Calculate the heat of formation of acetone from the following data:

$\frac{1}{2}{\mathrm{H}}_2 \left(\mathrm{g}\right)\to \mathrm{H} \left(\mathrm{g}\right); \mathrm{\Delta H}=52.1 \mathrm{kcal}$

$\frac{{\displaystyle 1}}{{\displaystyle 2}}{\mathrm{O}}_2 \left(\mathrm{g}\right)\to \mathrm{O} \left(\mathrm{g}\right); \mathrm{\Delta H}=59.16 \mathrm{kcal}$

$\mathrm{C} \left(\mathrm{s}\right)\to \mathrm{C} \left(\mathrm{g}\right); \mathrm{\Delta H}=171.7 \mathrm{kcal}$

Bond energies :

$\mathrm{C}-\mathrm{H}=99 \mathrm{kcal}$

$\mathrm{C}-\mathrm{C}=80 \mathrm{kcal}$

$\mathrm{C}=\mathrm{O}=81 \mathrm{kcal}$

Calculate the heat of formation of methyl alcohol (liquid) from the following data:

Heat of atomisation of $\mathrm{C}=170.9 \mathrm{kcal}$

Heat of atomisation of $\mathrm{H}=52.1 \mathrm{kcal}$

Heat of atomisation of $\mathrm{O}=59.6 \mathrm{kcal}$

Bond energies:

$\mathrm{C}-\mathrm{H}=99 \mathrm{kcal}$

$\mathrm{C}-\mathrm{O}=84 \mathrm{kcal}$

$\mathrm{O}-\mathrm{H}=110.55 \mathrm{kcal}$

Heat of liquefaction of $1$ mole of ${\mathrm{CH}}_3\mathrm{OH}=-8.4 \mathrm{kcal}$.

Calculate the heat of the following homogeneous gaseous reaction

${\mathrm{CH}}_3{\mathrm{COCH}}_3+2{\mathrm{O}}_2\to {\mathrm{CH}}_3\mathrm{COOH}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

from the following data:

Bond energies $\left(\mathrm{kJ}\right)$:

$\mathrm{C}-\mathrm{H}=414.49$
$\mathrm{C}-\mathrm{C}=347.92$
$\mathrm{C}=\mathrm{O}=724.32$
$\mathrm{O}=\mathrm{O}=494.04$
$\mathrm{O}-\mathrm{H}=462.64$
$\mathrm{C}-\mathrm{O}=967.13$

Resonance energy:

$-\mathrm{COOH}=117.23$
${\mathrm{CO}}_2=138.16$

Calculate the resonance energy of ${\mathrm{N}}_2\mathrm{O}$ from the following data:

${\mathrm{\Delta H}}_{\mathrm{f}}^{\circ }$ of ${\mathrm{N}}_2\mathrm{O}=82 \mathrm{kJ} {\mathrm{mole}}^{-1}$

Bond energies of $\mathrm{N}\equiv \mathrm{N}, \mathrm{N}=\mathrm{N}, \mathrm{O}=\mathrm{O}$ and $\mathrm{N}=\mathrm{O}$ bonds are $946, 418, 498$ and $607 \mathrm{kJ} {\mathrm{mole}}^{-1}$ respectively.

Calculate the heat of formation of $\mathrm{HCl} \left(\mathrm{g}\right)$ from the reaction: ${\mathrm{H}}_2 \left(\mathrm{g}\right)+{\mathrm{Cl}}_2 \left(\mathrm{g}\right) \to 2\mathrm{HCl} \left(\mathrm{g}\right); \mathrm{\Delta H}=-44 \mathrm{kcal}$.

$\left[\begin{array}{l}{\mathrm{H}}_2 \left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2 \left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O} \left(\mathrm{g}\right); \mathrm{\Delta H}=-241.8 \mathrm{kJ}\\ \mathrm{CO} \left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2 \left(\mathrm{g}\right)\to {\mathrm{CO}}_2 \left(\mathrm{g}\right); \mathrm{\Delta H}=-283 \mathrm{kJ}\end{array}\right]$

Calculate the heat evolved in the combustion of $112 \mathrm{litres}$ of water gas (mixture of equal volumes of ${\mathrm{H}}_2$ and $\mathrm{CO}$).

$\left[\begin{array}{l}{\mathrm{H}}_2 \left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2 \left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O} \left(\mathrm{g}\right); \mathrm{\Delta H}=-241.8 \mathrm{kJ}\\ {\mathrm{C}}_2{\mathrm{H}}_2 \left(\mathrm{g}\right)+2\frac{1}{2}{\mathrm{O}}_2 \left(\mathrm{g}\right)\to 2{\mathrm{CO}}_2 \left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{g}\right); \mathrm{\Delta H}=-1300 \mathrm{kJ}\end{array}\right]$

Equal volumes of ${\mathrm{C}}_2{\mathrm{H}}_2$ and ${\mathrm{H}}_2$ are combusted under identical conditions. What is the ratio of heats evolved in the two cases?