$\mathrm{S}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{ }{\to }{\mathrm{SO}}_2\left(\mathrm{g}\right)+\mathrm{x} \mathrm{kJ};$

$2{\mathrm{SO}}_3\left(\mathrm{g}\right)\stackrel{ }{\to }2{\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)-\mathrm{y} \mathrm{kJ};$

From the above data, calculate the heat of formation of ${\mathrm{SO}}_3 (\mathrm{in} \mathrm{kJ}/\mathrm{mole})$

$\mathrm{S}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{ }{\to }{\mathrm{SO}}_2\left(\mathrm{g}\right), ∆\mathrm{H}=-\mathrm{x} \mathrm{kJ}; ........\left(1\right)$

$2{\mathrm{SO}}_3\left(\mathrm{g}\right)\stackrel{ }{\to }2{\mathrm{SO}}_2\left(\mathrm{g}\right) +\hspace{0.17em}{\mathrm{O}}_2\left(\mathrm{g}\right), ∆\mathrm{H}=+\mathrm{y} \mathrm{kJ}; ........\left(2\right)$

${\mathrm{SO}}_3\left(\mathrm{g}\right)\stackrel{ }{\to }{\mathrm{SO}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right), ∆\mathrm{H}=+\frac{\mathrm{y}}{2} \mathrm{kJ}; .......\left(3\right)$

Eq (1) - Eq (3)

$\mathrm{S}\left(\mathrm{s}\right)+\frac{3}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_3\left(\mathrm{g}\right), ∆\mathrm{H}=-\left(\mathrm{x}+\frac{\mathrm{y}}{2}\right)$