Liquid State

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Introduction to Liquid State

The liquids differ from gases in one important aspect, in case of gases, the molecules are far apart from each other so that the volume occupied by the molecules as well as the forces of attraction between them are considered to be negligible, this is not so in case of liquids. In a liquid, the molecules are quite close together so that there are considerable forces of attraction between them and hence they are held together into a definite volume. However, these forces of attraction are not as large as exist between the constituent atoms, ions or molecules of a solid which fix these particles into definite positions so that the solids have a definite volume as well as a definite shape and a perfectly ordered arrangement of their constituent particles. The liquids possess fluidity like gases but incompressibility like solids. As a matter of fact, a liquid state may be considered as an intermediate state between the gas and the solid.
The behaviour of liquids gives some characteristic properties to the liquids such as a definite volume but has no fixed shape, incompressibility, diffusion, fluidity (or viscosity), evaporation (or vapour pressure), surface tension etc.These properties can be explained on the basis of ‘Kinetic molecular theory of liquids’ which is based upon the following postulates:

Postulates of Kinetic Molecular Theory of Liquid 

(i) A liquid is made up of molecules. 

(ii) The molecules of the liquid are quite close together. 

(iii) The intermolecular forces of attraction in a liquid are quite large.

(iv) The molecules of a liquid are in a state of constant rapid motion. 

(v) Absolute temperature of a liquid is directly proportional to the average kinetic energy of its molecules. 

Based upon these postulates, the characteristic properties of the liquids can be explained.

Properties of Liquids

Shape

Liquids possess no definite shape. In whatever container they are kept, they take their shape. This is because the molecules in a liquid are in a state of constant rapid motion.

Volume

Liquids possess a definite volume. Because of strong intermolecular forces of attraction among the liquid molecules, they are not free to move completely. (unlike gas molecules)

Density

Density of liquids is much higher than the density of gases. This is because the molecules in a liquid are quite close together. Thus, the molecules are much more closely packed than those of gases. 

Compressibility

Liquids are very less compressible when compared with gases. This is because the intermolecular distances of separation are much smaller in liquids than in gases.

Diffusion

Liquids diffuse like gases but the diffusion is much slower. This is because the liquid molecules are quite close, they undergo a much larger number of collisions with each other.

Vapour Pressure

Suppose some liquid is placed in an evacuated vessel connected to a manometer as shown in figure no.1. According to kinetic theory of liquids, the molecules of the liquid are constantly moving in different directions with different speeds. Thus, as these molecules are moving with different speeds, they possess different kinetic energies.

Concept of Vapour Pressure of a LiquidFig. No 1 Concept of Vapour Pressure of a Liquid

At any particular temperature, the energy of some of the molecules may be so high that they may overcome the forces of attraction by the neighbouring molecules and may leave the liquid and come in the space above the liquid. This process is called evaporation. As the time passes, more and more molecules of the liquid leave the liquid and come in the space above the liquid. The molecules thus present above the liquid are called vapour. The process in which the molecules move constantly in the vapor phase out of which some of them collide with the surface of the liquid and get recaptured by the liquid. The process is called Condensation

If the liquid is added into the evacuated vessel, then initially, as there are no molecules of the vapour, the rate of condensation is zero. However, if the temperature is kept constant, the evaporation continues at constant rate as shown in figure no. 3, by the straight line plot. However, as the time passes, because of the increase in the rate of condensation number of molecules in the vapour phase also increases.

Time dependence of rate of evaporation and rate of condensation in a closed vessel and attainment of equilibriumFig. No. 2 Time dependence of rate of evaporation and rate of condensation in a closed vessel and attainment of equilibrium

Ultimately, a stage comes when rate of condensation becomes equal to the rate of evaporation, that is, as many molecules re-enter into the liquid as leave the liquid in the same time. This state is called the State of Equilibrium. The pressure exerted by the vapour at this stage (as indicated on the manometer) is called Vapour Pressure or sometimes called Saturated Vapour Pressure as the vapour phase is saturated with vapour at this stage. Hence, 

Vapour pressure of a liquid is the pressure exerted by the vapour present above the liquid when vapour is in equilibrium with the liquid

Results of Process of Evaporation

(i) Cooling caused by Evaporation: When a liquid evaporates, the molecules having high energy leaves the liquid. As a result, the average kinetic energy of the remaining liquid decreases and hence the temperature falls.

