Name: Expressing Concentration by Mass Percent
Uploaded: 2019-07-19
Duration: 3 min 32 s
Description: Mass percentage is a way of representing the concentration of an element in a compound or a component in a mixture. Let us learn more through this video.

Question

The vapour pressure of

C_{6} H_{6}

and

C_{7} H_{8}

mixture at

50^{0} C

is given by

P (mm Hg) = 180 X_{B} + 90

, where

X_{B}

is the mole fraction of

C_{6} H_{6}

. A solution is prepared by mixing

12 mol C_{6} H_{6}

and

8 mol C_{7} H_{8}

and if vapours over this solution are removed and condensed into liquid and again brought to the temperature

50^{0} C

, what would be the mole fraction of

C_{6} H_{6}

in the vapour state? (Atomic weight of

C = 12, H = 1

)

Accepted Answer

If the vapour pressure of pure benzene and toluene are ${P_{B}}^{0}$ and ${P_{T}}^{0}$ and the mole fractions $X_{B}$ and $X_{T}$ , respectively, then, the total pressure of solution is $P_{S}$ .

$P_{S} = {P_{B}}^{0} X_{B} + {P_{T}}^{0} X_{T}$

Here,

$X_{B} + X_{T} = 1$ or $X_{T} = 1 - X_{B}$

$P_{S} = {P_{B}}^{0} X_{B} + {P_{T}}^{0} (1 - X_{B}) P_{S} = {P_{B}}^{0} X_{B} + {P_{T}}^{0} - {P_{T}}^{0} X_{B} P_{S} = {P_{T}}^{0} + ({P_{B}}^{0} - {P_{T}}^{0}) X_{B}$

From the given question,

$P = 90 + 180 X_{B} P_{S} = {P_{T}}^{0} + ({P_{T}}^{0} - {P_{B}}^{0}) X_{B}$

${P_{T}}^{0} = 90 mm Hg$ and ${P_{T}}^{0} - {P_{B}}^{0} = 180$

So, ${P_{B}}^{0} = 270 mm Hg$

$12 mol C_{6} H_{6}$ and $8 mol C_{7} H_{8}$

$X_{B} = \frac{12}{20} = \frac{3}{5}, X_{T} = \frac{8}{20} = \frac{2}{5} P_{B} = {P_{B}}^{0} X_{B} P_{B} = 270 \times \frac{3}{5} = 162 P_{S} = 90 + 180 \times \frac{3}{5} P_{S} = 198 mm Hg$

In vapour state, the equation is $P_{B} = P_{S} Y_{B}$ . Here, $Y_{B}$ is the mole fraction of benzene in the vapour state.

$Y_{B} = \frac{P_{B}}{P_{S}} Y_{B} = \frac{162}{198} = 0.83$

Solute	Dissociation/association reaction	Degree of dissociation/association	n	i
$KCl$		$1$
$H_{2} {SO}_{4}$		$1$
${CH}_{3} COOH$ (in water)		$0.2$
${CH}_{3} COOH$ (in benzene)		$0.5$
Urea
$NaBr$		$0.8$
A	$3 A \to A_{3}$	$1$

Important Questions on Solutions

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