Question

What is the molarity of ${{H}_{2}}S{{O}_{4}}$ solution that has the density of 1.84g/cc and contains 98% mass of ${{H}_{2}}S{{O}_{4}}$?
(A) 4.18M
(B) 8.14M
(C) 18.4M
(D) 18M

Answer 1

Hint: We need to know the volume of the solution in order to know the molarity of the solution. By basic physics, we can relate density, volume and mass as density is defined as mass per unit volume of a substance. This relation is helpful in this question.

Complete step by step solution:
-Molarity is defined as the ratio of the moles of the solute to the volume of the solution and can be expressed mathematically as
$molarity=\dfrac{moles\text{ }of\text{ }solute}{volume\text{ of solution}}=\dfrac{mol}{L}$
-In the given question, we are given the density of the solution and the percentage of mass of ${{H}_{2}}S{{O}_{4}}$. We are not given the volume of the solution but we know that we can find the volume of the solution if we know the density and the mass as all these three terms are related to each other as $density=\dfrac{mass}{volume}$
-We are given the density as 1.84g/cc. But the mass is given in percentage and not in grams. So we need to first find the mass of the solute in grams and then the volume can be evaluated by putting the values of density and mass in the above equation.
-98% mass of${{H}_{2}}S{{O}_{4}}$ means that there are 98 grams of solute of ${{H}_{2}}S{{O}_{4}}$in 100 grams of solution of ${{H}_{2}}S{{O}_{4}}$. So, if we take the mass of the solution to be 100 grams, then we get the mass of the solute to be 98 grams. Thus we get,
Mass of solute = 98 grams
Mass of solution = 100 grams
-Now, the volume of the solution can be obtained from the mass of the solution. We know,
$density=\dfrac{mass}{volume}$
So, $1.84$ = $\dfrac{100}{volume}$
So the $Volume of solution$ = $\dfrac{100}{1.84x{{10}^{3}}}=54.347x{{10}^{-3}}$
-$Moles of solute$= $\dfrac{wt.\text{ in grams}}{molecular\text{ wt}\text{.}}=\dfrac{98}{2x1+32+4x16}=\dfrac{98}{98}=1\text{ }mole$
So, $molarity=\dfrac{moles\text{ }of\text{ }solute}{volume\text{ of solution}}$
= $\dfrac{1}{54.37x{{10}^{-3}}}$
= $18.4 mol/L$

Therefore, the correct option is (C) $18.4M$.

Note: Always take into account the unit of all the quantities present in the question. Remember that 1M= mol/L. No other unit defines 1M. Also, keep into account the relationship between the units of mass and the units of volume. 1L = 1000ml and 1ml = 1cc. Also, the volume has to be taken of the solution and the moles are taken of the solute.