UNIT IB. �LIQUID STATE

US03 CCHE22

Syllabus

• Vapor Pressure and determination
• Surface tension and determination
• Viscosity and determination

Vapor pressure

The Physical properties of liquid states is studies in this unit. The quality of liquid state is characterize by means of physical properties of liquids. These physical properties are density, surface Tension , viscosity and vapor pressure etc.

Vapor pressure: (π): [Boiling of liquids]

Liquid state is physically equilibrium with its saturated vapor phase.

Vapor Pressure

Naturally, we know, the pressure is variables of gaseous state.

When liquid is boiled, the vapor phase molecular species exerts the pressure on surface of liquid is called vapor pressure.

We are know, at definite temperature water is evaporate in open vassal, pressure of vapor phase molecular system is measure by technique shown in fig.

Difference of atm. pressure and � vapor pressure

When liquid is heating at high temperature the vapor pressure is equal to atmosphere pressure of system, this temperature is called boiling point of liquid.

Boiling point is characteristic of all liquids. Practically, quality of liquid is determine in terms of boiling point of liquids.

Boiling point of H₂O is 100 ^oC, Boiling point of Benzene is 80^oC .

What is vapor pressure ? explain the � method of vapor pressure measurement.

• At constant temperature, pressure on vapor phase of liquid is equilibrium with surface particles of liquid is called vapor pressure.
• vapor pressure is property which describe the escape tendency or volatility of liquid component. The vapor pressure is increase with increase temp.

vapor pressure measurement � Isoteniscopic Method

• The Vapor pressure of liquid is measure by Isoteniscopic method. The method is given by Smith and Manzies.

Process:

• It is consist of bulb A about 2 cm diameter which connected with a U-tube B. this is limb with about 3.5 cm long. The longer end of U tube is fill up with mercury manometer, to a large assembly D. this is joined with suction pump or to air.
• The bulb A is more than half is filled with liquid sample under examination. This liquid is also filled into U-tube B so as to fill its lower portion, as shown in fig.

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Process

• The Isoteniscopic AB Contain the liquid is filled in suitable bath. The inside pressure is reduced by suction pump. Then the temp of bath is raised to boil the liquid at reduced pressure.
• In this way the air within A is replaced completely by a vapor of liquid. The pressure is so adjusted by admit air in D that the liquid stand at the similar level in the two limbs of the u-tube B.

vapor Pressure(π)

At this stage

The vapor pressure of the liquid

vapor in Bulb A = (The Barometric pressure ) _ (the height of

Mercury level in Manometer)

Vapor Pressure

SURFACE TENSION

• The existence of strong intermolecular forces of attraction on liquids surface is another important property known as Surface tension.
• e.g. Meniscus Shape of liquid in U Tube, Lowest surface area of dropped are example of force acting upon it.
• Consider a molecule P which is in the interior of a liquid. This molecule is attracted equally in all directions by the molecules around it. Thus , the effect is cancelled.
• Consider another molecule R near the surface.

SURFACE TENSION

SURFACE TENSION

• It is attracted sideways and toward the interior. The forces on the sides being counter balanced. The downward attractive forces are greater than the upward forces.
• This because there are more molecules of the liquid below than in the air above the surface. These attractive forces acting downward tend to draw the surface molecules into the body of the liquid. Due to this, surface will be reduced to a minimum.

SURFACE TENSION

• It is known that forces of attraction tend to decrease the energy of a system. In above case the attractive forces are more predominant in the bulk of the liquid than at the surface.
• Therefore the molecules in the bulk of liquid possess lower energy than those at the surface.
• In other words the molecules at the surface possess greater energy than those in the bulk.

SURFACE TENSION

• The molecules tend to move from a state of high energy to a state of lower energy. Thus, molecules move into the bulk from surface.
• Because of this movement, the number of molecules at the surface becomes less than that in the bulk.
• Therefore, the distance between any two molecules at the surface becomes greater than that in the bulk.

SURFACE TENSION

• Consequently, the surface molecules tend to move closer to one another in order to acquire a normal distance between them as before.
• Due to this reason drops of a liquid or bubbles of a gas are spherical in shape. A sphere has minimum surface for a given volume.
• Due to this tendency to contract, surface of a liquid behaves as if it were in a state of tension.

SURFACE TENSION

• The force that tend to contract the surface of liquid is known as surface tension.
• Surface tension is defined as the force in dynes acting at right angles to the surface of a liquid along one centimetre length of the surface.
• Its symbol is γ (gamma) and expressed in dynes cm^-1 in SI system , the unit of surface tension is Newton per meter (Nm^-1).
• 1 newton = 10⁵ dynes

EFFECT OF TEMPERATURE ON SURFACE TENSION

• We know that molecular kinetic energy is proportional to absolute temperature. As temperature of liquid increases, energy of its molecules increases.
• As energy of molecules increases, the intermolecular forces of attraction decreases. Hence, surface tension of liquid decreases with rise in temperature.

