Question

Give a relation between molarity and morality !

Derivation is must !

Answer 1

Molarity :-

Molarity (M) indicates the number of moles of solute per liter of solution (moles/Liter) and is one of the most common units used to measure the concentration of a solution. Molarity can be used to calculate the volume of solvent or the amount of solute.

Morality:-

principles concerning what is good and bad or right and wrong behaviour

Hope it helps

Answer 2

▪Definitions :-

☆》 Molarity (M) :-

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

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

☆》 Molality (m) :-

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

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

▪Relation Between Molarity and Molality :-

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

▪Derivation :-

We have ,

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

{ii} / {ii} ⟹

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

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

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

$\sf = \dfrac{1}{d} \bigg \{ \dfrac{m. M_2 }{1000} + 1 \bigg \} \\ \\ \large \purple{ \implies  \underline {\boxed{{\bf  \frac{d}{M}  =  \frac{1}{m} + \frac{ M_2 }{1000} } }}}$

▪Notations Used :-

1. W = Mass
2. M = Molar Mass
3. 1 = Solvent
4. 2 = Solute
5. n = number of moles
6. d = density in g/mL.