The total pressure of a gas and a few drops of water in a container is $830 \, mm$. If the temperature of the container is decreased by $1 \%$,the new pressure is $............ \, mm$. The water vapor pressures at the two temperatures are $30 \, mm$ and $25 \, mm$ respectively.

$A$ fixed mass '$m$' of a gas is subjected to a transformation of states from $K$ to $L$ to $M$ to $N$ and back to $K$ as shown in the figure.
$1.$ The succeeding operations that enable this transformation of states are:
$(A)$ Heating,cooling,heating,cooling
$(B)$ Cooling,heating,cooling,heating
$(C)$ Heating,cooling,cooling,heating
$(D)$ Cooling,heating,heating,cooling
$2.$ The pair of isochoric processes among the transformation of states is:
$(A)$ $K$ to $L$ and $L$ to $M$
$(B)$ $L$ to $M$ and $N$ to $K$
$(C)$ $L$ to $M$ and $M$ to $N$
$(D)$ $M$ to $N$ and $N$ to $K$
Give the answer for question $1$ and $2$.

If the density of a mixture of nitrogen and oxygen gases at $400 \ K$ and $1 \ atm$ pressure is $0.920 \ g \ L^{-1}$, what is the mole fraction of nitrogen in the mixture? ($R=0.082 \ L \ atm \ mol^{-1} \ K^{-1}$; assume ideal gas behavior for oxygen and nitrogen)

Select the incorrect statement using the phase diagram of a substance.

The total pressure in a container containing a gas and a few drops of water is $830 \, mm \, Hg$. If the temperature of the container is decreased by $1 \%$,what will be the new pressure of the container in $mm \, Hg$? The vapor pressure of water at the two temperatures is $30 \, mm \, Hg$ and $25 \, mm \, Hg$ respectively.

$0.5 \ mol$ each of $H_2, SO_2$ and $CH_4$ are present in a container. If a hole is made in the container,what will be the order of partial pressures of the gases remaining in the container after $3 \ hours$?