EFFECT OF TEMPERATURE ON SURFACE TENSION

• At critical temperature, the surface of separation between in a liquid and its vapour disappears and the surface tension falls to zero.
• Eaves found that surface tension varies linearly with temperature. He suggested the following expression for the variation of surface tension with temperature :

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EFFECT OF TEMPERATURE ON SURFACE TENSION

• γ (Mm/§) ^2/3 = a – Kt (1)

Where Mm is molar mass, § is density and γ is surface tension at temperature ‘t’, ’a’ and ‘k’ are constants.

• At the critical temperature (i.e., when t = tc),the surface tension is zero. Thus, equation (1) becomes
• 0 = a – K.tc
• Therefore, a = K.tc (2)

EFFECT OF TEMPERATURE ON SURFACE TENSION

Substituting equation (1) in equation (2)

• γ (Mm/§) ^2/3 = K(tc – t) (3)

This equation is satisfactory for number of liquids over a wide range of temperature.

• Surface tension vanishes roughly 6 ⁰ C above the critical temperature. Therefore , Ramsey and shields gave the following equation for the temperature dependence of surface tension :
• γ (Mm/§) ^2/3 = K(tc – t - 6)…. (4)

MEASUREMENT � OF SURFACE TENSION

• There are number of methods for the determine surface tension of liquid, Two of them are described below .
• (1) The capillary – rise method :
• This method is based on the rise of a liquid in a capillary tube. Put a capillary tube of radius r vertically into a liquid. The contact angle between the glass and liquid (e.g. water) is now zero.

MEASUREMENT � OF SURFACE TENSION

• Capillary rise Method

MEASUREMENT OF SURFACE TENSION

• Depending upon surface tension and density the liquid will rise instantaneously up to a certain height h. Liquid in the capillary is supported by force of surface tension.
• Suppose, density of liquid is §, radius of a capillary is r , height of liquid in capillary is h , the force of surface tension in dynes per cm is γ.

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MEASUREMENT OF SURFACE � TENSION

• Then , the total force due to surface tension , raising the liquid column upward

= γ x inside circumference of the capillary

= 2 πr γ dynes.

Force of gravity pulling the liquid downward

= weight of the liquid column.

• Weight of the liquid in the column = V.§.g dynes,

where V is the volume of the liquid in the tube .

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MEASUREMENT OF SURFACE TENSION

Since V = πr²h

For equilibrium , upward force = downward force

2 πrγ = πr²h§g

Therefore

γ = r.h.§.g / 2 dynes / cm (5)

• Thus , for measuring surface tension , we have to measure the height (h) and radius of the capillary tube in centimetres. The height is measured by a cathetometer and the radius of the capillary tube by a travelling microscope.

MEASUREMENT OF SURFACE � TENSION

• In deriving above equation it is assumed that the contact angle θ between the glass and the liquid is zero. θ is zero means wetting is perfect. If the angle is not zero, the vertical component of the upward force is 2 πrγ cosθ and hence,

γ = r.h.§.g / 2 cosθ ....... (6)

SURFACE � TENSION

We know that , when a capillary is dipped in mercury , mercury does not rise in it, on the contrary , the upper level of mercury in the capillary is lower than the surface of the free liquid as shown in figure.

This is because the contact angle θ is 180⁰ therefore cos180⁰ = -1 and according to equation (6) , h would be negative.

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MEASUREMENT � Of SURFACE TENSION

• Surface tension

MEASUREMENT � OF SURFACE TENSION

• The rise or fall of a liquid in a capillary can be understood by the concept of cohesion and adhesion.
• Cohesion means intermolecular attraction between like molecules in the liquid and adhesion means attraction between the liquid and the walls of the capillary.
• When adhesion is greater than cohesion , the liquid wets the wall and rises in the capillary.

MEASUREMENT � OF SURFACE TENSION

As for example water , chloroform , ethyl alcohol etc.

If cohesion is greater than adhesion , the liquid is depressed in the capillary.

Thus , when a drop of mercury is put on a glass surface it becomes spherical but if we put water on the surface it spreads on the surface.

