Question

$\large{ \pmb{ \sf Question : - }}$

Calculate the molality of a solution of ethanol in water in which the mole fraction of ethanol is 0.04

Step by step explanation pls ! ​

Answer 1

Answer :-

Molality of the solution is 2.31 m .

Explanation :-

We have :-

→ Ethanol is solute and water is solvent .

→ Mole fraction of ethanol = 0.04

________________________________

As mole fraction of ethanol is 0.04, so number of moles of it :-

= 0.04 moles

Moles of water :-

= 1 - 0.04

= 0.96

Mass of water :-

= No of moles × Molar mass

= 0.96 × 18

= 17.28 g

= 0.01728 kg

Molality of the solution :-

= Moles of solute/Mass of solvent (kg)

= 0.04/0.01728

= 4000/1728

= 2.31 m

Some Extra Information :-

We could have also solved this problem by using the realtionship bewteen molality (m) and mole fraction of solute (X₁) :-

m = (1000X₁)/(X₂ × MM)

• X₂ is mole fraction of solvent.

• MM is molar mass of solvent .

Answer 2

• $\boxed{\sf{\blue{Molality\:of\:a\:solution\:=\:\bf{2.31\:m}}}}$

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Explanation :

$\underline{\underline{\bf{\red{Given\::-}}}}$

• Mole fraction of ethanol = 0.04

$\underline{\underline{\bf{\red{To\:Find\::-}}}}$

• Molality of a solution = ?

$\underline{\underline{\bf{\red{Solution\::-}}}}$

• Mole fraction of ethanol is 0.04. Hence, number of it's moles is 0.04.
• Moles of water = 1 - 0.04 = 0.96

★ Calculating mass of water :-

$\quad\small\leadsto\quad\tt Mass\:of\:water = No \:of\: moles \:\times\:Molar\:mass$

$\quad\small\leadsto\quad\tt Mass\:of\:water = 0.96 \:\times\:18$

$\quad\small\leadsto\quad\bf {Mass\:of\:water = \pink{17.28\:g}}$

• In kg :-

$\quad\small\leadsto\quad\tt Mass\:of\:water = \dfrac{17.28}{1000}$

$\quad\small\leadsto\quad\bf {Mass\:of\:water = \green{0.01728\:kg}}$

★ Calculating molality of a solution :-

$\quad\small\leadsto\quad\tt Molality\:of\:a\:solution = \dfrac{Moles\:of\:solute}{Mass\:of\:solvent}$

$\quad\small\leadsto\quad\tt Molality\:of\:a\:solution = \dfrac{0.04}{0.01728}$

$\quad\small\leadsto\quad\tt Molality\:of\:a\:solution = \dfrac{0.04\:\times\:100000}{1728}$

$\quad\small\leadsto\quad\tt Molality\:of\:a\:solution = \dfrac{4000}{1728}$

$\quad\small\leadsto\quad\tt Molality\:of\:a\:solution = \dfrac{\cancel{4000}}{\cancel{1728}}$

$\quad\small\leadsto\quad\bf{ Molality\:of\:a\:solution = \purple{2.31\:m}}$

$\therefore\:{\underline{\sf{Hence,\:molality\:of\:a\:solution\:=\:\bf{2.31\:m}}}}$

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