If \(C\) (diamond) \(\to C\) (graphite)+X \(kJmo{l}^{-1}\) \(C(\text{ diamond })+{O}_{2}(g)\to C{O}_{2}(g)+YkJmo{l}^{-1}…

(a) Using Hess's Law, we sum the given reactions:
1. C (diamond) \(\to C\) (graphite) + X
2. C (diamond) \(+{O}_{2}\to C{O}_{2}+Y\)
3. C (graphite) \(+{O}_{2}\to C{O}_{2}+Z\)

Reversing (3):

\(C{O}_{2}\to C(\text{ graphite })+{O}_{2}-Z\)

Adding to (2):
C(diamond) → C(graphite) + (Y–Z)
Comparing with (1): X = Y – Z