Using these data: (a) $H_2S(g)$ $+$ $\frac{3}{2}O_2(g)$ $\longrightarrow$ $H_2O(l)$ $+$ $SO_2(g)$ $\Delta H_a $ $=$ $-562.6 \;kJ$ (b) $CS_2(l)$ $+$ $3O_2(g)$ $\longrightarrow$ $CO_2(g)$ $+$ $2SO_2(g)$ $\Delta H_b$ $=$ $-1075.2 \;kJ$, calculate the standard enthalpy of the following reaction: (c) $CS_2(l)$ $+$ $2H_2O(l)$ $\longrightarrow$ $CO_2(g)$ $+$ $2H_2S(g)$ $\Delta H_c$ $ =$ $ ?$
-2(a) $2H_2O(l)$ $+$ $2SO_2(g)$ $\longrightarrow$ $2H_2S(g)$ $+$ $3O_2(g)$ $-2\Delta H_a$ (b) $CS_2(l)$ $+$ $3O_2(g)$ $\longrightarrow$ $CO_2(g)$ $+$ $2SO_2(g)$ $\Delta H_b$
-2(a)+(b) $2H_2O(l)$ $+$ $2SO_2(g)$ $+$ $CS_2(l)$ $+$ $3O_2(g)$ $\longrightarrow$ $2H_2S(g)$ $+$ $3O_2(g)$ $+$ $CO_2(g)$ $+$ $2SO_2(g)$ $2\Delta H_a$ $-$ $\Delta H_b$ (c)=-2(a)+(b) $CS_2(l)$ $+$ $2H_2O(l)$ $\longrightarrow$ $CO_2(g)$ $+$ $2H_2S(g)$ $\Delta H_c$ $=$ $-2\Delta H_a$ $+$ $\Delta H_b$ $=$ $50\;kJ$