The amount of heat evolved when $500 \ cm^{3}$ of $0.1 \ M \ HCl$ is mixed with $200 \ cm^{3}$ of $0.2 \ M \ NaOH$ is (in $kJ$)

For a dimerization reaction,$2 A_{(g)} \rightarrow A_{2(g)}$ at $298 \ K$,$\Delta U^{\ominus} = -20 \ kJ \ mol^{-1}$,$\Delta S^{\ominus} = -30 \ J \ K^{-1} \ mol^{-1}$,then the $\Delta G^{\ominus}$ will be........ $J$

The heats of combustion of $C_{(s)}$,$H_{2(g)}$,and $C_{2}H_{6(g)}$ are $-x_{1}$,$-x_{2}$,and $-x_{3}$ respectively. The heat of formation of $C_{2}H_{6(g)}$ is:

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 $K$.

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 ........... $kJ \, mol^{-1}$.

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