Question

The specific gravity of sulphuric acid is 1.8.What volume of this sample of concentrated ${{H}_{2}}S{{O}_{4}}$ is required to prepare 500 ml 0.9 M ${{H}_{2}}S{{O}_{4}}$ solution?
 (A) 23.5 ml
 (B) 24.5 ml
 (C) 25.5 ml
 (D) 26.5 ml

Answer 1

Hint: From the specific gravity we can find the density and thus mass of the acid in a solution. From calculating the mass we would be able to calculate the number of moles of acid and it gives us molarity of stock solution. From this we can find the volume required to prepare the desired concentration of acid.

Complete step by step answer:
- Let's start with the concept of specific gravity. We can describe it as a ratio between the density of an object and a reference substance at the same temperature. Usually the reference substance is taken as water.
- As we can see, sulphuric acid specific gravity tells us what the density of a specific sulphuric acid solution is when compared with water. We are given that the specific gravity of sulphuric acid is 1.8. Hence, we can write the density of sulphuric acid as follows
${{\rho }_{{{H}_{2}}S{{O}_{4}}}}=1.8$

So now we know about the density of acid. In order to find the molarity of sulphuric acid, we need to pick a sample of the solution and have to figure out the number of moles of sulphuric acid present in it. By using the density, we can find the mass as follows
$1L\times \dfrac{1000ml}{1L}\times \dfrac{1.8}{1ml}$ = 1800 g
Thus, we can say that 1000 ml of sulphuric acid will weigh about 1800 g. Next, we are going to calculate the number of moles of acid by using the molar mass (molar mass of ${{H}_{2}}S{{O}_{4}}$=98 g)

Therefore, number of moles of ${{H}_{2}}S{{O}_{4}}$
= $\dfrac{Given\text{ }mass~~~}{Molar\text{ }mass}$
 =$\dfrac{1800}{98}$
  = 18.36

Thus, the molarity of the stock solution is 18.36 M.
We are asked to prepare a 500 ml solution of 0.9 Hence by using the equation ${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}$ we can write as follows
$18.36\times A=0.9\times 500$
Where A is the volume we need to find.
  $A=\dfrac{450}{18.36}$
  = 24.5 ml
So, the correct answer is “Option B”.

Note: If we are given the specific gravity of the solution, then in order to find the density from it, we should follow the following steps. (for sulphuric acid)
     Specific gravity (SG) = $\frac{{{\rho }_{{{H}_{2}}S{{O}_{4}}}}}{{{\rho }_{{{H}_{2}}O}}}$

Therefore, density of acid ${{\rho }_{{{H}_{2}}S{{O}_{4}}}}$ = SG× ${{\rho }_{{{H}_{2}}O}}$
 = 1.8 ×1
 ${{\rho }_{{{H}_{2}}S{{O}_{4}}}}$ = 1.8