States Of Matter

There are 2 conditions for liquefaction of gases:

• Low temperature

• High pressure

LOW TEMPERATURE: As the temperature of a gas is low, the kinetic energy of the molecule also decreases, which leads volume to get decrease. As the temperature decreases, molecules come close to each other and changes into a liquid.

HIGH PRESSURE: As the pressure increases, makes gas molecule come close to each other and convert into liquid. For each gas, there is a specific temperature above which gas never be liquefied, however, high pressure is applied.

Therefore the effect of temperature is more important than that of pressure.

The atmospheric pressure is very low at high altitudes, so at very low temperatures, vapour pressure of the liquid becomes equal to atmospheric pressure i.e. below boiling point. Liquid starts to boil much before the food is cooked. To avoid this situation, we use pressure cookers. Pressure cooker raises the pressure so that the boiling point of liquid increases. This helps in efficient cooking of food in a short time.

SURFACE TENSION is defined as the force acting per unit length perpendicular to the line drawn on the surface of liquid. The tension arises due to the attraction of the particle in a bulk in the surface layer of the liquid which minimizes the surface area. For the given volume of a liquid, the surface area of the sphere is minimum and the drop of liquid-like mercury or rain droplets are spherical. The inner force on the molecules of the surface minimizes the surface area and forms a drop.

CHARLE’S LAW state that the volume of a mass of gas is directly proportional to absolute temperature at constant pressure.

Here in the graph straight line is obtained. Slope lines are different at different temperature. All lines meet at absolute zero temperature (lowest imaginary temperature at which gas are supposed to occupy zero volume), where volume of gas is also zero. The volume temperature graph at different fixed pressure is called isobars.

London forces are present in polar molecules and monoatomic nonpolar molecules like H₂, O₂, N₂, He, Ne, Ar etc., which shows no bonding and exist with intermolecular forces.

The non-polar molecules are electrically symmetrical, so there is no dipole moment, but sometimes temporary dipoles can be formed. The non-polar molecule develop momentarily dipole due to unsymmetrical electronic charge.

INTERACTION ENERGY1/r⁶

‘r’ is the internuclear distance between two interacting particles.

These type of forces work only at a short distance of approximately 500 pm. The magnitude of forces depends on the polarisability of atom or molecule. Polarisability is the ease with which electron and nuclei get displaced for their positions. Stronger the London force, larger the polarisability.

Polar molecules have partial negative and partial positive charge or a dipole, Dipole-dipole forces act between molecules which are neutral but possess permanent dipole. The separation of charges depends on the electronegativity of the bonded atom. For example, Dipole-Dipole forces are present between two HCl molecules. Chlorine is more electronegative so pull half the pair of electron towards itself so chlorine has partial negative charge and hydrogen has partial positive charge.

Dipole-dipole forces are stronger than London forces because permanent dipoles are involved but weaker than ion-ion interaction because partial charges present in polar molecules are always less than unit electric charge (1.6Х10^-19) present on ions.

MOLE FRACTION=

Let the moles of dihydrogen=1 and dioxygen=4

Mole fraction of O₂=

=

Partial pressure= mole fraction Х Total pressure

= ×1

= 0.8atm

= 0.8×10⁵Nm^-2

= 8×10⁴Nm^-2

Gay Lussac gave a general relation between pressure and temperature of the gas. He said that pressure of given mass is directly proportional to the temperature at constant volume.

Gay Lussac law state that at constant volume, temperature is directly proportional to the pressure of a fixed amount of gas.

P α T (at constant volume)

P = kT

K = constant

We can write:

= k

The line showing pressure-temperature behaviour at constant volume are called ISOCHORES.

There are 2 conditions for liquefaction of gases:

• Low temperature

• High pressure

LOW TEMPERATURE: As the temperature of a gas is low, the kinetic energy of the molecule also decreases, which leads volume to get decrease. As the temperature decreases, molecules come close to each other and changes into a liquid.

