The heat of neutralisation of $NH_4OH$ and $HCl$ is:

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?

Nitroglycerine $(MW = 227.1)$ detonates according to the following equation:
$2 C_{3}H_{5}(NO_{3})_{3(l)} \longrightarrow 3 N_{2(g)} + \frac{1}{2} O_{2(g)} + 6 CO_{2(g)} + 5 H_{2}O_{(g)}$
The standard molar enthalpies of formation,$\Delta H_{f}^{\circ}$ for all the compounds are given below:
$\Delta H_{f}^{\circ}[C_{3}H_{5}(NO_{3})_{3}] = -364 \, kJ/mol$
$\Delta H_{f}^{\circ}[CO_{2(g)}] = -393.5 \, kJ/mol$
$\Delta H_{f}^{\circ}[H_{2}O_{(g)}] = -241.8 \, kJ/mol$
$\Delta H_{f}^{\circ}[N_{2(g)}] = 0 \, kJ/mol$
$\Delta H_{f}^{\circ}[O_{2(g)}] = 0 \, kJ/mol$
The enthalpy change when $10 \, g$ of nitroglycerine is detonated is $..... \, kJ$.

For the reaction $\frac{1}{2} X_2O_{(s)} \to X_{(s)} + \frac{1}{4} O_{2(g)}$ with $\Delta H = 90 \ kJ$,the enthalpy change for the reaction of $1 \ mol$ of $O_2$ with metal $X$ is ................ $kJ$.

For the reaction $2 H_2 + O_2 \rightarrow 2 H_2 O$,$\Delta H = -571 \ kJ$. Bond energy of $H-H = 435 \ kJ$ and $O=O = 498 \ kJ$. Then the average bond energy of $O-H$ bond will be:

The enthalpy of solution of $BaCl_{2(s)}$ and $BaCl_2 \cdot 2H_2O_{(s)}$ are $-20.6 \, kJ \, mol^{-1}$ and $8.8 \, kJ \, mol^{-1}$ respectively. The enthalpy change for the reaction $BaCl_{2(s)} + 2H_2O_{(l)} \to BaCl_2 \cdot 2H_2O_{(s)}$ is $...... \, kJ \, mol^{-1}$.