000} }}}}$

♣ Notations Used :-

W = Mass

M = Molar Mass

1 = Solvent

2 = Solute

n = number of moles

d = density in g/mL.

$\LARGE\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \Huge \red{\mathfrak{ \text{ A}nswer.}}$

-----------------------