Question

Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is ${ 0.040 }$.
[Take the volume of solution as the volume of water].

Answer 1

Hint: Molarity: It is a unit for expressing the concentration of a solution. It is defined as the number of moles of solute present per liter of the solution. Thus
Molarity = number of moles of solute/volume of solution (in liters)

Complete step-by-step answer:
It is given that,
Moles of solute = ${ 0.04mol }$
Moles of water = ${ 1-0.04 }$ = ${ 0.96mol }$
As we know that:
Number of moles= $\dfrac{Mass}{Molar Mass}$

${ Mass=Number\quad of\quad moles\times Molar\quad mass }$

Mass of ethanol = ${ 0.04mol\times 46gmol^{ -1 } }$ {Molar mass of ethanol = { 46g/mol }
                           = ${ 1.84g }$
Mass of water = ${ 0.96mol\times 18gmol^{ -1 } }= { 17.3g }$
 [Molar mass of water = ${ 18g/mol }$]
Mass of the solution = Mass of ethanol + Mass of water
                                  = ${ 1.84+17.3g }$ = ${19.1g}$

Assume the density of water is ${ 1gml^{ -1 } }$

So, the volume of the solution = $\dfrac{Mass}{Density }$
                                                 = $\dfrac{ 19.1 }{1}$ = 19.1mL
                                                 = ${ 0.0191L } { [1L = 1000mL] }$
As we know that the molarity is the number of moles of solute present in ${ 1L }$ of solution.

Hence, the molarity of the solution = $\dfrac{ 0.040 }{ 0.0191 }$ =${ 2.1M }$

Additional Information:
Mole fraction of any component is the number of moles of that component by the total number of moles of the solution.
 It is generally expressed as;
 ${ x }_{ 1 }$ =$\dfrac{ n_1} { n_1+ n_2}$

Note: The possibility to make a mistake is that you may consider the volume of solution in mL but you have to convert it in liters. Secondly, don’t confuse molarity with molality as these are two different terms.