Given:
$(i) \, C(\text{graphite}) + O_{2(g)} \to CO_{2(g)}; \Delta_r H^\ominus = x \, kJ \, mol^{-1}$
$(ii) \, C(\text{graphite}) + \frac{1}{2} O_{2(g)} \to CO_{(g)}; \Delta_r H^\ominus = y \, kJ \, mol^{-1}$
$(iii) \, CO_{(g)} + \frac{1}{2} O_{2(g)} \to CO_{2(g)}; \Delta_r H^\ominus = z \, kJ \, mol^{-1}$
Based on the above thermochemical equations,find out which one of the following algebraic relationships is correct?

The heat evolved in the combustion of benzene is given by the equation $C_6H_{6(l)} + 7.5 O_{2(g)} \to 3H_2O_{(l)} + 6CO_{2(g)}$,$\Delta H = -781.0 \ kcal \ mol^{-1}$. Which of the following quantities of heat energy will be evolved when $39 \ g$ of benzene is burnt in an open container?

The heat of combustion of solid benzoic acid at constant volume is $-321.30 \ kJ$ at $27^{\circ} C$. Its heat of combustion at constant pressure is :

Enthalpy of formation of $CO_{(g)}$,$CO_{2(g)}$,$N_2O_{(g)}$ and $N_2O_{4(g)}$ are $-110$,$-393$,$81$,and $9.7 \ kJ \ mol^{-1}$ respectively. Calculate $\Delta_r H$ for the following reaction: $N_2O_{4(g)} + 3 CO_{(g)} \longrightarrow N_2O_{(g)} + 3 CO_{2(g)}$

The oxidizing power of chlorine in an aqueous solution can be determined by the parameters given below. What is the total energy change in $kJ \ mol^{-1}$ for the conversion of $\frac{1}{2} Cl_{2(g)}$ to $Cl^-_{(aq)}$?
$\frac{1}{2} Cl_{2(g)}$ $\xrightarrow{\frac{1}{2} \Delta_{diss} H^\Theta} Cl_{(g)}$ $\xrightarrow{\Delta_{eg} H^\Theta} Cl^-_{(g)}$ $\xrightarrow{\Delta_{hyd} H^\Theta} Cl^-_{(aq)}$
(Given: $\Delta_{diss} H_{Cl_2}^\Theta = 240 \ kJ \ mol^{-1}$,$\Delta_{eg} H_{Cl}^\Theta = -349 \ kJ \ mol^{-1}$,$\Delta_{hyd} H_{Cl^-}^\Theta = -381 \ kJ \ mol^{-1}$)

The bond enthalpies of $H_2$,$X_2$ and $HX$ are in the ratio of $2 : 1 : 2$. If the enthalpy for formation of $HX$ is $-50 \ kJ \ mol^{-1}$,the bond enthalpy of $H_2$ is ..... $kJ \ mol^{-1}$