HIGH PRESSURE: As the pressure increases, makes gas molecule come close to each other and convert into liquid. For each gas, there is a specific temperature above which gas never be liquefied, however, high pressure is applied.

Therefore the effect of temperature is more important than that of pressure.

Liquefaction of so-called permanent gases like dihydrogen, helium is difficult, as they show positive deviation in the value of compressibility. So they require high pressure so that moleculescome close to each other and low the temperature to slow the movement of molecules. These 2 conditions tell about the liquefaction of gases. Therefore O₂> N₂> H₂,> He

Resistance to the flow of liquid is called viscosity.

F=η.A

Here,

is a velocity gradient, η is a viscosity coefficient, A is area

η =.

Putting, F = N, dx=m, A= m²,v=ms^-1

η= N/m². m/ms^-1

η= Nsm^-2

η is the proportionality constant , also known as coefficient of viscosity. SI unit of viscosity is Nsm^-2 = Pascal second (Pa s = 1kgm^-1s^-1)

There are 2 conditions for liquefaction of gases:

• Low temperature

• High pressure

LOW TEMPERATURE: As the temperature of a gas is low, the kinetic energy of the molecule also decreases, which leads volume to get decrease. As the temperature decreases, molecules come close to each other and changes into a liquid.

HIGH PRESSURE: As the pressure increases, makes gas molecule come close to each other and convert into liquid. For each gas, there is a specific temperature above which gas never be liquefied, however, high pressure is applied.

Therefore the effect of temperature is more important than that of pressure.

Shimla has the lowest atmosphericpressure so liquid will boilfirst there.The atmospheric pressure is very low at high altitudes, so at very low temperature, the vapour pressure of the liquid becomes equal to atmospheric pressure i.e. below boiling point. Liquid starts to boil much before the food is cooked.

A gas which obeys gas laws and equation- PV=NRT at all temperature and pressure is called ideal gas. So, in PV vs P graph, straight line parallel to the x-axis at all pressure and constant temperature and PV product is constant. Therefore B is the straight line for ideal gas.

Resistance to the flow of liquid is called viscosity.

F=η.A

Here,

is a velocity gradient, η is a viscosity coefficient, A is area

η = .

Putting, F = N, dx=m, A= m²,v=ms^-1

η= N/m². m/ms^-1

η= Nsm^-2

η is the proportionality constant , also known as coefficient of viscosity. SI unit of viscosity is Nsm^-2 = Pascal second (Pa s = 1kgm^-1s^-1)

Molecules with more kinetic energy can overcome the intermolecular forces to slip into one another in layers. So, when temperature increases, viscosity decreases

SURFACE TENSION is defined as the force acting per unit length perpendicular to the line drawn on the surface of liquid. The surface tension arises due to the attraction of the particle in a bulk in the surface layer of the liquid which minimizes the surface area. Increase in temperature, the kinetic energy of liquid molecule increases, which decreases intermolecular forces. It results from a decrease in inward force or pulling on the surface of liquid. So, surface tension decreases with increase in temperature.

As compared to the solid state as well as the liquid state, we find that in the gaseous state, the molecules have very high randomness in their motion, that is they do not follow any particular direction and similarly there is a disorder-ness in their motion.

This is due to the high entropy which the molecules present in the gaseous state possess. This entropy is the degree of randomness of the motion of the molecules. So more the entropy, more would be its disorder-ness or the randomness of the motion of the molecules.

From the diagram, we can see how there is disorder-ness or randomness in the motion of the gaseous molecules which is lesser for liquid and least or absent in solids.

We know, at STP (273K, 1 atm), 1 mole of any substance will contain Avogadro number of molecules, which is 6.023×10²³ and if it is a gas, it will occupy a volume of 22.4L. Also, molar mass of oxygen gas (O₂) is 32gm.

So, (ii) and (iii) are correct statements, but in the question, it is mentioned to find the incorrect options, so (i) and (iv) are the incorrect facts.

Gases tend to follow the ideal gas equation, that is , to become ideal gas, when the pressure is low and the temperature is high. If the gas tries to deviate from the ideal behaviour, then the conditions should be opposite that is high pressure and low temperature.