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MEASUREMENT � OF SURFACE TENSION

• (2) Double capillary rise method :
• To determine the surface tension of a liquid using this method , the difference in heights to which the liquid rises in the two capillaries of different radius is measured.
• The surface tension for capillary of radius r1,
• γ = ½ h1 § g r1 … (7)
• While for capillary of radius r2,

Double Capillary Method

MEASUREMENT � OF SURFACE TENSION

γ = ½ h2 § g r2 (8)

If r1 < r2 then h1 > h2 , and h = 2 γ/ § g r

Hence ,

h1 = 2 γ/ § g r1 (9)

And

h2 = 2 γ/ § g r2 (10)

• Therefore ,

Δh= h1 – h2

• = 2 γ/ § g r1 - 2 γ/ § g r2

Δh = 2 γ/ § g (1/r1 – 1/r2) (11)

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MEASUREMENT OF � SURFACE TENSION

• γ = Δh§g / 2 (r1 r2 / r2 – r1)…. (12)

Thus , if we know Δh,r1 and r2 then surface tension (γ) can be calculated.

VISCOSITY

• The flow is characteristic property of liquids. Viscosity means the resistance of a liquid to flow.
• Consider a liquid flowing through a narrow glass tube. The flow the liquid molecules can be analyzed in terms of molecular laminar layers arranged one over another.
• A laminar layer has negligible thickness.

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VISCOSITY

VISCOSITY

• The layer which is in contact with surface of the inner wall of the tube is stationary. The velocity of the successive layers increases as we move away from the surface.
• As a result, a velocity gradient is set up along z-axis . If the distance between the two layers is ‘r’ a velocity v + r(dv/dz).
• When a molecule moves from the faster layer to the slower layer, it gives momentum to the slower layer thereby speeding it up.

VISCOSITY

• When a molecule moves from the slower layer to the faster layer, it retards the faster layer.
• In this way , there arises a frictional force between two layers which gives rise to viscosity.
• Viscosity is defined as the resistance that one part of a liquid flowing with one velocity offers to another part of the liquid flowing with a different velocity.

VISCOSITY

• Thus , viscosity is the force of friction between two layers of a liquid moving with different velocities.
• To maintain the velocity gradient, we must apply an external force along y-axis. This force is proportional to the area and the velocity gradient, that is
• Fα A(dv/dz)
• Therefore ,
• F = -ηAdv/dz ..... (13)

VISCOSITY

• Where, η (Greek letter eta) is the proportionality constant. It is known as coefficient of viscosity .
• The minus sign shows that the viscous force on the faster layer is in the opposite direction to its motion.
• The equation (13) is Newton’s law of viscosity. The liquids which obey equation (13) is called lamina or streamlined flow.

VISCOSITY

Liquids which do not obey equation (13) are

called non – Newtonian liquids.

The reciprocal of viscosity is called fluidity φ. Thus , φ

= 1 / η

Units of viscosity in c.g.s. system :

From Eq. (13)

η = F/A(dz/dv)

If F is measured in dynes , dz in cm , A in cm² and dv in cm sec^-1 , then the units of η are

dynes * cm / cm^{2 *} cm sec^-1 = dynes cm^-2 sec.

VISCOSITY

• For simplicity, the units of viscosity, dynes sec. cm^- are called poises. Still more convenient units of viscosity are centipoises and mill poises (one mill poises = 0.001 poise and 1 centipoises = 0.01 poise).
• Units of viscosity in SI system:
• If F is measured in Newton's, dz in metres , A in square metres and dv in metres sec^-1 , then, we get the coefficient of viscosity in units of kg m^-1 s^-1 , as illustrated below:

VISCOSITY

η = F/AdZ/dv = kg m s^-2 m / m² m s^-1

= kg m^-1 s^-1

It can be easily shown that 1 poise=10^-1 kg m^-1 s^-1

1 poise = 1 dynes cm^-2 s

= 1 g cm s^-2 * cm^-2 s

= 1 g cm^-1 s^-1

= (1 x 10^-3 kg)(1 x 10^-2 m) ^-1 (s^-1)

= 10^-3 x 10² kg m^-1 s^-1

= 10^-1 kg m^-1 s^-1

DETERMINATION OF VISCOSITY

• The Ostwald’s viscometer method :
• This method is based on poiseuille’s law. This law relates rate o flow and coefficient of viscosity of a liquid by the following equation:
• η = πr⁴ tP/ 8Vl… (14)
• Where V is the volume in ml of the liquid flowing in t seconds through a narrow tube of radius r cm and length l cm under a hydrostatic pressure of P dynes per square centimeter and η is the coefficient of viscosity in poises.

