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.

At $27^{\circ} C$, $500 \ mL$ of helium diffuses in $30 \ minutes$. What is the time (in hours) taken for $1000 \ mL$ of $SO_2$ to diffuse under the same experimental conditions?

Which of the following statements is incorrect?

$1 \text{ mole}$ of gas $A$ and $1 \text{ mole}$ of gas $B$ at $27^{\circ} C$ were pumped into a $24.6 \ L$ volume pre-evacuated isolated flask. The catalyst coated inside the flask catalyses the following reaction $A_{(g)} + B_{(g)} \longrightarrow 2 D_{(g)}$. The kinetic energy of $D$ is $98.03 \ L \ atm$. Calculate the pressure realized at the end of the reaction. (in $atm$)

In a container,$0.5 \ mol$ each of $H_2, SO_2$,and $CH_4$ are taken. The order of their partial pressures after $3$ hours will be:

$A$ and $B$ are ideal gases. The molecular weights of $A$ and $B$ are in the ratio of $1: 4$. The pressure of a gas mixture containing equal weights of $A$ and $B$ is $P \text{ atm}$. What is the partial pressure (in $\text{atm}$) of $B$ in the mixture?