We know that the concept of ideal gas is hypothetical as no such gas exists whose molecules occupy negligible space and have no interactions, and which obeys the gas laws. The concept is just theoretical.

When we add salt to a vessel containing water, the surface area of water molecules decrease as some of them are replaced by salt molecules. Due to the less availability of water molecules on the surface, the vapour pressure decreases.

Also lowering the temperature of water will lower the kinetic energy of the water molecules, the randomness of the water molecules will also decrease on the surface so gradually the vapour pressure also decreases.

Decreasing the quantity of water or the volume of the vessel has no effect on the vapour pressure because no change is done to the orientation of these water molecules.

We know that 1 mole of any gas at STP (273K, 1 atm) will occupy 22.4L.

Also the molar weights of CO is 28gm, H₂O is 18gm, CH₄ is 16gm, NO is 30gm.

Now, 1 gm of these gases will occupy the maximum volume if the molar weight of that gas is the least.

As, volume occupied by 1gm of the gas =

Lesser the molar mass, higher is the volume occupied.

(a) Of all these, CH₄ has the least molar mass (16gm), so it would occupy the highest volume for 1gm of the gas.

(b) Similarly, higher the molar mass, lesser is the volume occupied.

Of all these, NO has the highest molar mass (30gm), so it would occupy the least volume for 1gm of the gas.

Chemical composition of water is not differing in any of these states. We know that three forms of physical states exist, namely solid, liquid and gas.

H₂O exists in the solid form as ice, it exists in the liquid form as water and as steam in the gas state. All of these states consist of H₂O_, due to which no change in the chemical composition of water is observed in these states.

The difference in all these three states is created by the physical properties as the molecules of the three different states are arranged in three different types therefore accounting to the difference in physical properties like molecular weights.

We can get an idea about the different factors which determine the states of matter from the combination of all the gas laws.

The first law is the Charles’ Law.

It states that when pressure is kept constant, volume of an ideal gas (V) is directly proportional to the absolute temperature (T).

∴For the first ideal gas,

V₁ =kT₁ [k is some proportionality constant]

So, …(i)

Similarly for the second gas,

…(ii)

Combining (i) and (ii),

This is Charles’ Law.

The second gas law is Boyle’s Law.

It states that when temperature is kept constant, pressure of the given mass of an ideal gas (P) is inversely proportional to the volume(V).

∴For the first ideal gas,

= [k is some proportionality constant]

So, …(i)

Similarly for the second gas,

So, …(ii)

Combining (i) and (ii),

This is Boyle’s Law.

When we combine the above two laws, we get a new law which is known as the ideal gas law.

The combined gas law is as follows:

=

Where P₁,V₁,T₁ and P₂,V₂,T₂ are the pressure, volume and temperature for two gases respectively.

So we get to know that pressure, volume and temperature along with mass are the factors which determine the state of matter.

• In halides, due to the presence of electronegative halogen atoms (F, Cl, Br, I), these halogen atoms acquire a delta negative (δ-) and H being very less electronegative acquires a delta positive (δ+) charge.

• Due to the formation of opposite polarities, it makes halide a polar molecule.

• Also intermolecular hydrogen bonding is observed in compound where very high electronegative elements like(O,F,N) are present. Due to intermolecular hydrogen bonding, the stability of the molecule increases along with physical properties like boiling point.

(a) Since the halides are a polar molecule, due to the presence of permanent dipoles, the dipole-dipole interactions along with the London forces are found in these halides (HF, HCl, HBr).

• Along with that, as we discussed earlier that the presence of very high electronegative elements (likeO,F,N), lead to intermolecular hydrogen bonding, in HF due to electronegative atom F, an additional intermolecular hydrogen bonding is present.

(b) It is told that

• Strength of London forces increases with the number of electrons in the molecule.

• In the periodic table, the first element of the group is F, followed by Cl, Br and I.

