J.R. S. answered 04/01/20
Ph.D. University Professor with 10+ years Tutoring Experience
The target reaction is... 2NOCl(g) ==> 2NO(g) + Cl2(g) [note: you gave an incorrect equation]
We will use Hess' Law to find the ∆H of this target reaction using the other 2 reactions that are given,.
(1) 2NO(g) ==> N2(g) + O2(g) ∆H = -180.6 kJ
(2) N2(g) + O2(g) + Cl2(g) ==> 2NOCl(g) ∆H = +103.4 kJ
reverse eq.(1): N2(g) + O2(g) ==> 2NO(g) ∆H = +180.6 kJ (note the change in sign)
reverse eq.(2): 2NOCl(g) ==> N2(g) + O2(g) + Cl2(g) ∆H = -103.4 (note the change in sign)
add these together and cancel like items on each side to get...
2NOCl(g) ==> Cl2(g) + 2NO(g) and this is the desired target equation from above.
We then have to add the corresponding ∆H values...
+180.6 kJ - 103.4 kJ = 77.2 kJ