(ii) Factors Affecting Vapour Pressure

Two important factors on which the vapour pressure of a liquid depends are:

(a) Nature of the Liquid

The molecules easily leave the liquid and come into the vapour phase when the intermolecular forces of attraction in the liquid are weak and hence the vapour pressure is higher. For example, the vapour pressure of acetone, benzene etc. is higher than that of water at the same temperature 

Vapour pressure–Temperature curves for some liquidsFig. No. 3 Vapour pressure–Temperature curves for some liquids

(b) Effect of Temperature

As the temperature of a liquid is increased, the vapour pressure of the liquid increases. This is evident from each curve in figure no. 3

Maxwell’s distribution of energies gives successful explanation about the increase of vapour pressure with increase in temperature. All the molecules do not have the same energy ( at a particular temperature). A plot of the fractions of molecules versus their corresponding kinetic energies is as shown in figure no. 4.

Maxwell’s Energy Distribution CurveFig. No. 4 Maxwell’s Energy Distribution Curve

The increase of vapour pressure with increase in temperature can be explained on the basis of Maxwell’s distribution of energies. At particular temperature all the molecules do not have same energies. Figure no. 4 shows plot of fraction of molecules vs kinetic energy. Only those molecules can escape from liquid into the vapour phase whose kinetic energy is more than Ea as shown in the figure no. 4. With increase in temperature, the curve shifts as shown. The fraction of molecules with kinetic energy greater than E increases ( areas under the curves on right hand side). As a result the molecules escaping into the vapour phase increases and so does the vapour pressure.

(iii) Boiling Point

As stated above, the increase in temperature would increase the vapour pressure of a liquid. The vapour escaping are only from the surface of the liquid. If we still increase the temperature the vapour pressure will be same as atmospheric pressure. And the vapour in the form of bubbles from below the surface start rising to the surface and escape into the air, if the temperature is further increased. The temperature at which this happens is called the boiling point. Thus, 

Thus the temperature at which the vapour pressure of the liquid becomes equal to the external pressure is defined as Boiling point of a liquid (that is, the atmospheric pressure).

The normal boiling point is a boiling point at which the external pressure becomes equal to normal atmospheric pressure (that is, 760 mm).

When the external pressure is equal to 1 bar, the boiling point is called Standard Boiling Point of the Liquid.

Standard boiling point of a liquid is slightly less than the normal boiling point because 1 bar is slightly less than 1 atm pressure (1 atm = 101325 Pa, 1 bar = 105 Pa). For Example, standard boiling point will be 996° (372.6 K) when normal boiling point of water is 100°C (373 K). The normal boiling point for any liquid is obtained from the vapour pressure-temperature curves, as shown in figure no. 3.

(iv) Heat of Vaporization (∆Hv)

When the liquid starts boiling, if extra heat is supplied to the liquid, it is used up not in increasing the temperature of the liquid but to overcome the intermolecular forces of attraction, existing in the liquid and thus changing the liquid into vapour. Hence, the temperature remains constant till whole of the liquid changes into vapour. 

The heat of vaporization of the liquid is defined as the amount of heat required to change 1 mole of the liquid into its vapour at the boiling point.

Greater the intermolecular forces of attraction present in a liquid, greater is the heat of vaporisation and higher is the boiling point. For Example, the heat of vaporisation and boiling point of water are more than those of ether, acetone, benzene etc.
One thing should be kept in mind that boiling does not occur when a liquid is heated in a closed vessel. On heating more and more vapours are formed. Hence, vapour pressure increases continuously. But the boundary between the liquid and the vapour remains visible because liquid is more dense than the vapour. As heating is continued density of vapour keeps on increasing but density of liquid keeps on decreasing because liquid expands and the molecules move apart. Ultimately, a temperature is reached where the density of the vapour and the liquid becomes equal and the boundary of separation between the liquid and the vapour disappears. This is called critical temperature.

Surface Tension

Surface tension is a characteristic property of liquids which arises because the molecules of the liquid at the surface are at different situation than those in the interior of the liquid. For Example, a molecule is attracted equally in all directions as it is surrounded by other molecules and shown in figure no. 5 

Surface Tension of a LiquidFig. No. 5 Surface Tension of a Liquid

Hence, the net force of attraction acting on the molecule is zero. However, the molecule lying at the surface experience greater force of attraction by the molecules lying in the bulk of the liquid when compared with the molecules lying above it in the vapour phase. Thus, a net inward attraction is experienced by the molecule lying at the surface. As a result of this inward pull on all molecules lying at the surface, the surface behaves as if it were under tension (like a stretched membrane). Due to this property of liquids, a net inward attraction is experienced by the surface. That is why this property of liquids is called Surface Tension. Hence, 

Surface tension of a liquid is defined as the force acting at right angles to the surface along one centimeter length of the surface.