• So, HI has the most number of electrons in the molecule (as I hasthe highest atomic number amongst F and Cl) and HF has the least number of electrons.

• Thus, London interactions increase from HF to HI.

• But in a polar molecule like halides, more the electronegativity is of the halogen atom, more polar is the molecule (as delta negative charge δ-increases).

• As electronegativity increases from I to F, dipole-dipole interactions increase from HI to HF.

• Boiling point increases from HI to HCl (as I^- is a very large ion, it is bonded by Van der Waal’s forces, so more energy is required to break the bonds. As the size of the ions decrease, lesser energy is required).

• From this trend, we can conclude that the London’s forces are predominant because these interactions also increase from HF to HI.

(c) Ad we discussed earlier that the presence of very high electronegative elements (like O,F,N), lead to intermolecular hydrogen bonding, in HF due to electronegative atom F, an additional intermolecular hydrogen bonding is present.

In HCl, size of Cl^- ion is very small, due to which the bonded Van der Waal’s forces are very weak, so less energy is required to break the bonds. Thus Boiling point is the least.

We know that 1 mole of any gases at STP (273K, 1 atm) occupy a volume of 22.4L.

As we are asked to find molar volume (volume of 1 mole of the gas), therefore these gases occupy 22.4L of volume.

According to Boyle’s law, at constant temperature, the volume of a gas is inversely proportional to its pressure,

According to Charle’s law, Volume of the gas is directly proportional to its kelvin temperature at constant temperature,

According to Avogadro’s law, if equal number of molecule of different gases at identical temperature and pressure condition than occupy same amount of volume.

If a gas follows Boyle’s law, Avogadro’s law, Charles law. Then gas is called ideal gas. From these three gas law we get ideal gas law.

i.e.

Where, P= pressure, V = volume of the gas n= no. of mole, T= temperature

All gases are not ideal gas. Real gas doesn’t obey the gas law at normal temperature and pressure condition. Gas behaves ideally under two conditions these are - (i) the volume of molecule of a gas is negligible as compared to its complete volume. (ii) There is no attraction force between the gases.

Real gas obey these law only under limited conditions of low pressure and high temperature .At low pressure , system volume increases but volume of real gas become negligible , molecules occupy no volume relative to system .So gas behave as ideal . At high temperature gas molecules movement become fastersuch that there is no intermolecular attraction, hence real gas behave ideal.

Both ‘A’ and ‘B’ gas are in same condition of temperature and pressure .On increasing pressure gas ‘A’ liquefies but ‘B’ does not . At high pressure gas molecule come closer to each other and gas converted to liquid. But this phenomenon is based on critical temperature. Here ‘A’ gas liquefies easily that means gas ‘A’ is below its critical temperature. Gas ‘B’ not liquefy on applying high pressure because gas ‘B’ is above its critical temperature

The universal gas constant;

Its unit is obtained from expression, R=

Pressure = = =

Volume = length³

So, ==

Thus, unit of R is energy per mole per Kelvin. R is the amount of

Work (energy) obtained from per mole of gas when its temperature raised by 1 kelvin.

Unit R depends on units of P, V and T. If pressure is measured in Pascal, per

Mole volume is measured in m³ and temperature is measured in Kelvin then

Unit of ‘R’ are in Pa m³K^-1mol^-1 or JK^-1mol^-1. Joule is the unit of work done so

‘R’ is work done per Kelvin per mole. For 1 mole gas

The dimensions of the universal gas constant R are energy per degree per mole. In the metre-kilogram-second system, the value of R is 8.3144598 joules per Kelvin per mole.

Hence R only depends on unit of different parameter P, V, n, T. So R values same for all gases.

The statement is correct. Assumption true only at low pressure and high temperature of gaseous molecule. At low pressure, system volume increases but volume of real gas become negligible, molecules occupy no volume relative to system. At high temperature gas molecules movement become fastersuch that there is no intermolecular attraction. Under this condition gas behave as ideal gas.It is impossible to liquefy an ideal gas since ideal gas have no force of attraction between the gaseous molecules.

