cruz lectures gases

GASES

In this chapter, we examine and learn to use the laws governing the behavior of gases. These laws, combined with the other properties of gases, form the basis for the Kinetic molecular theory of gases.

Properties of Gaseous State

Following are the five properties of gases which can be measured experimentally.

 1 Gases are easily compressible. The molecules in a gas are very far apart due to very low intermolecular forces. By external pressure they can be brought closer, thereby compressing the gas. 2 Gases do not have definite volume. Molecules move easily and occupy the entire volume of the container and take the shape of the container. 3 Gases exert pressure in all directions. Molecules are always in a state of rapid zig zag motion, colliding with each other and with the walls of the container. Collisions account for pressure. As the same number of molecules strike a given surface in unit time, gases exert pressure uniformly in all directions. 4 Gases diffuse easily. Molecules of other substances can fill a large space between gaseous molecules. This is nothing but diffusion. 5 Gases have low density. Due to large space, the number of units of molecules per unit volume of gas is very low compared to solids or liquids.

Gas Laws :

The quantitative relationship between volume, pressure, temperature and the rate of diffusion for a given quantity of gas are termed as ’Gas Laws’.

These Laws are

* Boyle’s law
* Charles’ law
* Pressure-temperature law
* Graham’s law of diffusion

Boyle’s Law

Robert Boyle, in 1662, published a mathematical statement on the relation between the volume and pressure of gas at constant temperature called Boyle’s Law. This law states that "At constant temperature, volume of a definite mass of a dry gas is inversely proportional to its pressure."

It can be mathematically expressed as :

The magnitude of constant depends on temperature, mass and nature of a gas.

Boyle’s law can be useful in calculating the volume of a gas at any required pressure if the volume at some other pressure is known by using the following equation.

P1V1 = P2V2 = K

If 10 dm3 of nitrogen gas originally at 20.26 KPa is allowed to reach a pressure of 40.52 KPa while keeping temperature constant, final volume can be calculated as follows :

P1 = 20.26 KPa P2 = 40.52 KPa

V1 = 10 dm3 V2 = ?

According to Boyle's Law

= 5 dm3

It can be seen that since volume and pressure are inversely proportional, on increasing pressure, the volume decreases.

Example :

The volume of a certain gas at constant temperature was found to be 14 liters when the pressure was 1.2 kg/ cm2 If the pressure is decreased by 30% find the final volume of the gas.

V1 = 14 liters P1 = 1.2 kg/cm2

V2 = ? P2 = P1 - 30%

According to Boyle's law

P1V1 = P2V2

The final volume of the gas is 20 liters.

Charle's Law

Jacques Charles, in 1787, formulated the relationship between the volume and temperature of a given mass of a dry gas at constant pressure called Charles' Law which states that "At constant pressure, the volume of a fixed mass of dry gas is directly proportional to the absolute temperature;

It can be mathematically expressed as

The magnitude of constant depends on pressure, mass and nature of a gas.

Charles' law is useful for calculating the volume of a gas at any required temperature if the volume at some other temperature is known by using the following equation.

V1 = T1

V2 = T2

Example :

A gas at constant pressure is kept at 1000C. On decreasing the temperature to 500C, the gas occupies a volume of 800 ml. Find the initial volume of the gas.

V1 = ? T1 = 1000C = 100 + 273 K = 373 K

V2 = 800 ml T2 = 500C = 50 + 273 K = 323 K

According to Charles' Law

Initial volume of the gas was 923.8 ml.

Pressure Temperature Law

The Pressure and Temperature law is similar to Charles' law. It states that "For a given mass of a dry gas, the pressure is directly proportional to the absolute temperature, if the volume is kept constant."

It can be mathematically expressed as

P µ T, if V is constant

P = constant ´ T

This law can be useful in calculating the pressure of a gas at any required temperature if the pressure at some other temperature is known by using the following equation :

If 25 dm3 of a gas at 36.5 KPa is cooled from 298 K to 136 K, keeping the volume constant, the final pressure can be calculated as follows :

P1 = 36.5 KPa / P2 = ?

