Gas laws from KTG

Q. Which of the following is the correct statement of Boyle's law?

1. At a given temperature, pressure of a given mass of gas is inversely proportional to its volume.
2. At a given temperature, pressure of a given mass of gas is directly proportional to its volume.
3. At a given volume, pressure of a given mass of gas is inversely proportional to its temperature.
4. At a given volume, pressure of a given mass of gas is directly proportional to its temperature.

Q.

A vessel has $6\mathrm{g}$ of oxygen at pressure P and temperature of $400\mathrm{K}$. A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is at $\frac{\mathrm{P}}{2}$ and the temperature is $300\mathrm{K}$?

Q. Which of the following is the correct statement of Charle's law?

1. At a given temperature, pressure of a given mass of gas is inversely proportional to its volume.
2. At a given temperature, pressure of a given mass of gas is directly proportional to its volume.
3. At a given pressure, volume of a given mass of gas is inversely proportional to its absolute temperature.
4. At a given pressure, volume of a given mass of gas is directly proportional to its absolute temperature.

Q.

Two gases of equal mass are in thermal equilibrium. If $P_a,P_b$ and $V_a$ and $V_b$ are their respective pressures and volumes, then which relation is true

1. $P_a\ne P_b;V_a=V_b$

2. $P_a=P_b;V_a\ne V_b$

3. $\frac{P_a}{V_a}=\frac{P_b}{V_b}$

4. $P_a{V}_a=P_b{V}_b$

Q. Graham's law states that at same pressure and temperature, rate of diffusion of a gas is inversely proportional to its molecular mass.

1. False
2. True

Q. What does the following plot represent for an ideal gas?

1. Charles's Law
2. Boyle's Law
3. Avogadro's Law
4. Gay-Lussac's Law

Q. A gas flushes out of a container through a pin hole four times quickly as methane. The molecular weight of the gas is

1. $2\text{g}$
2. $1\text{g}$
3. $16\text{g}$
4. $8\text{g}$

Q. $1000\text{cc}$ of an ideal gas at constant pressure is heated from ${27}^{\circ }\text{C}$ to ${327}^{\circ }\text{C}.$ The new volume will be

1. $1500\text{cc}$
2. $2000\text{cc}$
3. $1000\text{cc}$
4. $750\text{cc}$

Q. Which one of the graph represents the behaviour of an ideal gas at constant temperature?

1. 
2. 
3. 
4. 

Q. A closed vessel contains $8\text{g}$ of oxygen and $7\text{g}$ of nitrogen. The total pressure is $10$ atm at a given temperature. If now, oxygen is absorbed by introducing a suitable absorbent, the pressure of the remaining gas in atm will be

1. $2$
2. $10$
3. $4$
4. $5$

Q. Which of the following differentiate between diffusion and effusion?

1. Diffusion is the intermixing of the gas molecules at any direction and effusion is the reverse of diffusion.
2. Diffusion is the property of the gas molecules and effusion is the property of the gas container only.
3. Diffusion occurs at any direction, whereas effusion occurs under the potential difference.
4. Diffusion is the intermixing of the gas molecules due to concentration gradient, whereas effusion is the escaping of gas molecules through the pores without collision.

Q.

The molecular weight of gas A is 10 times greater than the molecular weight of gas B . These two gases are taken in cylinders of 5L volume at 1 atm pressure and ${27}^{o}C$. Comment on the number of molecules in the two gases. Justify with respect of kinetic molecular theory of gases.

Q.

Boyle's law holds for an ideal gas during

1. Isobaric changes

2. Isothermal changes

3. Isochoric changes

4. Isotonic changes

Q. A bottle is closed by a cork which contains air at a temperature of $7^{\circ }$C and pressure of 1 atm. The cork can withstand a pressure upto 1.3 atm. Then upto what maximum temperature can we heat the bottle so that the cork gets ejected? (Neglect thermal expansion of the bottle)

1. ${50}^{\circ }$C
2. ${80}^{\circ }$C
3. ${91}^{\circ }$C
4. ${130}^{\circ }$C

Q. A mixture of Nitrogen and Oxygen has volume $3000{\text{cm}}^3$ at temperature $300\text{K}$, pressure $200\text{kPa}$ and mass $6.88\text{g}$. Then, which of the following options is/are correct?
[Take $R=8.3\text{J/mol K}$]

1. Mass of Nitrogen in the mixture is $5.6\text{g}$.
2. Mass of Nitrogen in the mixture is $1.28\text{g}$.
3. Mass of Oxygen in the mixture is $1.28\text{g}$.
4. Mass of oxygen in the mixture is $5.6\text{g}$.

