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Mole Fraction

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Question

A solution is made with Solvent A (molar mass 40 g/mol) by slowly adding solute B. A curve is plotted between molality of the solution vs $\frac{x_{B}}{x_{A}}$ where $x_{B}$ and $x_{A}$ represents the mole fraction of solute and solvent respectively.
Calculate the slope of the curve.

A

10 mol/g

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B

10 g/mol

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C

25 g/mol

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D

25 mol/g

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Solution

The correct option is D 25 mol/g
Molality is given by
$m = \frac{1000 \times n_{B}}{n_{A} \times m_{A}}$ (i)
Where $n_{A}$ and $n_{B}$ are moles of solvent and solute respectively and $M_{A}$ is molar mass of solvent in g/mol
Also mole fraction of the solute is given by
$x_{B} = \frac{n_{B}}{n_{A} + n_{B}}$ (ii)
Substituting the value of $n_{A}$ from eq (ii)
we will get
$m = \frac{1000}{M_{A}} \times \frac{x_{B}}{x_{A}}$
$∴ s l o p e = \frac{1000}{M_{A}} = 25 m o l / g$

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Similar questions

Q. A solution is made with Solvent A (molar mass 40 g/mol) by slowly adding solute B. A curve is plotted between molality of the solution vs

\frac{x_{B}}{x_{A}}

x_{B}

x_{A}

represents the mole fraction of solute and solvent respectively.
Calculate the slope of the curve.

Molality: It is defined as the number of moles of the solute present in 1 kg of the solvent. It is denoted by 'm'
Molality (m) =

\frac{N u m b e r o f m o l e s o f s o l u t e}{N u m b e r o f k i l o g r a m s o f t h e s o l v e n t}

w_{A}

grams of the solute of molecular mass

m_{A}

w_{B}

grams of the solvent, then
Molality (m) =

\frac{w_{A}}{m_{A} \times w_{B}} \times 1000

Relation between mole fraction and Molality :

X_{A} = \frac{n}{N + n} a n d X_{B} = \frac{N}{N + n}

\frac{X_{A}}{X_{B}} = \frac{n}{N} = \frac{M o l e s o f s o l u t e}{M o l e s o f s o l v e n t} = \frac{W_{A} \times m_{B}}{w_{B} \times m_{A}}

\frac{X_{A} \times 1000}{X_{B} \times m_{B}} = \frac{w_{A} \times 1000}{W_{B} \times m_{A}} = m

\frac{X_{A} \times 1000}{(1 - X_{A}) m_{B}} = m

If the ratio of the mole fraction of a solute is changed from

\frac{1}{3}

\frac{1}{2}

800

g of solvent then, the ratio of molality will be :

Q. Calculate the molality of a 1.5 M aqueous salt solution in a solvent X, if the mole fraction of the salt in the solution is 0.25.
(Molar mass of solvent = 40 g/mol)

Q. Calculate the molality of a

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aqueous salt solution in a solvent X, if the mole fraction of the salt in the solution is

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Q. A solid solution is made up of two solids "A" and "B". Mass percentage of "A" is 40% by mass in a solid solution. Find the molar mass of "B" if the mole fraction of "A"

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