The value of $\Delta_{f} H^{o}$ for $NH_3$ is $-91.8 \ kJ \ mol^{-1}$. Calculate the enthalpy change for the following reaction: $2NH_{3(g)} \to N_{2(g)} + 3H_{2(g)}$

The heat of solution of $Na_2SO_{4(s)}$ and $Na_2SO_4 \cdot 10H_2O_{(s)}$ are $-2.34 \ kJ \ mol^{-1}$ and $78.87 \ kJ \ mol^{-1}$ respectively. The heat of hydration of $Na_2SO_{4(s)}$ is:

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 $..... \, kJ$.

Identify the law for the statement "Overall the enthalpy change for a reaction is equal to the sum of enthalpy changes of individual steps in the reaction".

What is the value of $\Delta H^{\circ}$ for the formation of ethanol from ethene gas and liquid water from the following data (in $kJ$)?
$(i)$ $C_2H_5OH_{(l)} + 3O_{2_{(g)}} \longrightarrow 2CO_{2_{(g)}} + 3H_2O_{(l)}$ $\Delta H^{\circ} = -1368 \ kJ$
$(ii)$ $C_2H_{4_{(g)}} + 3O_{2_{(g)}} \longrightarrow 2CO_{2_{(g)}} + 2H_2O_{(l)}$ $\Delta H^{\circ} = -1410 \ kJ$

The enthalpies of combustion of $C(s)$, $H_2(g)$, and $CH_4(g)$ are $-390 \text{ kJ/mol}$, $-285 \text{ kJ/mol}$, and $-890 \text{ kJ/mol}$ respectively. Calculate the enthalpy of formation of methane $(CH_4)$.