DEteRMINATION OF VISCOSITY

• Hydrostatic pressure P of a liquid column is
• P = hρg
• Where h is the height of the column and § is the density of the liquid. Poiseuille’s equation becomes.
• η = πr⁴ t hρg / 8Vl… (15)
• The experimental measurement of P,r,l and V offers considerable difficulty. Therefore it is not possible to find the absolute coefficient of viscosity (η) straight way from poiseuille’s equation.

DETERMINATION OF VISCOSITY

• Ordinarily , the viscosity of a liquid is determined with respect to that of water. This is known as relative viscosity.
• In order to determine relative viscosity of liquid , the times of flow for equal volumes of water and the liquid under examination is measured through the same capillary.
• If t1 and t2 are the times of flow of the same volume of water and the liquid and η1 and η2 are their respective coefficients of viscosity, then

DETERMINATION OF VISCOSITY

• η1/ η2 =(πr⁴ t1 hρ1g / 8Vl) x (8Vl / πr⁴t2hρ2g)
• Where ρ1 and ρ2 are the densities of water and the liquid respectively,
• The value of h is the same in both cases due to equal volumes of water and liquid , therefore,
• η1/ η2 = ρ1 t1 / ρ2 t2 ..... (16)
• The Ostwald’s viscometer as shown in figure is used to measure viscosity by this method.

DETERMINATION OF VISCOSITY

• Ostwaal Viscometer

DETERMINATION OF VISCOSITY

• It is first cleaned with chromic acid and then dried. Bulb B is filled with known volume of water, the water is sucked into the bulb A with the help of a rubber tube at the end C till it rises to the mark M.
• The time taken by water to flow through two marks is noted by stop watch. Suppose this is time t1.

DETERMINATION OF VISCOSITY

• The viscometer is dried and the same volume of the liquid under examination is taken into the bulb B and the process is repeated.
• Let the time of flow be t2. thus knowing η1,§1, §2, we can calculate η2 for any liquid using equation (16)

EFFECT OF TEMPERATURE ON VISCOSITY

• The ‘Hole’ Theory :
• The viscosity of liquid decreases with increase in temperature. This can be explained by hole theory.
• According to this theory, there are vacancies or holes in a liquid. The liquid molecules keep on moving continuously into these holes. Thus, holes also moves.

EFFECT OF TEMPERATURE ON VISCOSITY

• This process requires energy. Therefore, a liquid molecule requires some activation energy to move into a ‘hole’.
• As the activation energy becomes increasingly available at increasing temperature of viscosity decreases with increase in temperature.
• The relationship between η and temperature is

η = A e ^Ea/RT …. (17)

EFFECT OF TEMPERATURE ON VISCOSITY

• Where A and Ea are constants for a given liquid. Ea is called the activation energy.
• In contrast to liquids , in case of gases , η increase in temperature.

THE REYNOLD’S NUMBER

The flow of a fluid through a pipe of radius ‘r’ is given by a number called Reynolds number Nr

Nr = 2 rνρ/η.... (18)

• Where v is the average bulk velocity of the fluid , ρ is the density and η the coefficient of viscosity.
• If Nr is greater than 4000, the flow is turbulent and if it is less than 2100, the flow is laminar.

THE REYNOLD’S NUMBER

• In a laminar flow , a velocity is given by
• v = ΔP(R² – r²)/4ηl.... (19)
• Where P is the pressure drop over a length l and r is the distance from the axis of the pipe of radius R.
• The volume of liquid flowing in time t through a pipe of radius R is given by
• V = πR⁴ (ΔP)t/8ηl... (20)

Cal.

Ex:

Assignment Que.

MCQ

(1)……… Method is used to determine the vapor of

liquids

(a) Ostwald method (b) Capillary method

(c) Isoteniscopic method (d) Drop number method

(2) Which of the following is physical property of liquid ? �(a) M.W (b) Vapor Pressure (c) Enthalpy (d) M.P

MCQ

(3) Surface tension is determine by ……… method’

(a) Ostwald method (b) Capillary method

(c) Isoteniscopic method (d) Gravimetric

(4) Viscosity is …….. Force of fluid

(a) Supportive (b) elastic (c) opposite (d) none

(5) The unit of surface tension is……..

(a) dynes (b) dynes/cm (c) Newton (d) cm/s

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S.Q

(1) Give the method to determination of vapor

pressure

(2) Define the following terms

(i) vapor pressure (ii) surface tension

(iii) viscosity

(3) Give the c.g.s and m.k.s unit of surface tension

(4) Give the unit of Viscosity

LQ

(1) What is vapor pressure? explain the method to determination of vapor pressure of liquids

(2) Give the definition of surface tension and explain any method to determination of surface tension.

(3) What is viscosity ? Describe the method to determination of viscosity.