Question

150 ml of ethyl alcohol is diluted by adding water, then the molarity of a solution is: (Given, the density of ethyl alcohol = 0.78)
(a)- 2.54
(b)- 11.7
(c)- 2.99
(d)- 3.99

Answer 1

Hint: The molarity of the solution is the ratio of the number of moles to the volume of the solution. The number of moles can be calculated by dividing the given mass by the molar mass of the compound.


Complete step by step answer:
Molarity: The molarity of the solution is defined as the number of moles of the solute which is present in 1 L volume of the solution. We can represent it by the symbol, M.
Its formula is:
\[Molarity=\dfrac{\text{Moles of the solute}}{\text{Volume of the solution}}\]
Moles of the component is defined as the ratio of a given mass to the molar mass.
Its formula is:
\[Moles=\dfrac{given\text{ }mass}{\text{molar mass }}\]
Given the density of the solute (ethyl alcohol) is 0.78.
We know that the density is equal to the ratio of mass to the volume. So the mass can be calculated by multiplying the density to the volume.
The given volume of ethyl alcohol is 150 ml.
$Mass=Density\text{ x }Volume$
$Mass=0.78\text{ x 150}$
 $Mass=117\text{ grams}$
The formula of ethyl alcohol is ${{C}_{2}}{{H}_{5}}OH$ and the molecular mass is $46\text{ g/mol}$
So, the number of moles will be:
\[Moles=\dfrac{given\text{ }mass}{\text{molar mass }}\]
\[Moles=\dfrac{117}{\text{46 }}=2.54\text{ moles}\]
So, the number of moles is 2.54.
The volume of the solution is 1 liter, in which 150 ml is ethyl alcohol and 850 ml of water.
So, the molarity of the solution will be:
\[Molarity=\dfrac{\text{Moles of the solute}}{\text{Volume of the solution}}\]
\[Molarity=\dfrac{\text{Moles of the solute}}{\text{Volume of the solution}}=\dfrac{2.54}{1}=2.54\text{ M}\]
So, the molarity is 2.54.

Therefore, the correct answer is an option (a)- 2.54.

Note: The volume of the solution must be taken in liters only. If the concentration or density of the solute is given in kg or any other unit, it has to be converted into grams because these are the standard units taken for the calculation of Molarity.