Question

Calculate the molarity,molality,and mole fraction of ethyl alcohol in a solution of total volume $95ml$ prepared by adding $50ml$ of ethyl alcohol ( $density = 0.789m{l^{ - 1}}$ ) to $50ml$ water ( $density = 1.00m{l^{ - 1}}$ ).

Answer 1

Hint: A mole is defined as the amount of a substance that contains exactly $6.023 \times {10^{23}}$ number of atoms or molecules or ions. This is avogadro law. This is not compulsory because the number of moles of a molecule is equal to the number of moles of its constituent elements.
The number of moles in a given sample of an element/compound is the ratio of mass of the compound and the molar mass of the compound. It is given as:
$n = \dfrac{w}{m}$
Where, $n$ = number of moles
 $w$ = weight of the compound
$m$ = molar mass of the compound
Molarity of a solution is defined as the ratio of number of moles of solute and the volume of solution in liters. Molarity is represented by M.
$M = \dfrac{n}{V}$
Where,
M =molality of the solution that is to be calculated
n =number of moles of the solute
V =volume of solution given in terms of litres
Molality is a measure of number of moles of solute present in $1kg$ of solvent The SI unit for molality is moles per kilogram of solvent.
$m = \dfrac{n}{w}$
Mole fraction is the ratio of the number of molecules of a particular component in a mixture and the total number of moles in the given mixture. The mole fraction can be represented by $\chi $.
LET:
${n_A}$ = moles of solute
${n_B}$ = moles of solvent
${\chi _A}$ = mole fraction of solute
${\chi _B}$ = mole fraction of solvent
So,
${\chi _A} = \dfrac{{{n_A}}}{{{n_A} + {n_B}}}$
And, ${\chi _B} = \dfrac{{{n_B}}}{{{n_A} + {n_B}}}$
And also, ${\chi _A} + {\chi _B} = 1$

Complete step by step answer:
Given:Volume of solution= $95ml$
$densit{y_{ethyl\; alcohol}} = 0.789gm{l^{ - 1}}$
$densit{y_{water}} = 1.0gm{l^{ - 1}}$
To find molarity and molality first we have to find number of moles of solute(the component of a solution that is not present in excess)
Molar mass of Ethyl alcohol = $12 \times 2 + 5 + 16 + 1 \Rightarrow 46$
Molar mass of water = $2 \times 1 + 16 \Rightarrow 18$
No. of moles of ethyl alcohol= $\dfrac{{volume \times density}}{{molar \;mass}}$ $ \Rightarrow \dfrac{{50 \times 0.789}}{{46}} \Rightarrow 0.8576$
Similarly, No. Of moles of water = $\dfrac{{50 \times 1}}{{18}} \Rightarrow 2.777$
Molarity= $\dfrac{{0.8576 \times 1000}}{{95}} \Rightarrow 9.027M$
Molality = $\dfrac{{0.8576 \times 1000}}{{50}} \Rightarrow 17.152m$
Mole fraction= $\dfrac{{0.8576}}{{0.8576 + 2.777}} \Rightarrow 0.236$

Note: The Atomic mass of an element is the mass of one atom of the element expressed in atomic mass units (amu). For example, the atomic mass of carbon is 12.011 atomic mass units since carbon samples generally contain $98.89\% $ of the carbon-12 isotope , $1.11\% $ of carbon-13 isotope , and trace amounts of carbon-14.