Hexane [CH₃(CH₂)₄CH₃)] has weak London dispersion forces because it is a non polar molecule . But water and alcohol is polar molecule there exist H- bonding and dipole- dipole interaction. These forces are stronger than London force. Due to this water and alcohol has strong interaction between the molecules than hexane, Hexane has low surface tension than other two.

H-bonding is stronger in water than alcohol, so water has strong intermolecular attraction than alcohol. Increasing order of surface tension is - Hexane alcohol water

The gas collected over water is called moist and pressure exerted by saturated water vapour is called aqueous tension.

The total pressure of the gas is P _{moist gas} = P _{dry gas}

As exerted water vapour is present i.e. aqueous tension.Which is correction term from total pressure.

By applying this correction term we get a new equation,shown below -

P _{dry gas} =P _{moist gas} – aqueous tension

Therefore, the correction term applied to the total pressure of the gas to get the pressure of dry gas is P _{moist gas} – aqueous tension

Thermal energy arises due to motion of atoms or molecules in the body. If we increase temperature then then the kinetic energy of atom and molecule increase rapidly, due to this motion of atom or molecule become faster. Hence thermal energy arises.

H-bonding: strong H- bonding present between the HF molecules due to high polarity of H-F bond.

Dipole- dipole interaction:

These interactions occur when two dipolar molecules interact with each other via space. In this, partially negative portion of one polar molecule is attracted to partially positive portion of second polar molecule.

The Kinetic Theory of Gases assumes that collisions between gas molecules and the walls of a container are perfectly elastic, gas particles do not have any volume, and there are no repulsive or attractive forces between molecules, but these assumptions is for Ideal Gases.

When the temperature is increases, the kinetic energy of the molecules starts to increase as well. Hence, if we continued to increase the temperature the gas molecules continues to go far apart from the other of its own molecules at very high temperature the molecules of the gases are very and the molecules do not interacts. And at this point the gas starts behaving as the ideal gas.

Hence, we can say that, these assumptions which are made in Kinetic Theory of Gases are true under following conditions only, i.e at very low pressure and at high temperatures, because at low pressures, the volume of the molecules tends to become negligible as compared to the total volume of the gas and at high temperatures the molecules are very far from each other and hence, they do not interact and hence the assumption is applicable at high temperature.

(i) Compressibility factor, Z is defined as the ratio of the product of pressure and volume to the product of number of moles, gas constant and temperature.

For ideal gas, the value of Z is 1.

Because, we know according to ideal gas equation,

PV = nRT

So, Z =

=

= 1

(ii) As at the temperature which is above the Boyle’s temperature, PV is greater than nRT for real gases so, the value of Z will also be greater than 1 i.e Z>1, which shows the positive deviation in the compressibility factor above Boyle’s temperature.

The critical temperature (T_c) of any gasis defined as the value of temperature above which no gas can be liquefied, and the pressure at the critical temperature is calledcritical pressure (P_c).

So, as the CO₂ gas cannot be liquefied at temperature which is greater than its critical temperature i.e 30.98°C even by applying any pressure. So as the given temperature is 32°C by applying a pressure of 80atm the CO₂ gas cannot be liquefied.

(i) As the Vander Waals constants,‘b’ is approximately equal to the total volume of the molecules of a gas. Hence, the increasing order of ‘b’ is as follows:

He < H₂< O₂< CO₂

This is because the parameter ‘b′ is proportional to the proper volume of a single particle, and the volume of CO₂ is maximum followed by O₂ which is followed by H₂ and He. Or in other words the value of ‘b’ is directly proportional to the size of gas molecules. Hence we get the order shown above.

The volume of CO₂ is maximum; this is because CO₂ contains 3 atoms, whereas O₂ has greater volume than H₂ because Oxygen atom has 2 shells whereas H has only one shell. Hence, H is smaller in size than O. And He is having the lowest volume because it is single atom and has only one shell like H, but unlike He, H-H is having greater volume than He.

