# Liquid State Notes

## Trouton's Rule:

The entropy of vaporization of most of the liquids at their boiling points is almost the same and has the value between 85-88 J.mol^{-1}K^{-1}. Trouton's rule holds good for liquids in which hydrogen bonding is absent.

### Trouton's Rule Download pdf

### Which of the following molecules does not follow Trouton's rule

A. C_{6}H_{6}

B. C_{6}H_{12}

C. CCl_{4}*D. NH _{3}*

### The liquid that deviates from the Trouton’s rule is

A. Hydrochloric acid

B. Sulphuric acid

C. Phosphoric acid*D. Acetic acid*

## Molar Volume:

Molar volume of any substance is the volume occupied by one mole of the substance. This is easily determined by dividing the molecular mass by the density of the compound (i.e V=M/D). According to Avogadro's hypothesis, the molar volume of all gases at S.T.P. is 22.4L.

It is the volume so expressed in ml. or c.c.. If molecular weight and density of a substance are known, molar volume can easily be calculated.

## Kopp's Rule:

Kopp in 1842 state that the molar volume of a liquid at its boiling point is equal to the sum of the atomic volume of its constituent atoms. This is known as Kopp’s rule.

According to Kopp's rule it has been found that the molar volumes of two members of a homologous series of organic liquids differ by about 22 mL, for each CH_{2} group Kopp calculated the volume equivalent of each element by a simple arithmetic means.

## Parachor:

Macleod in 1923 gave the following relation between the surface tension (γ) and density (D) for a normal liquid-

C=γ^{1/4}/(D −d)

where d is vapour density of the liquid at given temperature and C is constant.

In 1924, Sugden modified the above equation as-

γ^{1/4}/(D −d)=MC=P

where M is the molecular weight of the liquid and P is the parachor.

At ordinary temperature, d is very small in comparision to D then-

M γ^{1/4}/D=P

If γ=1 at a particular temperature, then-

M/D=P

Thus, at a particular temperature, the molar volume of a liquid having surface tension unity is called **Parachor**.

If two liquids having the same surface tension are taken whose molecular weights are M_{1} and M_{2} and their densities are D_{1} and D_{2} respectively, then-

M_{1} γ^{1/4}/D_{1}=P_{1}

and

M_{2} γ^{1/4}/D_{2}=P_{2}

P_{1}/P_{2}=(M_{1}/D_{1})/ (M_{2}/D_{2})

So, the ratio of parachors of two liquids having the same surface tension is equal to the ratio of molar volumes. Parachor is both an additive and constitutive property.

### Parachor Value of some Elements and Groups:

Element | P Value | Group | P Value |
---|---|---|---|

C | 8.6 | C=O | 44.4 |

H | 15.7 | OH | 30.2 |

N | 12.5 | COOH | 73.7 |

O | 19.8 | NO_{2} | 73.8 |

Cl | 55.2 | Double Bond | 19.9 |

Br | 68.8 | Triple Bond | 40.6 |

I | 90.3 | Six Membered Ring | 1.4 |

## Application of Parachor:

Parachor data are used to determine the structure of molecules and the nature of bonds.

Example:

Two structure proposed for QUINONE-

**Structure-1**

6C=6 X 8.6=51.6

4H=4 X 15.7=62.8

2O=2 X 19.8=39.6

Four double bonds=4 X 19.9=79.6

one 6 membered ring=1 X 1.4=1.4

So, Calculated Parachor=235 **Structure-2**

6C=6 X 8.6=51.6

4H=4 X 15.7=62.8

2O=2 X 19.8=39.6

Three double bonds=3 X 19.9=59.7

Two 6 membered ring=2 X 1.4=2.8

So, Calculated Parachor=216.5

Since the experimental Parachor is 236.8. Hence structure-1 is correct for QUINONE.

## Rheochor:

It was introduced by Newton Friend in 1943. Rheochor is a constant obtained by multiplying molar volume and eighth root of the co-efficient of viscosity. It is denoted by letter Capital 'R'.

R=( M/D ) X η^{1/8}

If η=1 then-

M/D=R

So, we can say that Rheochor is the molar volume of the liquid at the temperature at which its viscosity is unity. Like Parachor, Rheochor is both additive and constitutive. However it has not proved of much use in solving structural problems.

