At $300 \ K$, $3.0 \ \text{moles}$ of an ideal gas at $3.0 \ \text{atm}$ pressure is compressed isothermally to one half of its volume by an external pressure of $6.0 \ \text{atm}$. The work done (in $kJ$) is. Given, $R=0.082 \ \text{L atm K}^{-1} \text{mol}^{-1}$ $(1 \ \text{L atm} = 101.3 \ \text{J})$.

Water vapor is an ideal gas. Calculate the internal energy change $(\Delta U)$ when $1 \, \text{mol}$ of water is vaporized at $1 \, \text{bar}$ pressure and $100 \, ^{\circ}C$. (Given: Molar enthalpy of vaporization of water at $1 \, \text{bar}$ and $373 \, K = 41 \, kJ \, \text{mol}^{-1}$ and $R = 8.3 \, J \, \text{mol}^{-1} \, K^{-1}$)

Identify the incorrect statements from the following.
$I$. For adiabatic process,$\Delta U = w_{ad}$
$II$. Enthalpy is an intensive property
$III$. For the process,$H_2O_{(l)} \rightarrow H_2O_{(s)}$,the entropy increases

The heat evolved in the combustion of methane is given by the following equation: $CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$; $\Delta H = -890.3 \ kJ$. How many grams of methane would be required to produce $445.15 \ kJ$ of heat of combustion?

The combustion of one mole of benzene takes place at $298 \, K$ and $1 \, atm$. After combustion,$CO_{2(g)}$ and $H_2O_{(l)}$ are produced and $3267.0 \, kJ$ of heat is liberated. Calculate the standard enthalpy of formation,$\Delta_f H^{\ominus}$ of benzene. Standard enthalpies of formation of $CO_{2(g)}$ and $H_2O_{(l)}$ are $-393.5 \, kJ \, mol^{-1}$ and $-285.83 \, kJ \, mol^{-1}$ respectively.

For a reaction $2 CO_{(g)} + O_{2(g)} \rightleftharpoons 2 CO_{2(g)}$,$\Delta_{r} G^0 = -128 \ kJ$ at $300 \ K$. If $\Delta_{r} S^0$ of the reaction is $-40 \ J \ K^{-1}$,calculate $\Delta_{r} U$ of the reaction. (in $kJ$)