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Question

Given, 
$$C(s)+{O}_{2}(g)\rightarrow {CO}_{2}(g); \Delta H=-395\ kJ$$
$$S(s)+{O}_{2}(g)\rightarrow {SO}_{2}(g);\Delta H=-295\ kJ$$
$$C{S}_{2}(l)+3{O}_{2}(g)\rightarrow {CO}_{2}(g)+2{SO}_{2}(g);\Delta H=-1110\ kJ$$
The heat of formation of $$C{S}_{2}(l)$$ is:


A
250 kJ
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B
62.5 kJ
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C
31.25 kJ
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D
125 kJ
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Solution

The correct option is A $$125\ kJ$$
Since, the formation reaction of $$CS_2$$ is,
$$C(s) + 2S(s) \rightarrow CS_2(l)$$
Since, the formation reaction of $$CS_2$$ can also be derived using the given reaction as,
$$1^{st} \text{reaction} +2\times 2^{nd} \text{ reaction} - 3^{rd} \text{ reaction}$$
Hence, the enthalpy of the reaction,
 
$$[1^{st} \text{reaction} +2\times 2^{nd} \text{ reaction} - 3^{rd} \text{ reaction}]$$ $$=\Delta H_{1^{st} \text{reaction}} +2\times \Delta H_{2^{nd} \text{ reaction}} -\Delta H_{3^{rd} \text{ reaction}}$$ $$=\text{heat of formation of CS}_2(l)$$
Hence, $$ \Delta H_{f(CS_2)} = -395 + 2\times (-295) - (-1110) = 125kJ$$
Hence, the answer is option $$D$$.

Chemistry

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