Question

The mole fraction of benzene in a solution in toluene is 0.50. Calculate the weight percent of benzene in the solution.

Answer 1

Hint : In the production of phase diagrams, the mole fraction is widely utilised. It comes with a lot of benefits. It is not temperature dependent (like molar concentration) and does not require knowledge of the phase(s) densities. By weighing the right masses of the elements, a mixture with a known mole fraction can be made.

Complete Step By Step Answer:
The mole fraction, or molar fraction ( ${x_i}$ ), is defined in chemistry as a unit of the quantity of a constituent (expressed in moles), ${n_i}$ divided by the total quantity of all components in a mixture (also represented in moles). –
${x_i} = \dfrac{{{n_i}}}{{{n_{{\text{tot}}}}}}$
The mole percent, molar percentage, or molar proportion is the same notion represented with a denominator of 100. (mol percent )
Assume that the benzene concentration in the solution is x.
This indicates that the mass of benzene in a 100 g solution is x g,
while the mass of toluene is (100 - x)g.
The molecular mass of benzene is 78g
Whereas the molecular mass of toluene is 92g
Hence using the formula it is given as
$\therefore \quad \dfrac{{{n_B}}}{{\left( {{n_B} + {n_T}} \right)}} = 0.50$
$\dfrac{{x/78}}{{x/78 + (100 - x)/92}} = 0.50$
$\dfrac{x}{{78}} \times \dfrac{{78 \times 92}}{{92x + 78(100 - x)}} = 0.50$
$92x = 46x + 3900 - 39x{\text{ }}$
$85x = 3900{\text{ }}$
$\Rightarrow x = 45.9\%$
Weight percent is 45.9%.

Note :
Because it does not include the name of the unit mole, the National Institute of Standards and Technology prefers the phrase amount-of-substance fraction to mole fraction. Molar concentration is a proportion of moles to volume, whereas mole fraction is a ratio of moles to moles. Mass fraction (percentage by weight, wt percent ) and volume fraction (percentage by volume, vol percent ) are two more ways of describing the composition of a mixture using a dimensionless quantity.