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Chemistry Question on Thermodynamics

Given: C(graphite)+(O)2(g)→(CO)2(g) ;(?)r(H)o=−393.5( kJ mol)−1\text{C} \left(\text{graphite}\right) + \left(\text{O}\right)_{2} \left(\text{g}\right) \rightarrow \left(\text{CO}\right)_{2} \left(\text{g}\right) \, ; \left(\text{?}\right)_{\text{r}} \left(\text{H}\right)^{\text{o}} = - 393.5 \left(\text{ kJ mol}\right)^{- 1} (H)2(g)+12(O)2(g)→(H)2O(l);(?)r(H)o=−285.8 kJ mo(l)−1\left(\text{H}\right)_{2}\left(\text{g}\right)+\frac{1}{2}\left(\text{O}\right)_{2}\left(\text{g}\right) \rightarrow \left(\text{H}\right)_{2}\text{O}\left(\text{l}\right);\left(\text{?}\right)_{\text{r}}\left(\text{H}\right)^{\text{o}}=-285.8 \, \text{k}\text{J} \, \text{m}\text{o}\left(\text{l}\right)^{- 1} C(O)2(g)+2(H)2O(l)→C(H)4(g)+2(O)2(g);(?)r(H)o=+890.3 kJ mo(l)−1\text{C}\left(\text{O}\right)_{2}\left(\text{g}\right)+2\left(\text{H}\right)_{2}\text{O}\left(\text{l}\right) \rightarrow \text{C}\left(\text{H}\right)_{4}\left(\text{g}\right)+2\left(\text{O}\right)_{2}\left(\text{g}\right);\left(\text{?}\right)_{\text{r}}\left(\text{H}\right)^{\text{o}}=+890.3 \, \text{k}\text{J} \, \text{m}\text{o}\left(\text{l}\right)^{- 1} Based on the above thermochemical equations, the value of ?rHo\text{?}_{\text{r}}\text{H}^{\text{o}} at 298 K\text{298 K} for the reaction C(graphite)+2(H)2(g)→C(H)4(g)\text{C}\left(\text{g} \text{r} \text{a} \text{p} \text{h} \text{i} \text{t} \text{e}\right)+2\left(\text{H}\right)_{2}\left(\text{g}\right) \rightarrow \text{C}\left(\text{H}\right)_{4}\left(\text{g}\right) will be:

A

+144.0 kJ mol−1+144.0 \, \text{k}\text{J} \, \text{m}\text{o}\text{l}^{- 1}

B

−74.8 kJ mol−1-74.8 \, \text{k}\text{J} \, \text{m}\text{o}\text{l}^{- 1}

C

−144.0 kJ mol−1-144.0 \, \text{k}\text{J} \, \text{m}\text{o}\text{l}^{- 1}

D

+74.8 kJ mol−1+74.8 \, \text{k}\text{J} \, \text{m}\text{o}\text{l}^{- 1}

Answer

−74.8 kJ mol−1-74.8 \, \text{k}\text{J} \, \text{m}\text{o}\text{l}^{- 1}

Explanation

Solution

For reaction (CO)2((g)+2H)2O(l)→(CH)4((g)+2O)2(g)\left(\text{CO}\right)_{\text{2}} \left(\text{(g)+2H}\right)_{\text{2}} \text{O(l)} \rightarrow \left(\text{CH}\right)_{\text{4}} \left(\text{(g)+2O}\right)_{\text{2}} \text{(g)} (?)r(H)o=S((?)f(H)o)products−S((?)f(H)o)reactants\left(\text{?}\right)_{\text{r}}\left(\text{H}\right)^{\text{o}}=\text{S}\left(\left(\text{?}\right)_{\text{f}} \left(\text{H}\right)^{\text{o}}\right)_{\text{p} \text{r} \text{o} \text{d} \text{u} \text{c} \text{t} \text{s}}-\text{S}\left(\left(\text{?}\right)_{\text{f}} \left(\text{H}\right)^{\text{o}}\right)_{\text{r} \text{e} \text{a} \text{c} \text{t} \text{a} \text{n} \text{t} \text{s}} =[(?)r(H)o(C(H)4)+2×0)−(?)f(H)o(C(O)2)+2(?)f(H)o(H)2O)]= [(\text{?})_{\text{r}} (\text{H})^{\text{o}} (\text{C} (\text{H})_{4}) + 2 \times 0) - (\text{?})_{\text{f}} (\text{H})^{\text{o}} (\text{C} (\text{O})_{2}) + 2 (\text{?})_{\text{f}} (\text{H})^{\text{o}} (\text{H})_{2} \text{O} _{\text{}})] +890.3=[(?)f(H)o(C(H)4)]−[−393.5+2×(−285.8)]+890.3=\left[\left(\text{?}\right)_{\text{f}} \left(\text{H}\right)^{\text{o}} \left(\text{C} \left(\text{H}\right)_{4}\right)\right]-\left[- 393.5 + 2 \times \left(- 285.8\right)\right] ?fHo\text{?}_{\text{f}} \text{H}^{\text{o}} of (CH)4 (g)=−74.8 kJ/mol\left(\text{CH}\right)_{4 \, } \text{(g)} = - 74.8 \text{ kJ} / \text{mol}