Q. By what percentage should the pressure of a given mass of gas be increased so as to decrease its volume by 10$\%$ at a constant temperature?

1. $8.1\%$
2. $9.1\%$
3. $10.1\%$
4. $11.1\%$

Q. If a given mass of gas occupies a volume of $10\text{cc}$ at $1\text{atm}$ pressure and temperature ${100}^{\circ }\text{C}$. What will be its volume at $4\text{atm}$, the temperature being the same?

1. $104\text{cc}$
2. $2.5\text{cc}$
3. $400\text{cc}$
4. $10\text{cc}$

Q. A bottle is closed by a cork which contains air at a temperature of $7^{\circ }$C and pressure of 1 atm. The cork can withstand a pressure upto 1.3 atm. Then upto what maximum temperature can we heat the bottle so that the cork gets ejected? (Neglect thermal expansion of the bottle)

1. ${50}^{\circ }$C
2. ${80}^{\circ }$C
3. ${91}^{\circ }$C
4. ${130}^{\circ }$C

Q.

400 cm³ of hydrogen is at normal temperature. Find the temperature of gas for the following volume when pressure remains constant.

Volume increases by 800 %

Q.

The volume of a gas at ${200}^{\circ }C$ is 200 ml. If the temperature is reduced to $-{20}^{\circ }C$ at constant pressure, its volume will be

1. 172.6 ml

2. 17.26 ml

3. 192.7 ml

4. 19.27 ml

Q. If by keeping the temperature constant, the pressure of a gas is decreased by $20\%$, then the percentage change in volume of the gas will be

1. + $20\%$
2. - $20\%$
3. + $25\%$
4. - $25\%$

Q. A narrow glass tube of length $100\text{cm}$ is closed at both ends. It lies horizontally with $20\text{cm}$ of mercury column in the middle dividing the tube into two compartments I and II of equal length. The air in each compartment is at standard temperature and pressure. The tube is then turned to a vertical position. By what distance will the mercury column be displaced?

Q. An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho )$
$($Assume that the radius of bubble is neglegible$)$

1. $V_0$
2. $V_0\left(\frac{\rho gh}{P}\right)$
3. $\frac{V_0}{(1+\frac{\rho gh}{P})}$
4. $V_0(1+\frac{\rho gh}{P})$

Q. You are given sample of $1{\text{cm}}^3$ of $H_2$, $1{\text{cm}}^3$ of $O_2$ and $1{\text{cm}}^3$ of $C{l}_2$ which are at STP. The sample which has maximum number of molecules is

1. $H_2$
2. $O_2$
3. $C{l}_2$
4. All have same value

Q. If a given mass of gas occupies a volume of $10\text{cc}$ at $1\text{atm}$ pressure and temperature ${100}^{\circ }\text{C}$. What will be its volume at $4\text{atm}$, the temperature being the same?

1. $104\text{cc}$
2. $2.5\text{cc}$
3. $400\text{cc}$
4. $10\text{cc}$

Q. An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho )$
$($Assume that the radius of bubble is neglegible$)$

1. $V_0$
2. $V_0\left(\frac{\rho gh}{P}\right)$
3. $\frac{V_0}{(1+\frac{\rho gh}{P})}$
4. $V_0(1+\frac{\rho gh}{P})$

Q. The rate of diffusion of two gases $A$ and $B$ is in the ratio of $1:2$ and the $B$ and $C$ in the ratio $1:8$, the rate of diffusion of $C$ with respect to $A$ is

1. $1:12$
2. $12$
3. $1:16$
4. $16$

Q. $2\text{moles}$ of gas $A$ effuses from a container in $10\text{min}$. How many moles of gas $B$ would effuse through the same container in same time under similar conditions. Ratio of specific gas constant for gas $A$ to the gas $B$ is $1:16$.

1. $2$
2. $1$
3. $4$
4. $8$

Q. Which of the following is/are state variables of a gas?

1. Pressure
2. Volume
3. Temperature
4. None of the above.