For the reaction,$C_3H_{8(g)} + 5O_{2(g)} \to 3CO_{2(g)} + 4H_2O_{(l)}$ at constant temperature,$\Delta H - \Delta E$ is

Observe the following reaction: $ABO_{3(s)} \xrightarrow{1000 \ K} AO_{(s)} + BO_{2(g)}$. $\Delta_{r} H$ for this reaction is $x \ kJ \ mol^{-1}$. What is its $\Delta_{r} U$ (in $kJ \ mol^{-1}$) at the same temperature? $(R = 8.3 \ J \ mol^{-1} \ K^{-1})$

What is the work done during the oxidation of $4 \ mol$ of $SO_{2(g)}$ to $SO_{3(g)}$ at $27^{\circ} C$ (in $kJ$)? $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

Calculate the change in internal energy of the system if $37.6 \ J$ of work is done by the system with heat loss of $14.6 \ J$ (in $J$)?

Derive the relationship between $\Delta H$ and $\Delta U$ for an ideal gas. Explain each term involved in the equation.

For the reaction,$N_{2(g)} + 3 H_{2(g)} \rightarrow 2 NH_{3(g)}$,$\Delta H$ is equal to