An ideal gas Xhas same density at 1 bar pressure as that of dinitrogen at 2 bar at 298K What is the molar mass of the gas X (2024)

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

An ideal gas filled in a cylinder occupies volume,$V$. The gas is compressed isothermally to the volume,$\frac{V}{3}$. Now the cylinder valve is opened and the gas is allowed to leak keeping the temperature the same. What percentage of the number of molecules escape to bring the pressure in the cylinder back to its original value.

10 moles of a mixture of hydrogen and oxygen gases at a pressure of 1 atm at a constant volume and temperature, react to form 3.6 g of liquid water. The pressure of the resulting mixture will be closest to:

An ideal gas undergoes a circular cycle centred at $4\mathrm{atm}$, $4\mathrm{L}$ as shown in the diagram.

The maximum temperature attained in this process is close to

A gas such as carbon monoxide would be most likely to obey the ideal gas law at:

The average distance between molecules of an ideal gas at STP is approximately of the order of

One mole of an ideal gas undergoes a linear process as shown in the figure below. Its temperature expressed as a function of volume, $V$ is-

Two closed bulbs of equal volume $\left(\mathrm{V}\right)$containing an ideal gas initially at pressure ${\mathrm{p}}_{\mathrm{i}}$ and temperature ${\mathrm{T}}_1$ are connected through a narrow tube of negligible volume, as shown in the figure below. The temperature of one of the bulbs is then raised to ${\mathrm{T}}_2.$ The final pressure ${\mathrm{P}}_{\mathrm{f}}$ is:

A given sample of an ideal gas occupies a volume, $V$ at a pressure, $P$ and absolute temperature,$T$. The mass of each molecule of the gas is $\text{m}$. Which of the following gives the density of the gas?

The temperature of an open room of volume $30{\mathrm{m}}^3$ increases from $17°\mathrm{C}$ to $27°\mathrm{C}$ due to the sunshine. The atmospheric pressure in the room remains $1\times {10}^5\mathrm{Pa}$.If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f-n_i$ will be:

An ideal gas follows a process described by $P{V}^2=C\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\left(P_1,V_1,T_1\right)\mathrm{t}\mathrm{o}\left(P_2,V_2,T_2\right)$ (C is a constant). Then

An open vessel at ${27}^{o}C$ is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature to which the vessel has been heated is:

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?

A long cylindrical pipe of radius $20\mathrm{cm}$ is closed at its upper end and has an airtight piston of negligible mass as shown. When $\mathrm{a}$ $50\mathrm{kg}$ mass is attached to the other end of piston, it moves down by adistance, $\Delta l$ before coming to equilibrium. Assuming air to be an ideal gas, $\frac{\Delta l}{l}$ (see figure) is close to $\left(g=10\mathrm{m}{\mathrm{s}}^{-2}\right.$, one atmospheric pressure is ${10}^5\mathrm{Pa}$ ),

Modern vacuum pumps can evacuate a vessel down to a pressure of $\text{4.0}\times 10^{-15}$atm. at room temperature (300 K). Taking R = 8.3 JK^-1 mole^-1, 1 atm = 10⁵ Pa and ${\text{N}}_{\text{Avogadro}}=6\times 10^{23}{mole}^{-1}$, the mean distance between molecules of gas in an evacuated vessel will be of the order of :

The equation of state for $2\mathrm{g}$ of oxygen at a pressure $p$and temperature $T$, when occupying a volume $V$will be

One mole of an ideal gas passes through a process where pressure and volume obey the relation $\mathrm{P}={\mathrm{P}}_{\mathrm{o}}\left[1-\frac{1}{2}{\left(\frac{{\mathrm{V}}_{\mathrm{o}}}{\mathrm{V}}\right)}^2\right]$ . Here ${\mathrm{P}}_{\mathrm{o}}$ and ${\mathrm{V}}_{\mathrm{o}}$ are constants. Calculate the change in the temperature of the gas if its volume changes from ${\mathrm{V}}_{\mathrm{o}}\mathrm{}$ to $2{\mathrm{V}}_{\mathrm{o}}$ .

A cylinder closed at both ends is separated into two equal parts ($45\mathrm{cm}$ each) by a piston impermeable to heat. Both the parts contain the same masses of gas at a temperature of $300\mathrm{K}$ and a pressure of $1\mathrm{}\mathrm{atm}$. If now the gas in one of the parts is heated such that the piston shifts by $5\mathrm{cm}$, then the temperature and the pressure of the gas in this part after heating is

A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is $l_1,$ and that below the piston is $l_2,$ such that $l_1>l_2.$ Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T.$ If the piston is stationary, its mass$m$will be given by:
($R$ is universal gas constant and $g$ is the acceleration due to gravity)

$0.5$ moles of gas $\mathrm{A}$ and $\mathrm{x}$ moles of gas $\mathrm{B}$ exert a pressure of $200\mathrm{P}\mathrm{a}$ in a container of volume $10\mathrm{}{\mathrm{m}}^3$ at $1000\mathrm{}\mathrm{K}$ . Given, $\mathrm{R}$ is the gas constant in ${\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1},\mathrm{x}$ is: