Question

Commercially available concentrated hydrochloric acid contains 38% HCl by mass.
(i) What is the molarity of the solution (density of solution = 1.19 $ gm{{L}^{-1}}$)?
(ii) What volume of concentrated HCl is required to make 1.0L of a 0.10M HCl?

Answer 1

Hint: To solve this question we have to use the formula of molarity which is given as
$Molarity=\dfrac{no.\,of\,moles}{Volume(L)}$.
Here 38% of HCl means 38g of HCl present in the 100g of the solution. To find the volume we have to apply the equation of normality which is given as ${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}$.

Complete step by step solution:
From your chemistry lessons you have learned about the molarity and the equation of normality which we are going to use here. Molarity is defined as the number of moles (n) of solute which is divided by the volume (V) of the solution in liters. And the formula of molarity is given as $Molarity=\dfrac{no.\,of\,moles}{Volume(L)}$.
Let us discuss each of the question one by one:
(i) What is the molarity of the solution (density of solution = 1.19$gm{{L}^{-1}}$)?
In the question it is given that 38% HCl by mass which means 38g of HCl present in the 100g of the solution. Here we have to find the molarity. So, to find the volume of the solution we have a formula that is:
\[Volume=\dfrac{Mass}{density}\]
Here, density is given as 1.19$gm{{L}^{-1}}$and the mass of the solution is 100g. Therefore the volume will be:
\[Volume=\dfrac{100}{1.19}=84.03\,mL\]
Now, we have to find the moles of HCl and as we know that $moles=\dfrac{given\,mass}{molar\,mass}$. Mass of HCl is given as 38 g and the molecular weight of HCl is 36.5. So, after putting the values we will get:
\[moles=\dfrac{38}{36.5}=1.04\]
Now put the value of moles and the volume in the equation (1), we will get :
\[Molarity=\dfrac{No.\,of\,moles\,of\,HCl}{Volume(L)}\]
\[Molarity=\dfrac{1.04\times 1000}{84}=12.38M\]
(1 ml = 0.001 L)

Thus the molarity of the solution will be 12.38 M.

(ii) What volume of concentrated HCl is required to make 1.0L of a 0.10M HCl?
Here, we have to use the equation of normality that is given as ${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}$
Where, M = molarity
and V = volume.
In the question the value of ${{M}_{1}}$is given as 12.38 M, ${{M}_{2}}$is given as 0.10 M and the value of ${{V}_{2}}$ is given as 1.0 L. Here we have to find the value of ${{V}_{1}}$. So, after putting all the values in the equation we will get:
\[12.38\times {{V}_{1}}=0.10\times 0.1\]
\[\therefore {{V}_{1}}=8.08L\]

Thus the volume of concentrated HCl is 8.08L.

Note: As we know that molarity is defined as the no. of moles of solute divided by the volume of the solution and not the moles of solute divided by the volume of the solvent. Take care of the unit of the volume while finding the molarity because volume will be in L and not in ml.