Thus, the units of surface tension are dynes per cm (or Newton per meter, that is, N m-1 in the S.I system)
Further, the surface of the liquid is bound to contract to the smallest possible area for a given volume of the liquid because of the inward pull on the molecules at the surface,. This gives the lowest energy state of the liquid. It is for this reason that the drops of a liquid are spherical because for a given volume, a sphere has minimum surface area.

Work has to be done against the inward pull to increase the area of the surface. For Example, consider a soap solution film contained rectangular wire frame ADCB in which the side BC is movable (figure no.6). In order to extend the surface area of the film, the movable wire has to be pulled from position BC to position B’C’. Thus, some work has to be done against the force of surface tension. 

The work in ergs required to be done to increase or extend the surface area by 1 sq. cm is called surface energy.

The units of surface energy are, therefore, ergs per sq. cm (or joules per sq. meter, that is, J m-2 in S.1. system). 

In terms of dimensions,

Surface Energy = Work per sq. cm.

= (Force × length) per sq. cm. 

These units are the same as those of surface tension. Thus, the surface energy is same thing as surface tension. Hence, the definition of surface energy is sometimes taken as the definition of surface tension.

Concept of surface energyFig. No. 6 Concept of surface energy 

Rise of a Liquid in a Capillary tube

Suppose one end of a capillary tube is put into a liquid that wets glass. We observe that upto a certain height the liquid rises into the capillary tube. The liquid inside the capillary tube experiences a push because of inward pull of surface tension. This is the reason for rise of oil into the wick of an oil lamp or water below the surface of the earth rises in the plants through the roots or ink rises in a blotting paper,

It may be mentioned here that in case of liquids which do not wet glass, For Example, mercury, the level inside the capillary falls below the level outside (figure no. 7) Further, whereas the upper surface of a liquid that wets glass is concave, that of mercury is convex.

(a) Water rise in Capillary (b) Mercury level falls in capillaryFig. No. 7 (a) Water rise in Capillary (b) Mercury level falls in capillary

Such a curved surface of a liquid is known as Meniscus. The concave meniscus of water and m. convex meniscus of mercury in a glass tube may be explained on the basis of ‘cohesive’ and ‘adhesive’ forces. The attractive forces existing between the molecules of the same substance are known as cohesive (ones, For Example, between the molecules of water or molecules of mercury etc. whereas those existing between the molecules of different substances are known as adhesive forces, For Example, between water and glass or mercury and glass etc. In case of water taken in a glass tube, adhesive forces are stronger than cohesive forces whereas it is reverse for mercury taken in a glass tube.

Viscosity

We know that all liquids do not possess the same speed at time of flowing. Some liquids like water, ether etc. very fast while some liquids like castor oil, glycerin flow slowly. This indicates that every liquid has some resistance to flow.

The internal resistance to flow possessed by a liquid is called its Viscosity.

The liquids which flow slowly, have high internal resistance which is due to strong intermolecular forces and, therefore, are said to be more viscous or are said to have high viscosity. On the other hand, the liquids which flow rapidly have low internal resistance which is due to weak intermolecular forces and hence are said to be less viscous or are said to have low viscosity.

To understand the nature of the internal resistance or friction existing within a liquid, consider a liquid flowing through a narrow tube figure no. 8 b

Flow through a Narrow tubeFig. No. 8 Flow through a Narrow tube

All parts of the liquid do not move through the tube with the same velocity. Imagine the liquid to be made up of a large number of thin cylindrical coaxial layers. The layer which is more closer with the walls of the tube is almost stationary. As we move from the walls towards the centre of the tube, the velocity of the cylindrical layers keeps on increasing till it is maximum at the centre. This type of flow in which there is a regular gradation of velocity in going from one layer to the next is called laminar Flow. Conversely, we may say that as we move from the centre towards the walls, the velocity of the layers keeps on decreasing. In other words, there exists some resistance or friction to the layer immediately below it.

Viscosity is the force of friction which one part of the liquid offers to another part of the liquid.
The flow of a liquid on a fixed horizontal surface may be represented in a similar manner as show in figure no. 9
 Flow through a narrow tube

Fig. No. 9 Flow through a narrow tube

It has been found that the force of friction (f) between two layers each having area ‘A’ sq. cm separated by a distance dx cm, and having a velocity dv cm/sec difference of dv cm/sec, 

where n is a constant known as coefficient of viscosity. dv/dx is called velocity gradient.

If dx = 1 cm, A = 1 sq. cm and dv = 1cm/sec,

Then, f = n

Hence,

Coefficient of viscosity may be defined as the force of friction (in dynes) required to maintain a velocity difference of 1 cm/sec between two parallel layers, 1 cm apart and each having an area of 1 sq. cm.

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