(I) "\\frac{1}{2}H_2(g)+ \\frac{1}{2}O_2(g) \\rightarrow OH(g)" "\\Delta H_{rxn} = 42.1 kJ"
(II) "H_2(g) \\rightarrow 2H(g)" "\\Delta H_{rxn} = 435.9 kJ"
(III) "H_2(g) + \\frac{1}{2}O_2(g) \\rightarrow H_2O(g)" "\\Delta H_{rxn} = -241.8 kJ"
To get "\\Delta H_{rxn}" for the formation of OH and H from water we should add "- (III) + (I)+\\frac{(II)}{2}"
-(III) "H_2O(g) \\rightarrow H_2(g) + \\frac{1}{2}O_2(g)" "\\Delta H_{rxn} = 241.8 kJ"
(I) "\\frac{1}{2}H_2(g) + \\frac{1}{2} O_2(g)\\rightarrow OH(g)" "\\Delta H_{rxn} = 42.1 kJ"
"\\frac{(II)}{2}" "\\frac {1}{2}H_2 (g) \\rightarrow H(g)" "\\Delta H_{rxn} = \\frac{435.9}{2} = 217.95 kJ"
After addition:
"H_2O(g) + \\frac{1}{2}H_2(g)+\\frac{1}{2}O_2(g) + \\frac{1}{2}H_2(g) \\rightarrow H_2(g)+\\frac{1}{2}O_2(g) + OH(g)+ H(g)"
"H_2O(g) \\rightarrow OH(g) + H(g)" "\\Delta H_{rxn} = 241.8 + 42.1 +217.95 =501.85 kJ"
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