Question

Density of a ${{H}_{2}}S{{O}_{4}}$ solution is $1.2g/ml$ and it is 40% ${{H}_{2}}S{{O}_{4}}$ by weight. Determine molarity of this solution.
A. $2.9M$
B. $3.9M$
C. $4.9M$
D. $5.9M$

Answer 1

We first define molarity. Then we find the molar mass of ${{H}_{2}}S{{O}_{4}}$ . Finally we get the molarity of the given solution by using the formula $Molarity=\dfrac{n}{v}$ where $n$ is number of moles of solute and $v$ is the number of litres of the solution.

Complete step by step answer: Let us first discuss molarity briefly.
The molarity of a solution is the number of moles of solute dissolved in one litre solution. To calculate molarity, we divide the number of moles of the solute by the volume of the solution expressed in litres.
We were given that the density of ${{H}_{2}}S{{O}_{4}}$ solution is $1.2g/ml$.
We were also given that it is 40% ${{H}_{2}}S{{O}_{4}}$ by weight.
So let us convert the formula of molarity into the terms of density and molar mass.
We get,
$Molarity=\dfrac{n}{v}=\dfrac{n\times density}{Molar\text{ }mass}$
Now, let us calculate the molar mass of ${{H}_{2}}S{{O}_{4}}$.
Let us first write the atomic mass of each atom in ${{H}_{2}}S{{O}_{4}}$.
Atomic mass of hydrogen = 1
Atomic mass of sulphur = 32
Atomic mass of oxygen = 16
Now, molar mass of $~{{H}_{2}}S{{O}_{4}}=2\left( 1 \right)+32+4\left( 16 \right)=2+32+64=98g/mol$
So, by using the formula of molarity, we get,
\begin{aligned} & Molarity=\dfrac{40%\times 1.2g/ml}{98} \\\ & \\\ & \Rightarrow Molarity=\dfrac{\dfrac{40}{100}\times 1000\times 1.2g/lt}{98} \\\ & \\\ & \Rightarrow Molarity=\dfrac{40\times 10\times 1.2}{98} \\\ & \\\ & \Rightarrow Molarity=\dfrac{480}{98} \\\ & \\\ & \Rightarrow Molarity=4.89\approx 4.9M \\\ \end{aligned}
So, the correct answer is “Option C”.

Note: The possibilities for making mistakes in this type of problems are, One may make a mistake while changing the units of density from g/ml to g/lt. One must know the atomic mass of the elements to find the molar mass of the given compound.