From the following data:
$CH_3OH_{(l)} + \frac{3}{2}O_{2(g)} \longrightarrow CO_{2(g)} + 2H_2O_{(l)}$; $\Delta_rH^{\circ} = -726 \ kJ \ mol^{-1}$
$H_{2(g)} + \frac{1}{2}O_{2(g)} \longrightarrow H_2O_{(l)}$; $\Delta_rH^{\circ} = -286 \ kJ \ mol^{-1}$
$C_{(graphite)} + O_{2(g)} \longrightarrow CO_{2(g)}$; $\Delta_rH^{\circ} = -393 \ kJ \ mol^{-1}$
The standard enthalpy of formation of $CH_3OH_{(l)}$ in $kJ \ mol^{-1}$ 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?

While performing a thermodynamics experiment,a student made the following observations:
$HCl + NaOH \rightarrow NaCl + H_{2}O$ $\Delta H = -57.3 \ kJ \ mol^{-1}$
$CH_{3}COOH + NaOH \rightarrow CH_{3}COONa + H_{2}O$ $\Delta H = -55.3 \ kJ \ mol^{-1}$
The enthalpy of ionization of $CH_{3}COOH$ as calculated by the student is $kJ \ mol^{-1}$. (nearest integer)

Comment on the thermodynamic stability of $NO_{(g)}$,given:
$\frac{1}{2} N_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow NO_{(g)}; \Delta_r H^{\ominus} = 90 \, kJ \, mol^{-1}$
$NO_{(g)} + \frac{1}{2} O_{2(g)} \rightarrow NO_{2(g)}; \Delta_r H^{\ominus} = -74 \, kJ \, mol^{-1}$

Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$
Assertion $(A)$: Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always $-57 \ kJ \ mol^{-1}$.
Reason $(R)$: Enthalpy of neutralisation is the amount of heat liberated when one mole of $H^{+}$ ions furnished by acid combine with one mole of $OH^{-}$ ions furnished by base to form one mole of water.
In the light of the above statements,choose the correct answer from the options given below.

Given: $S + \frac{3}{2} O_2 \to SO_3 + 2x \ \text{kcal}$,$\Delta H = -2x \ \text{kcal}$ and $SO_2 + \frac{1}{2} O_2 \to SO_3 + y \ \text{kcal}$,$\Delta H = -y \ \text{kcal}$. Find the heat of formation of $SO_2$.