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(a) CO₂ and N₂O 

Boyle’s law states that at a given temperature. the volume occupied by a fixed mass of a gas is inversely proportional to its pressure.

V ∝ 1/P ; 

where T and n are fixed or PV = Constant = k

Charles’ law:

• V ∝ T at constant P and n (or) = V/T Constant A balloon filled with air at room temperature and cooled to a much lower temperature. the size of the balloon is reduced. Because if the temperature of the gas decreases, the volume also decreases in a direct proportion. 
• When temperature is reduced, the gas molecules inside in over slower due to decreased temperature and hence the volume decreases.

Given w/v = 0.1784 kg/m³ = 0.1784 g/litre at STP

It means 1 litre of gas at STP occupies 0.1784 g weight 

Now by changing P the V becomes 1.4 x l litre, where weight remains same. 

Thus,

d = w/v = 0.1784/1.4 = 0.1274 kg/m³ = 0.1274 g/litre.

(d) both assertion and reason are false

Correct Statement: Critical temperature of CO₂ is 304 K. It means that CO₂ cannot be liquefied above 304 K, whatever the pressure may applied. Pressure is inversely proportional to volume.

 (a) \(\frac{an^2}{V^2}\)

PV = nRT .........(1)

PV = w/m RT

w/V = Pm/RT

or, a = Pm/RT ...........(2)

By eq. (2) at constant temperature for a given gas d ∝ P.

 (d) \(\frac{PV}{nRT}\)

(a) Statement-I and liare correct and Statement-II is the correct explanation of Statement-I

(b) V / T = Constant 

Critical temperature of a gas is defined as the temperature above which it cannot be liquefied even at high pressures. 

∴ When cooling starts from 700 K, H₂O vill liquefied first, then followed by ammonia and finally carbon dioxide will liquefied.

(a) it a gas is compressed to a smaller volume at constant temperature, pressure is increased. At high pressure with a smaller volume, the gas deviates from ideal behaviour.

(b) If a gas temperature is raised keeping the volume constant, the pressure of the gas will increase. At high pressure, the gas deviates from ideal behaviour.

(c) if more gas is introduced into the same volume and at the same temperature, the number of moles are increasing. if the volume remains same, the increased number of moles collide with each other and kinetic energy increases and pressure decreases. At increased pressure, the gas deviates from ideal behaviour.

Answer: (c) 10^-4 K 

(b) Gadolinium sulphate

Answer: (b) PV= RT

Ideal gas: A gas that follows Boyle’s law, Charles’ law and Avogadro law strictly is called an ideal gas. It is assumed that intermolecular forces are not present between the molecules of an ideal gas.

Real gases: Gases which deviate from ideal gas behavior are known as real gases. NH₃ is expected to show more deviation. Since NH₃ is polar in nature and it can be liquefied easily.

• Linde’s method: Joule-Thomson effect is used to get liquid air or any other gas. 
• Claude’s process: In addition to Joule-Thomson effect, the gas is allowed to perform mechanical work so that more cooling is produced. 
• Adiabatic process: This method of cooling is produced by removing the magnetic property of magnetic material e.g. Gadolinium sulphate. By this method, a temperature of 10^-4 K i.e. as low as zero Kelvin can be achieved.

The pressure decreases with the increase in altitude because there are fewer molecules per unit volume of air. Above 9200 m (30,000 ft),

For example, where most commercial airplanes fly, the pressure is so low that one could pass out for lack of oxygen. 

For this reason most airplanes cabins arc artificially pressurized.

• When one ascends a mountain in a plain, the external pressure drops while the pressure within the air cavities remains the same. 
• This creates an imbalance. The greater internal pressure forces the eardrum to bulge outward causing pain. 
• With time and with the help of a yawn or two, the excess air within your ear’s cavities escapes thereby equalizing the internal and external pressure and relieving the pain.

(d) (i), (ii) and (iii)

(a) A - 3, B - 1, C - 4, D - 2

Answer: (b) N₂

• Hydrogen, nitrogen, oxygen, fluorine and chlorine exist as gaseous diatomic molecules. 
• Another form of oxygen namely ozone tr iatomic molecule exist as a gas at room temperature. 
• Noble gases namely helium, neon, argon, krypton, xenon and radon are mono atomic gases

(c) Graham’s law of diffusion

(a) P₁V₁ = P₂ V₂ 

(i). The mathematical relationship between the volume of a gas and the number of moles is V ∝ n

(ii). \(\frac{V_1}{n_1}=\frac{V_2}{n_2}\) = Constant 

Where V₁ and n₁ are the volume and number of moles of a gas and V₂ and n₂ are the values of volume and number of moles of same gas at a different set of conditions. 

