Calculate the difference between $\Delta H$ and $\Delta U$ for the following reaction at $25^{\circ} C$:
$C_2H_{6(g)} + 3.5O_{2(g)} \rightarrow 2CO_{2(g)} + 3H_2O_{(l)}$
(Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$) (in $kJ$)

The standard entropies of $X_2$,$Y_2$,and $XY_3$ are $60$,$40$,and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3$,$\Delta H = -30 \ kJ$ at equilibrium. What is the temperature of the system in $K$?

Which of the following is not a correct statement?

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 $kJ$)

For the following reaction $Fe_2O_{3(s)} + 3 CO_{(g)} \longrightarrow 2 Fe_{(s)} + 3 CO_{2(g)}$,$\Delta H^{\circ} = -29.8 \ kJ$ and $\Delta S^{\circ} = 15 \ JK^{-1}$. What is the value of $\Delta S_{\text{total}}$ at $298 \ K$ (in $JK^{-1}$)?

For the reaction $2H_{(g)} \to H_{2(g)}$,the signs of $\Delta H$ and $\Delta S$ are: