For the reaction $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3$,$\Delta H = -30 \ kJ/mol$. Given $\Delta S_{X_2} = 60 \ J/mol \cdot K$,$\Delta S_{Y_2} = 40 \ J/mol \cdot K$,and $\Delta S_{XY_3} = 50 \ J/mol \cdot K$,calculate the temperature at equilibrium in $K$.

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?

For the reaction of one mole of zinc dust with one mole of sulphuric acid in a bomb calorimeter,$\Delta U$ and $w$ correspond to

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature:
$(a)$ $|w_{reversible}|$ for expansion in infinite stage.
$(b)$ $|w_{irreversible}|$ for expansion in single stage.
$(c)$ $|w_{reversible}|$ for compression in infinite stage.
$(d)$ $|w_{irreversible}|$ for compression in single stage.
Choose the correct answer from the options given below:

$A$ sample of gas is compressed from an initial volume of $2V_0$ to $V_0$ using three different processes.
First: Using reversible isothermal.
Second: Using reversible adiabatic.
Third: Using irreversible adiabatic under a constant external pressure.
Then

For the hypothetical reaction
$A_{2(g)} + B_{2(g)} \rightleftharpoons 2AB_{(g)}$
$\Delta_r G^o$ and $\Delta_r S^o$ are $20 \ kJ/mol$ and $-20 \ J K^{-1} mol^{-1}$ respectively at $200 \ K$.
If $\Delta_r C_P$ is $20 \ J K^{-1} mol^{-1}$ then $\Delta_r H^o$ at $400 \ K$ is.....$kJ/mol$