The molarity of H₂SO₄ is 18 M. Its density is 1.8 g mL^-1. Hence, molality is: 

Molarity of H₂SO₄ is 18 M which indicates that 18 moles of H₂SO₄ present in 1 L of solution. Mass present in 18 moles of H₂SO₄ is calculated as:

$\begin{array}{ccc}\mathrm{Number} \mathrm{of} \mathrm{moles} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4& =& \frac{\mathrm{Given} \mathrm{mass} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4}{\mathrm{Molar} \mathrm{mass} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4}\\ 18 \mathrm{mol}& =& \frac{\mathrm{Given} \mathrm{mass} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4}{{\displaystyle \frac{98 \mathrm{g}}{\mathrm{mol}}}\times {\displaystyle \frac{1 \mathrm{kg}}{1000 \mathrm{g}}}}\\ \mathrm{Given} \mathrm{mass} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4& =& 1.764 \mathrm{kg}\end{array}$

Density of 18 M H₂SO₄ solution is 1.8 g/mL which indicates that 1.8 g is present in 1 mL and is also said that 1800 g (or 1.8 kg) present in 1 L of solution.

$\begin{array}{ccc}\frac{1.8 \mathrm{g}}{\mathrm{mL}}& =& \frac{1.8 \mathrm{g}}{\mathrm{mL}\times {\displaystyle \frac{1 \mathrm{L}}{1000 \mathrm{mL}}}}\\ & =& 1800 \mathrm{g}/\mathrm{L}\\ & =& \frac{1800 \mathrm{g}\times {\displaystyle \frac{1 \mathrm{kg}}{1000 \mathrm{g}}}}{\mathrm{L}}\\ & =& 1.8 \mathrm{kg}/\mathrm{L}\end{array}$

In H₂SO₄ solution, total volume of solution is 1.8 kg and the mass of H₂SO₄ is 1.764 kg. Mass of water is:

$\begin{array}{ccc}\mathrm{Mass} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4 \mathrm{solution}& =& \mathrm{Mass} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4+\mathrm{Mass} \mathrm{of} \mathrm{water}\\ 1.8 \mathrm{kg}& =& 1.764 \mathrm{kg}+\mathrm{Mass} \mathrm{of} \mathrm{water}\\ \mathrm{Mass} \mathrm{of} \mathrm{water}& =& 0.036 \mathrm{kg}\end{array}$

Molality of H₂SO₄ is calculated as:

$\begin{array}{ccc}\mathrm{Molality}& =& \frac{\mathrm{Number} \mathrm{of} \mathrm{moles} \mathrm{of} {\mathrm{H}}_2{\mathrm{SO}}_4}{\mathrm{Volume} \mathrm{of} \mathrm{solvent} (\mathrm{in} \mathrm{kg})}\\ & =& \frac{18 \mathrm{mol}}{0.036 \mathrm{kg}}\\ & =& 500 \mathrm{m}\end{array}$