# Concentrated sulphuric acid has a density of 1.9 g/mL and 99%\[{{H}_{2}}S{{O}_{4}}\] by mass. Calculate the molarity of the acid:

(a)- 18.19 M

(b)- 24.19 M

(c)- 19.19 M

(d)- 9.19 M

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**Hint:**The volume of any substance can be calculated by dividing the mass of that substance to the density of the substance. The percentage can be converted into gram in 100grams of the solution. Molarity of the solution is calculated by dividing the moles of the solute and volume of the solution.

**Complete answer:**

A solution is the homogeneous mixture of two or more non-reaction substances. There are two components of the solution, one which is a larger amount is called the solvent and the other with a smaller amount is called the solute.

The concentration of the solution can be expressed in many ways. One of the important methods is finding the molarity.

The molarity of a solution can be expressed as the number of moles of the solute present in the solution per liter.

\[\text{molarity = }\dfrac{\text{moles of the solute}}{\text{volume of the solution in litres}}\]

For calculating the number of moles, the given mass of the solute is divided by the molecular mass of the solute.

\[\text{moles = }\dfrac{\text{mass of the solute}}{\text{molecular mass}}\]

As the question states 99% \[{{H}_{2}}S{{O}_{4}}\]by mass, which means that 99 g of the\[{{H}_{2}}S{{O}_{4}}\] is present in the 100 g of solution.

Hence, the mass is 99 grams.

And the density of\[{{H}_{2}}S{{O}_{4}}\] is given = 1.9 g / mL

So, the moles of \[{{H}_{2}}S{{O}_{4}}\] is calculated by dividing the given mass i.e., 99 to the molecular mass of \[{{H}_{2}}S{{O}_{4}}\]

The molecular mass of \[{{H}_{2}}S{{O}_{4}}\] is 98 g

Hence, the moles of \[{{H}_{2}}S{{O}_{4}}\] is: \[\dfrac{99}{98}\]

Now, for the volume of the solution, divide the mass of the solution to the density of the solute, we get: \[\dfrac{100}{1.9}\]

Therefore, putting these values in the equation of molarity, we get:

\[\text{molarity = }\dfrac{\text{moles of the solute}}{\text{volume of the solution in litres}}=\dfrac{99/98}{100/1.9\text{x}1000}=\dfrac{99}{98}\text{x}\dfrac{100}{1.9}\text{x}1000=19.19M\]

**Hence, the molarity is 19.19 M. So, the correct option is (c).**

**Note:**Whenever the percentage of the solute is given it must be converted into the grams. Don’t get confused between the formula of molarity and molality. The volume of the solution is always taken in liters.