Using these data: (a) $S(s)$ $+$ $\frac{3}{2}O_2(g)$ $\longrightarrow$ $SO_3(g)$ $\Delta H_a$ $ =$ $ -395.2\; kJ$ (b) $2SO_2(g)$ $+$ $O_2(g)$ $\longrightarrow$ $2SO_3(g)$ $\Delta H_b$ $ = $ $-198.2\; kJ$, calculate the standard enthalpy of the following reaction: (c) $S(s)$ $ + $ $O_2(g)$ $\longrightarrow$ $SO_2(g)$ $\Delta H_c $ $=$ $?$
2(a) $2S(s)$ $+$ $3O_2(g)$ $\longrightarrow$ $2SO_3(g)$ $2\Delta H_a$ -(b) $2SO_3(g)$ $\longrightarrow$ $2SO_2(g)$ $+$ $O_2(g)$ $-\Delta H_b$
2(a)-(b) $2S(s)+3O_2(g)$ $+$ $2SO_3(g)$ $\longrightarrow$ $2SO_3(g)$ $+$ $2SO_2(g)$ $+$ $O_2(g)$ $2\Delta H_a$ $-$ $\Delta H_b$ 2(a)-(b) $2S(s)$ $+$ $2O_2(g)$ $\longrightarrow$ $2SO_2(g)$ $2\Delta H_a$ $-$ $\Delta H_b$
(c) $S(s)$ + $O_2(g)$ $\longrightarrow$ $SO_2(g)$ $\Delta H_c$ $=$ $\frac{2\Delta H_a-\Delta H_b}{2}$ $=$ $-296.1\;kJ$