Given the following thermochemical equations:
$(i) S_{(s)} + \frac{3}{2} O_{2(g)} \rightarrow SO_{3(g)} + 2x \, kcal$
$(ii) SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow SO_{3(g)} + y \, kcal$
Find the heat of formation of $SO_{2(g)}$.

How much energy in $kJ$ is required to convert $54 \ g$ of ice at $0 \ ^\circ C$ to water at $27 \ ^\circ C$? $\left( \Delta H_{fusion} = 6.01 \ kJ \ mol^{-1}, C_{p(liquid)} = 4.18 \ J \ K^{-1} \ g^{-1} \right)$

For the reaction $A_{(g)} + 2B_{(g)} \to 2C_{(g)} + 3D_{(g)}$,the value of $\Delta E$ at $27\ ^oC$ is $19.0\ kcal$. The value of $\Delta H$ for the reaction would be.......$kcal$ $(R = 2.0\ cal\ K^{-1} mol^{-1})$

Fill in the blanks given below:
$(i)$ The law of thermodynamics is actually the law of ......... .
$(ii)$ $A$ thermometer measures temperature according to the ......... law of thermodynamics.
$(iii)$ The foundation of thermochemistry is based on the ......... law of thermodynamics.
$(iv)$ The amount of heat required to raise the temperature of a substance by $1^{\circ}C$ is called the ......... of that substance.

$A$ calorimeter contains $0.2 \ kg$ of water at $30^{\circ} C$. $0.1 \ kg$ of water at $60^{\circ} C$ is added to it,the mixture is well stirred and the resulting temperature is found to be $35^{\circ} C$. The water equivalent of the calorimeter is $:-$ (in $J / K$)

For the following combustion reaction occurring in an automobile: $2C_{8}H_{18(g)} + 25O_{2(g)} \to 16CO_{2(g)} + 18H_{2}O_{(g)}$,what are the signs of $\Delta H$,$\Delta S$,and $\Delta G$?