# Liquid State-Bsc I

## Liquid State-Bsc I

Vapour Pressure

The pressure exerted by the vapour in equilibrium with the liquid at fixed temperature is known as vapour pressure of liquid at that temperature.

Factors affecting vapour pressure

1. Temperature
Vapour pressure of a liquid increases with increase in temperature. The rate of evaporation increases , the concentration of particles in vapour stage increases resulting increase in vapour pressure.
2. Nature of liquid
Vapour pressure of liquid increases with decrease in inter molecular forces between liquid molecules.
Ether >alcohol > water
3. Presence of impurities
The non volatile impurities decreases exposed surface area of liquid for evaporation . Thus, it leads to decrease in vapour pressure.

Surface Tension

Surface tension can be defined as the force that acts at right angles to an imaginary line of unit length at the surface of the liquid at rest. It’s SI unit is Newton per meter and dynes per centimeter in CGS system.

Surface Tension of liquid changes with change in temperature. When temperature increases K.E of molecules also increases resulting decrease in inter molecular forces and thus decrease in the inward pull acting on the surface of liquid. Hence, surface tension decreases with increase in temperature.

Uses of Surface Tension

1. Cleansing action of soap and detergents is due to lowering the surface tension between water and greeze.
2. Efficiency of tooth paste and mouth wash is based on the lowering the surface tension.

Determination of Surface Tension

1. By Capillary Rise Method

Let us consider a capillary tube of radius ‘r’ is dipped into a liquid of density $$\rho$$. If ‘h’ is the height of capillary rise forming concave meniscus and \gamma be the surface tension acting along the inner circumference of the tube that exactly supports the weight of liquid column,

Upward force due to surface tension,
Upward force = inner circumference of the liquid $$\times$$
vertical component of surface tension

= $$2 \pi r \gamma cos \theta$$

Also, Downward force due to weight = mass $$\times$$  acc. due to gravity
=density of liquid
$$\times$$ volume $$\times$$ acc. due to gravity
= $$\rho \pi r^{2} h$$

At equilibrium ,
Upward force = Downward force

or, $$2 \pi r \gamma cos \theta = \rho \pi r^{2} h g$$

or, $$\gamma = \frac{r h \rho g}{2 cos \theta}$$

1. By Drop Weight Method

When a liquid is allowed to drop through a tube having a capillary at it’s end, the drop is supported by the upward force of surface tension acting at the outer circumference of the tube. The weight of the drop (mg) pulls it downward.
i.e
mg=2πrγ
where, m=mass of the drop
g=acc. due to gravity
r= outer radius of the tube

γ = surface tension

About 20 drops of the given liquid is received from the drop pipette , weight of one drop of liquid is determined. Simlarly, the weight of one drop reference liquid is measured.

Then we know that,
$$m_1 g = 2 \pi r \gamma_{1}$$……..(1)
$$m_2 g = 2 \pi r \gamma_{2}$$……..(2)
Dividing equation (1) by (2) we get,

$$\frac{\gamma}{\gamma}$$
Hence, surface tension of liquid can be determined by taking value of reference liquid.

Viscosity and Coefficient of Viscosity

Viscosity of a liquid is the resistance experienced by a liquid during it’s flow. It is also kind of internal friction of a liquid. Liquid having high viscosity flows slow (eg: glycerine , oil etc. ) and liquid having less viscosity flows rapidly (eg : water, alcohol etc.)
The viscous force F is given by,
F =
\eta AηA \frac{dv}{dx}dxdv
where, \eta = coeff. of viscosity
dv= difference of velocity between two layers
dx= distance of separation of two layers

When A = 1cm^{2} V= 1 cm/sec and x= 1cm ,
F = \eta
A=1cm2V=1cm/secandx=1cm,<br>F=η
Hence, coefficient of viscosity can be defined as the force of resistance per unit area required to maintain a unit difference of velocity between two parallel liquid layers seperated by unit length apart.

Determination of Coeff. of Viscosity using Ostwald Viscometer

Ostwald viscometer is based on Poiseuille Law. According to this, the volume ‘V’ of a liquid which flows through a narrow tube of a radius ‘r’ and length ‘l’ under the pressure P at any instant ,
V=
\frac{\pi r^{4} P t}{8 \eta l}8ηlπr4Pt
or, \etaη =\frac{8 V l} {\pi r^{4} P t}πr4Pt8Vl…………(1)

For two different liquids,
Let ,
t_{1}t1 and t_{2}t2 be the time of flow of a fixed volume V through the same capillary tube then expression for relative viscosity( \eta_{1} / \eta_{2}η1/η2) is determined as:

\frac{\eta_{1}}{\eta_{2}} = \frac{\pi P_{1} r^{4} t_{1}}{8lV} \times \frac{8lV}{\pi P_{2} r^{4} t_{2}}η2η1​​=8lVπP1r4t1​​×πP2r4t28lV
\frac{P_{1} t_{1}}{P_{2} t_{2}}P2t2P1t1​​
Since pressure is directly proportional to density of liquid,
\frac{\eta_{1}}{\eta_{2}} = \frac{d_{1} t_{1}}{d_{2} t_{2}}η2η1​​=d2t2d1t1​​
Hence , coefficient of viscosity of a liquid can be determined using the value of reference liquid.