Question

Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040. (Assume the density of water to be one).

Answer 1

Molarity is an expression that is used to calculate or measure the concentration of a solution. It relates the no. of moles of solute to the per litre of the solution, just like normality. Mole fraction of a solute is simply defined as the ratio of the number of moles of the solute divided by the total number of moles present in the solution.

Complete step by step answer:

Molarity (M) indicates the number of moles of solute per litre of solution (moles/Litre) and is one of the most common units used to measure the concentration of a solution. The formula of molarity is given as follows:

$Molarity\quad =\quad \dfrac { No.\quad of\quad moles\quad of\quad solute }{ Volume\quad of\quad solution }$

Given in the question, Moles of ethanol = 0.04 mol

Therefore, moles of water = 1 - 0.04 = 0.96 mol

Mass of ethanol = 0.04 mol x 46 g/mol = 1.84 g

Mass of water = 0.96 mol x 18 g/mol = 17.3 g

Mass of the solution = 17.3 g + 1.84 g = 19.1 g

Given, the density of water = 1 g/ml

Volume of the solution is given as:

$Volume\quad of\quad solution\quad =\quad \dfrac { Mass }{ Density }$

$\implies Volume\quad of\quad solution\quad =\quad \dfrac { 19.1 }{ 1 } \quad mL\quad =\quad 19.1\quad mL\quad =\quad 0.0191\quad L$

Now, let us calculate the molarity of the solution.

$Molarity\quad =\quad \dfrac { No.\quad of\quad moles\quad of\quad solute }{ Volume\quad of\quad solution }$

$\implies Molarity\quad =\quad \dfrac { 0.040 }{ 0.0191 } \quad =\quad 2.1\quad M$

Therefore, the molarity of the solution is 2.1 M.

Note: Molarity and molality are two different quantities used to find the concentration of the solution. Molarity (M) is defined as the number of moles of solute per liter of solution. And molality (m) is defined as the number of moles of solute per kilogram of solvent. Make sure you do not confuse them.