For the reaction at $300 \, K$,$A_{(g)} + B_{(g)} \to C_{(g)}$,given $\Delta U = -3 \, kcal$ and $\Delta S = -10 \, cal/K$. The value of $\Delta G$ will be $...... \, cal$.

Match the transformations in column $I$ with appropriate options in column $II$.

Column $I$	Column $II$
$A$. $CO_{2(s)} \rightarrow CO_{2(g)}$	$p$. phase transition
$B$. $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$	$q$. allotropic change
$C$. $2H_{(g)} \rightarrow H_{2(g)}$	$r$. $\Delta H$ is positive
$D$. $P_{(\text{white, solid})} \rightarrow P_{(\text{red, solid})}$	$s$. $\Delta S$ is positive
	$t$. $\Delta S$ is negative

What is the work done in $erg$ for the reversible expansion of $1 \, \text{mole}$ of an ideal gas from $10 \, L$ to $20 \, L$ at $25 \, ^oC$?

$7 \ g$ of $N_{2(g)}$ at $27 \ ^oC$ is expanded reversibly and isothermally from an initial pressure of $0.5 \ MPa$ to a final pressure of $0.1 \ MPa$. Determine the approximate work done $[\ln \ 5 = 1.6]$ ..... $J$

If $100$ mole of $H_2O_2$ decomposes at $1$ bar and $300$ $K$,the work done $(kJ)$ by $50$ mole of $O_{2(g)}$ as it expands against $1$ bar pressure is............. $kJ$
$2H_2O_{2(l)} \rightleftharpoons 2H_2O_{(l)} + O_{2(g)}$
$(R = 8.3 \ J \ K^{-1} \ mol^{-1})$

$200 \ mL$ of $0.2 \ M \ HCl$ is mixed with $300 \ mL$ of $0.1 \ M \ NaOH$. The molar heat of neutralization of this reaction is $-57.1 \ kJ \ mol^{-1}$. The increase in temperature in $^{\circ}C$ of the system on mixing is $x \times 10^{-2}$. The value of $x$ is ....... . (Nearest integer)
[Given : Specific heat of water $= 4.18 \ J \ g^{-1} \ K^{-1}$
Density of water $= 1.00 \ g \ cm^{-3}$]
(Assume no volume change on mixing)