(ii) The value of‘a’ for any gas depends on the strength of inter molecular attraction. Molecules having the weakest forces of attraction has the smallest value of ‘a’ whereas the molecules having the strongest force of attraction has the largest a values.

Hence, as the surface area of CH₄ is highest so, it has highest Vander Waal’s force of attraction so, has highest value of ‘a’, followed by O₂ and H₂.

So the decreasing order is found to be:

CH₄> O₂> H₂

We have:

P _ideal = P _real+

P_ideal– P_real=

Now, putting the value of units of pressure, volumes and n, we have

The unit of ‘a’ when the pressure is taken in Nm^-2, number of moles in “mol” and volume in m³ is

Now, when pressure is in atmosphere and volume in dm³ than, the value of ‘a’ is:

a =

Surface tension is defined as the tension that exist on the surface of a liquid, this tension is the result of the attraction of the particles in the surface layer by the bulk of the liquid, so the molecule present at the surface tends to minimize surface area. The two phenomena that can be explained on the basis of surface tension are:

1. Bubbles are in round shape due to surface tension.

2. A needle is able to float in water is because of surface tension present on the surface of water.

Water has hydrogen bonding existing as intermolecular forces, hexane has Vander Waal force of attraction existing as intermolecular force, glycerine also has hydrogen bonding as a major intermolecular force( has 6 hydrogen bond formed)

The increasing order of their viscosities is:

Glycerine > Water > hexane

Order is so because, Glycerine has most number of hydrogen bond, followed by water, and followed by hexane which has Vander Waal force of attraction.

Presence of high intermolecular interaction leads to the appearance of Viscosity.

As the temperature increases, it leads to weakening the intermolecular forces operating between its particles(because increasing the temperature leads to increases in the vibration of bond and due to rapid vibration bond strength decreases and as also kinetic energy of molecule is increased due to which the interaction is decreased).Hence, as the temperature increases viscosity decreases because the viscosity is decreases when the intermolecular forces operating reduced.

Hence, as the temperature increases the viscosity decreases.

According to the graph:

(i) As the temperature is constant, and the pressure is increasing the change in the volume is seen as decreasing exponentially.

As we know that when the pressure increases at the constant temperature the volume decreases.

(ii) At the constant pressure, by increasing temperature the volume of gas increases.

(This can easily be seen by graph, by drawing the line parallel to volume axis. When we draw a line parallel to Volume axis, it cuts blue line (200K) as well as the green line(400K), the point at which the line parallel to volume axis cuts the blue and green line, we draw another line perpendicular to Volume axis to get the values of the volume at 200K and 400K.) The yellow line shows the two value of volume at constant pressure.

According to the graph:

(i) At low pressure as the red curve and the blue curve are approaching each other, which shows that the real gas is behaving as ideal gas at the low pressure.

(ii) At high pressure as the red curve and the blue curve are deviating and going away from each other, which indicates that the real gas and ideal gas have distinct characters at high pressure

(iii) The green line shows the point, at which the real gas behaves as an ideal gas.

(i)-(c)

(ii)- (a), (b)

(iii)- (d)

(i) Pressure vs temperature at constant molar volume is known as Isochores, as Isochore means a line on a graph plotted for the variation of the temperature of any gas with its pressure,keeping volume constant.

Hence, the term used for Pressure vs temperature at constant molar volume graph is Iscochores.

(ii)Pressure vs volume graph at constant temperature is known as an Isotherms graph or Constant temperature curve, this is because we know that the word “Isothermal” means temperature remains constant for that particular system and if we are taking about any process in which no change in temperature occurs during the course of the reaction the process is called "isothermal process".

Hence, when we plot Pressure vs volume graph at constant temperature it is called an Isotherms graph.

(iii) Volume vs temperature graph at constant pressure is known as Isobars.

As we all know that any system having constant pressure, is known as the isobaric system, and when we plot Volume vs temperature graph keeping pressure constant, it is better to be known as Isobaric graph.

