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 $kJ$)

Calculate the work done in $kJ$ when $3$ moles of an ideal gas at $27^{\circ} C$ expand isothermally and reversibly from $10 \ atm$ to $1 \ atm$ $[R=8.314 \ J \ K^{-1} \ mol^{-1}]$

Given
$C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)};$
$\Delta_rH^o = -393.5 \, kJ \, mol^{-1}$
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O_{(l)};$
$\Delta_rH^o = -285.8 \, kJ \, mol^{-1}$
$CO_{2(g)} + 2H_2O_{(l)} \rightarrow CH_{4(g)} + 2O_{2(g)};$
$\Delta_rH^o = + 890.3 \, kJ \, mol^{-1}$
Based on the above thermochemical equations,the value of $\Delta_rH^o$ at $298 \, K$ for the reaction
$C_{(graphite)} + 2H_{2(g)} \rightarrow CH_{4(g)}$ will be ........... $kJ \, mol^{-1}$.

$A$ gas expands from $3 \ dm^{3}$ to $5 \ dm^{3}$ against a constant pressure of $3 \ atm$. The work done during this expansion is used to heat $10 \ mol$ of water at $290 \ K$. What will be the final temperature of the water in $K$? (Specific heat of water = $4.184 \ J \ g^{-1} \ K^{-1}$)

The temperature of $1 \ mol$ of an ideal gas is increased by $2 \ ^oC$ at constant pressure. The work done is:

One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is $...........J$ (nearest integer). Given: $\log 2=0.3, \ln 10=2.3$