(iii). If the volume of the gas increase then the number of moles of the gas also increases. 

(iv). At a certain temperature and pressure, the volume of a gas is dirctly proportional to the number of the moles of the gas.

Answer: (a) V ∝ T

\((c) \frac{r_A}{r_B}=\sqrt\frac{M_B}{M_A}\)

Answer: (a) F / a

Answer: (b) Pascal 

(a) Boyle’s law

 \((c)\,\left(P+\frac{an^2}{V^2}\right)(V-nb)=nRT\)

• Graham’s law of diffusion is useful to determine the molecular mass of the gas if the rate of diffusion is known. 
• Graham’s law forms the basis of the process of enriching the isotopes of U²³⁵ from other isotopes and also useful in isotopic separation of deuterium and protium.

Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. 

Mathematically V ∝ n

\( \frac{V_1}{n_1}= \frac{V_2}{n_2}\) = constant

It is difficult to drink water with a straw on the top of Mount Everest. This is because the reduced atmospheric pressure is less effective in pushing water into the straw at the top of the mountain because gravity falls off gradually with height. The air pressure falls off, there isn’t enough atmospheric pressure to push the water up in the straw all the way to the mouth.

(a) decreases

Aerosol cans carry clear warning of heating of the can. As the temperature rises, pressure in the can will increase and ambient temperatures about 120°F may lead to explosions. So aerosol cans should always be stored in dry areas where they will not be exposed to excessive temperatures. You should never throw an aerosol can onto a fire or leave it in the direct sunlight. even it is empty. This is because the pressure will build up so much that the can will burst. It is due to 2 reasons. 

• The gas pressure increases. 
• More of the liquefied propellant turns into a gas

Diffusion:

• Diffusion is the spreading of molecules of a substance throughout a space or a second substance.
• Diffusion refers to the ability of the gases to mix with each other.
• Example, Spreading of something such as brown tea liquid spreading through the water in a tea cup.

Effusion:

• Effusion is the escape of gas molecules through a very small hole in a membrane into an evacuated area.
• Effusion is a ability of a gas to travel through a small pin-hole.
• Example, pouring out something like the soap studs bubbling out from a bucket of water.

Graham’s law of diffusion: 

The rate of diffusion or effusion is inversely proportional to the square root of molecular mass of a gas through an orifice.

\(\frac{r_A}{r_B}=\sqrt{{M_B}{M_A}}\)

r_A , r_B = rate of diffusion of gases A, B 

M_A , M_B = Molecular mass of gases A, B

Answer: (d) Oxygen

The volume of vessel remains constant and some moles are given out. Thus volume of gas = 1 litre. 

(a) In aerated water bottles, CO₂ gas is passed through the aqueous solution under pressure because the solubility of the gas in water is not very high. In summer, the solubility of the gas in water is likely to decrease because of the rise in temperature. Thus, in summer, more of gas will be present above the liquid surface in the glass bottle. 

In case, the pressure of the gas becomes too high, the glass will not be able to withstand the pressure and the bottle may explode. To avoid this, the bottles are kept under water. As a result, the temperature is likely to decrease and the solubility of CO₂ is likely to increase in aqueous solution resulting in decreased pressure.

(b) Liquid ammonia bottle contains the gas under very high pressure. If the bottle is opened as such, then the sudden decrease in pressure will lead to a large increase in volume of the gas. As a result, the gas will come out of the bottle all of a sudden with force. This will lead to the breakage of the bottle and also causes accident.

However, if the bottle is cooled under tap water for sometime, there will be a decrease in the volume of a gas to a large extent. if the seal is opened now, the gas will corne out of the bottle at a slower rate, reduces the chances of accident.

(c) The pressure of air is directly proportional to the temperature. Since the temperature is higher in summer than in higher, the pressure of the air in the tube of the lyre is likely to be quite high as compared to winter. It is quite likely that the tube may burst under high pressure in summer, Therefore, it is advisable to inflate the types to lesser pressure in summer than in winter.

(d) The volume of the gas is inversely proportional to pressure at a given temperature according to Boyle’s law. As the weather balloon ascends, the pressure tends to decrease. As a result, the volume of the gas inside the balloon or the size of the balloon is likely to increase.

(c) Diffusion

In space, there is no pressure, if we do wear a pressurised suit, our body will die. In space, we have to wear a pressurised suit, otherwise our body will continue to push out and blow up like a balloon. It would look cool, but we will be dead. So the astronauts in space must wear a pressurised suit (protective suits).