Question

Determine the molality of a solution of benzene dissolved in toluene (methylbenzene) for which the mole fraction of benzene is 0.176. Give your answer to 2 decimal places

Answer 1

Answer:

2.32 m

Explanation:

So, according to definition of mole fraction:

$Mole\ fraction\ of\ benzene=\frac {n_{benzene}}{n_{benzene}+n_{toluene}}$

Mole fraction = 0.176

Applying values as:

$0.176=\frac {n_{benzene}}{n_{benzene}+n_{toluene}}$

$0.176\times ({n_{benzene}+n_{toluene}})={n_{benzene}}$

So,

$0.176\times n_{toluene}}=0.824\times {n_{benzene}}$

${n_{benzene}}=\frac {0.176}{0.824}\times n_{toluene}}$

${n_{benzene}}=0.2136\times n_{toluene}}$

Also, Molar mass of toluene = 92.14 g/mol

Thus,

The formula for the calculation of moles is shown below:

$moles = \frac{Mass\ taken}{Molar\ mass}$

$Mass=92.14\times n_{toluene}}\ g$

Also, 1 g = 0.001 kg

So,

$Mass\ of\ toluene=0.09214\times n_{toluene}}\ kg$

Molality is defined as the moles of the solute present in 1 kg of the solvent.

It is represented by 'm'.

Thus,  

$Molality\ (m)=\frac {0.2136\times n_{toluene}}{0.09214\times n_{toluene}}$

Molality of benzene = 2.32 m