(i) – (e)

(ii) – (d)

(iii) – (b)

(iv) – (a)

(i)Boyle’s law states that “at constant temperature, the pressure of a fixed amount of gas(n moles)varies inversely with its volume.Which means that if we increase the pressure, the volume of the gas will be decreased and it is understandable by the example of LPG Gas cylinder in which so high pressure is maintained so that the gas liquefied and attain very small volume of cylinder.

If we write Boyle’s law mathematically, we get:

p at constant n and T

Where p = pressure of a gas

V = Volume of the gas

n = fixed amount of gas

T = constant temperature

(ii) Charle’s law states that “pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature”.

If we increase the temperature the Volume of gas increases.

If we write Charle’s law mathematically, we get:

VT at constant n and p

Where p = pressure of a gas

V = Volume of the gas

n = fixed amount of gas

T = constant temperature

(iii) Dalton’s law states that “the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressure of individual gases”.

We know that the pressure exerted by individual gas in the mixture is called partial pressure of that gas.

So, if we write the Dalton’s law mathematically, we get:

p Total = p1 + p2 + p3+...... at constant T, V

Where p1, p2, p3….etc are the partial pressure of gas 1, gas 2, gas 3 ……respectively.

p Total = the total pressure exerted by the mixture of non-reactive gases.

V = Volume of the gas

T = constant temperature

(iv) ) Avogadro law states that “the equal volumes of all gases under the same conditions of temperature and pressure contains equal number of molecules”.

It means 1 L of any two gas at same T and p, will contain same number of moles of that two different gases, irrespective of their molar mass etc.

It can be written mathematically as:

V n at constant T and p

Where V = Volume of the gas

T = constant temperature

n = fixed amount of gas

p = pressure (constant)

(i) – (b)

(ii) – (c)

(iii) – (a)

Plot (i) shows the plot of p vs V, which is nothing but the Boyle’s law plot,

As according to the Boyle’s law:

p1V1 = p2V2 = constant

if we plot the p vs V graph, we observe that the V increase exponentially with the decrease in the pressure.

Plot (ii) again shows the plot of p vs , which is representing the Boyle’s law plot,

As according to the Boyle’s law:

p vs.

Which means if p increases, also increases, and vice versa.

Hence, straight line passing through origin is formed.

(i)

We know that the thermal energy is the kind of energy which is generated due to the motion of atoms or molecules. The motion of molecules tries to keep the molecules away from each other, but the intermolecular forces of attraction is trying to keep the molecules or atoms together.

Hence, we can see the two forces are acting in opposite direction so, there is a need of balance between two forces.

As the different molecules have different strength of intermolecular forces and also different values of the thermal energy as well. Hence, the balance between two forces leads to existence of three states of matter.

(ii)

We know that at constant temperature, pV vs V plot for real gases is not a straight line.

This is because, for pV vs V graph to be straight line, the volume of the gas should be negligible, but it is not possible for the real gases, because they have some volume and hence they show deviation from the straight line.

Now discussing reason,

At high pressure all gases have Z > 1 but at intermediate pressure most gases have Z < 1, this statement is true but it is not the correct explanation of Assertion.

Hence, (ii) is correct option.

(iii)

The Boiling point can be defined as “the temperature at which vapour pressure of a liquid is equal to the external pressure “.

Hence, assertion is true.

Now, the reason, at high altitude atmospheric pressure is high, is found to be false because the pressure decreases as the altitude increases

Hence, (iii) option is correct.

(i)

We know that gases do not liquefy above their critical temperature, even on applying high pressure.

This is because as the temperature reaches above the critical temperature, the speed of the molecule becomes very high due to which the intermolecular attractions is not enough to hold the molecules together and hence they escape because of their high speed.

Now discussing the reason, we observed that the reason is true and is correct explanation of the assertion.

Hence, (i) option is correct.

(i)

We know that at critical temperature the boundary between the liquid and the gas vanishes and as a result of this removal of liquid –gas boundary, the liquid passes into gaseous state imperceptibly and continuously.

As the reason is true and correct explanation of the assertion.

