Question

An X molal solution of a compound in benzene has a mole solute equal to 0.2. The value of X is:
A. 14
B. 3.2
C. 1.4
D. 2

Answer 1

Hint: - Molality is a way to express the concentration of a solution. The molality (m) of a solution is the moles of solute divided by the kilograms of solvent. For example a solution that contains 1.0 mol of NaCl dissolved into 1.0 kg of water is a “one-molal” solution of sodium chloride.

Complete answer:
$ Molality = \dfrac{{Number\;of\;moles}}{{Mass\;of\;Solvent(kg)}}$
0.2 is the mole fraction of the solute in Benzene
Mole fraction of Benzene=1-0.2= 0.8
Molar mass of Benzene= 78 $\dfrac{g}{{mol}}$
Molality of solution be $x$
Molality can be found using the following formula:
M=$\dfrac{{1000 \times 2}}{{{x_1} \times {M_1}}}$

Therefore, $x$=$\dfrac{{1000 \times 2}}{{(0.8 \times 78)}}$
$x$=3.205 $\dfrac{{moles}}{{kg}}$

Note: - Relation Between Mole Fraction and Molality –
$m = \dfrac{{{x_b} \times 1000}}{{{x_a}(solvent)}} \times M \cdot M$ of solvent where, ${x_b}$= Mole fraction of solute ${x_a}$= Mole fraction of solvent $M.M$= molecular mass of solvent. It is the easiest and fastest way to solve questions related with molality and mole fraction.