If $\quad C$ (diamond $) \rightarrow C$ (graphite) $+X \mathrm{~kJ} \mathrm{~mol}^{-1}$

C (diamond) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{Y} \mathrm{kJ} \mathrm{mol}{ }^{-1}$

C (graphite) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{Z} \mathrm{kJ} \mathrm{mol}^{-1}$

at constant temperature. Then

<p>Given,</p> <p>$${C_{(diamond)}}\buildrel {} \over \longrightarrow {C_{(graphite)}} + X\,kJ\,mo{l^{ - 1}}$$ ............ (1)</p> <p>$${C_{(diamond)}} + {O_2}(g)\buildrel {} \over \longrightarrow C{O_2}(g) + Y\,kJ\,mo{l^{ - 1}}$$ ............. (2)</p> <p>$${C_{(graphite)}} + {O_2}(g)\buildrel {} \over \longrightarrow C{O_2}(g) + Z\,kJ\,mo{l^{ - 1}}$$ .............. (3)</p> <p>Condition for temperature : constant</p> <p>Hess's law is applied here. (Hess's law of constant heat summation)</p> <p>The given reactions (2) and (3),</p> <p>(2) - (3) $\Rightarrow$</p> <p>$${C_{(diamond)}} + {O_2}(g) - \left( {{C_{(graphite)}} + {O_2}(g)} \right)\buildrel {} \over \longrightarrow C{O_2}(g) + Y - \left( {C{O_2}(g) + Z} \right)$$</p> <p>$${C_{(diamond)}} + {O_2}(g) - {C_{(grpahite)}} - {O_2}(g)\buildrel {} \over \longrightarrow C{O_2}(g) + Y - C{O_2}(g) - Z$$</p> <p>${C_{(diamond)}} - {C_{(graphite)}} \to Y - Z$</p> <p>${C_{(diamond)}} \to {C_{(graphite)}} + (Y - Z)$ ............. (4)</p> <p>Comparing (1) and (4),</p> <p>$X = Y - Z$</p> <p>So, the correct answer is option (2) $X = Y - Z$</p>