Hence, (i) is correct option.

Liquids tend to reduce the number of molecules or their surface tension at their surface because at the surface there are unbalanced attractive forces at the surface of liquid which tends to pull the molecules back into the bulk liquid leaving the minimum number of molecules on the surface or decreasing the surface tension due to this reason or that’s why small drops have spherical shape. So, A is false and R is true.

(i) CO₂ exists as in the gaseous state between the points ‘a’ and ‘b ’at temperature T₁ because from point ‘a’ to ‘b’ volume starts decreasing and the pressure increases and the gaseous molecules start to come closer but exists in the gaseous state only.

(ii) At the temperature T₁ CO₂ starts liquefying at the point ‘b’. Because at point ‘b’ the liquefication has just started or commences.

(iii) At the temperature T_2, CO₂ will be completely liquefied at the point ‘g’. Because in the curve at the temperature T₂ point ‘f’ to ‘g’ represents the phase where the gas is being converted to liquid and at point ‘g’ all the gas has being converted to liquid.

(iv)As stated in the graph T₃ > T_C > T₂ > T₁. Temperature T₃ > T_C i.e. the critical temperature so condensation will not take place when the temperature is T₃. Because critical temperature is the temperature of a gas above which gas cannot be liquified howsoever high pressure is applied and T₃ is greater than T_C.

(v)At the temperature T₁ curve the equilibrium of liquid and gaseous state of CO₂ is represented between the point’s ‘b’ and ‘c’. Because between the points ‘b’ and ‘c’ the pressure being constant volume of gas decreases till point ‘c’ so between these points CO₂ gas partially exists as in liquid and in gaseous state i.e. existing in equilibrium.

i) Boiling point of liquid A is: 315 K (approx.) and the boiling point of B is: 345 K (approx.)

ii) In the closed vessel the liquid C will not boil because the pressure is kept on increasing in the vessel because the vessel is closed and the vapours generated by heating of liquid C keeps on increasing due to which there is no external atmospheric pressure which is needed to be exceeded to boil off the liquid.

iii) Since at high altitude, atmospheric pressure is low say = 60mm of hg (given) so as according to the graph Temperature corresponding to 60mm of hg = 313 K. So liquid D will boil at 313 K.

iv) At hill stations, the normal atmospheric pressure is less than the pressure at plains or at sea level. Due to this reason it takes longer time to cook food on hill stations. So, with the use of pressure cooker, the pressure of water is increased due to which water boils at even low temperature within a short period of time and the food doesn’t take long time to get cooked.

In a closed vessel, below the critical point, the surface ofseparation between the liquid and its vapour is clearly visible but at the critical point the densities of liquid and the vapours become equal and the boundaries of their separation which existed below the critical point now disappears at the critical point.

The fluid at this stage is called “Supercritical fluid”. These super critical fluids have the efficiency of dissolving the organic substances.

On heating, glass melts and the surface of the surface of the liquid tends to take the rounded shape at the edges which has minimum surface area. The property of liquid responsible for this phenomenon is “Surface Tension” of the liquid due to which the melted glass tends to take the minimum surface area i.e. sphere or spherical shape. This phenomenon is also known as the “fire polishing of the glass”.

Laminar flow is described when all the fluids (gas or liquid) flow in the layers form.

When the liquid flows on the surface the layer of liquid which is in immediate contact with the surface is stationary. The velocity of the subsequent upper layers increases as the distance of the layers increases from the fixed layer which is stationary and in direct contact with the surface.

This type of flow which shows the gradation in the velocity in passing from one layer to another next is called Laminar flow.

Diagram showing the laminar flow of liquids.

In the given figure, we can move from A to F vertically by increasing the temperature, then we can reach the point G by compressing the gas at constant temperature along the isotherm, the pressure will increase. Now, move vertically down towards D by lowering the temperature.

As soon as we will cross the point H on critical isotherm, we get liquid. If the process is carried out at the critical temperature, substance always remain in one phase only. This is known as the continuity of state between the gaseous and liquid state.