## Surface Tension

Surface tension is a property of liquid which arises due to the different situation of the liquid molecules on the surface and in the bulk of the liquid.

A molecule lying inside (bulk) the liquid is surrounded by other molecules and so is attracted equally in all directions. Thus, the resultant force of attraction acting on the molecule is zero.

However, A molecule lying at the surface of liquid is attracted by liquid molecules from the bulk of the liquid and feel inward pull. As a result of this inward pull on all molecules lying at the surface, the surface behave as if it were under tension and the surface of the liquid tends to the smallest possible area for a given volume of the liquid. This gives the lowest energy state of the liquid.

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

unit of surface tension is dyne per centimetre or Newton per metre.

Surface tension is a property that arises due to the intermolecular forces of attraction among the liquid molecules. Greater the intermolecular force of attraction, higher is the surface tension of the liquid.

Surface tension of liquid generally decreases with increase of temperature and becomes zero at the critical temperature. Surface tension decreases with increase in temperature is due to on increasing the temperature, the kinetic energy of the molecules increases ,and, therefore the intermolecular attraction decreases.

## Surface Energy

The work in ergs required to be done to increase or extend the surface area by one square centimeter is called surface energy.

The unit of surface energy is ergs per square centimeter or joules per square meter.

## What is the Effect of Temperature on Surface Tension ?

The surface tension of liquid is generally decreases with increase of temperature and becomes zero at critical temperature. The decrease in surface tension with increase of temperature is due to the fact that with increase of temperature, the kinetic energy of the molecules increases and hence intermolecular attraction decreases.

## Viscosity

Viscosity is a property of liquid which resist to flow. Due to viscosity some liquid flow slowly and some liquid flow quickly. Viscosity is nothing but internal reistance to flow possessed by liquid.

Liquids which flow slowly, have high internal resistance which is due to strong intermolecular forces says more viscous or are of high viscosity.

However, Liquids which flow rapidly have low internal resistance which is due to weak intermolecular forces says less viscous or are of low viscosity.

Greater are the intermolecular forces, higher is the viscosity of the liquid. Viscosity decreases with increasing the temperature. Kinetic energy increases on increasing temperature and so intermolecular force of attraction decreases, consequently, viscosity decreases and liquid flow quickly.

We know that liquid flow in layers in a tube. Liquid that contact in the surface of tube is almost stationary. As we move from the surface towards the centre of the tube, the velocity of the liquid layers keeps on increasing till it is maximum at the centre.

The force of friction F between two layers each having area A cm^{2}, separated by a distance dx cm , and having a velocity difference of dv cm/sec ,is given by-

F ∝ A ( dv / dx )

F = η A ( dv/dx)

where η is coefficient of viscosity.

dv / dx is viscosity gradient

If dx = 1cm, A = 1cm^{2} and dV = 1cm/sec

F = η

Coefficient of viscosity may be defined as the force of friction 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.

The unit of viscosity are dynes sec cm^{-2}.This is also called 1 Poise.

## What is the Effect of Temperature on Viscosity ?

The viscosity of a liquid is generally decreases with rise in temperature. This decrease is about 2% per degree rise of temperature in many cases. This has been explained in terms of Hole Theory of liquids.

The variation of viscosity (η) with temperature can be expressed by the following relationship-

η = Ae^{Ea/RT} -----[Equation-1]

where A is constant and Ea is called the activation energy for viscous flow.

Taking natural log on both sides, we get-

ln η = A + Ea/RT

or ln η = ln A + Ea/R + 1/T -----[Equation-2]

A plot of ln η versus 1/T should be a straight line

The gas viscosity (η) will increase with temperature. According to the kinetic theory of gases, viscosity should be proportional to the square root of the absolute temperature, in practice, it increases more rapidly.

## What is the Effect of Pressure on Viscosity ?

On increasing pressure, viscosity of liquids increases. This is due to fact that decrease in the number of holes as the pressure increases. Therefore it becomes more difficult for liquid molecules to move around and thus it becomes more difficult for them to flow.