T1 = 298 K T2 = 136 K

= 16.66 KPa

Gay Lussac Law

In 1805, Gay Lussac observed a phenomenon based on his experiments on different gases. He framed his observations in the Law of combining volumes of Gases which states that "when gases react they do so in volumes which bear simple whole number ratios to one another and to the volume of the products, if gaseous, when measured at the same conditions of pressure and temperature.

Example

1. One volume of H2 combines with one volume of Br2 to form two volumes of HBr gas

Ratio of reactions and products 1 : 1 : 2

2. One volume of N2 combines with 3 volumes of H2 to produce two volumes of NH3 gas

Ratio of reactions and products 1 : 3 : 2

Example

500 cm3 of Nitric oxide (NO) reacted with 300 cm3 of O2 to form nitrogen dioxide (NO2). What would be the composition of final mass?

\ 2 vol of NO requires 1 vol O2

2 cm3 of NO requires 1 cm3 O2

\ 500 cm3 will require 250 cm3 of O2

Now

2 vol of NO yields 2 vol of NO2

\ 2 cm3 of NO yields 2 cm3 of NO2

\ 500 cm3 NO yields 500 cm3 of NO2

The resulting mixture consists of

1. Unused O2 = (300 - 250) = 50cm3

2. Product NO2 formed = 500 cm3

Avogadro’s Law states that "equal volumes of different gases

under the same conditions of temperature and pressure contain an equal number of molecules."

It is defined as the number of molecules present in 22.4 dm3 of gas ,
or gram-molecule weight of any substance at N. T. P.

i.e. NA = 6.023 ´ 1023

e.g.

1) 22.4 dm3 of H2 gas at N.T.P. contains 6.023 ´ 1023 H2 molecules.

2) 1 gm molecule of N2 (i.e. 28 gms of nitrogen) contains 6.023 ´ 1023 nitrogen molecules.

Graham’s Law of Diffusion

The phenomenon of diffusion of a gas can be defined as the tendency of a gas to spread uniformly throughout the space available to it.

The relation between its density and the rate of diffusion of a gas can be represented by Graham’s law which states that "The rate of diffusion of a gas is inversely proportional to the square root of its density under given conditions of temperature and pressure."

Vapor density of a gas can be calculated if 0.08 dm3 of gas diffuses in the same time as 0.002 dm3 of chlorine having vapor density 35.5.

r1 = rate of diffusion of gas = 0.08 dm3/t

r2 = rate of diffusion of chlorine = 0.002 dm3/t

D1 = ?

D2 = 35.5

General or Ideal Gas Equation

The General or Ideal Gas Equation is obtained by combining relations such as Boyle’s Law, Charles’ Law and Avogadro’s Law.

 PV = nRT where P- Pressure V - Volume R - Constant T - Temperature

This relation is referred to as ’Ideal gas Equation’ as it holds good only when the gases are behaving as 'ideal' or perfect gases.

R can be calculated as follows :

We know that 1 mole of an ideal gas occupies 22.4 liter at S.T.P. (Standard Temperature & Pressure, i.e 1 atm. pressure and 273 K )

Units of Gas constant R

1) R = 0.082 liter atm deg-1 mol-1

2) R = 8.31 ´ 107 ergs deg-1 mol-1

3) R = 8.31 J deg-1 mol-1

4) R = 2 cal K-1 mol-1

Finally at Glance

 No. Gas Law Mathematical expression At constant 1. Boyle’s P1V1 = P2V2 Temperature 2. Charles V1/ V2 = T1/T2 Pressure 3. Pressure-Temperature P1/T1 = P2/T2 Volume 4. Graham’s Temperature Pressure 5. Gas equation PV = nRT --