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# A sample of $H_2SO_4$ solution is labeled 98% by weight. What is the molarity of acid, given that the density of $H_2SO_4$ solution is 1.8g/ml.

$\begin{array}{1 1}(a)\;16M\\(b)\;18M\\(c)\;20M\\(d)\;22M\end{array}$

Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution, $M = \large\frac{\text{ Moles of solute }}{\text{Molarity Volume of solution in litre}}$
Let the Volume be $V = 1\;L = 1000\;mL$ Therefore mass of the solution $= 1.8 \times 1000 = 1800\;g$
Mass of the solute $= 98\; \%\; \text{of}\; 1800 = 1764\;g$
Molarity volume of solution in liter $= 98\;L$
$\Rightarrow$ Molarity $M = \large\frac{1764}{98}$$= 18M$
edited Jul 16, 2014