## 5.7 Kinetic Energy And Molecular Speeds

Molecules of gases remain in continuous motion. While moving they collide with each other and with the walls of the container. This results in change of their speed and redistribution of energy. So the speed and energy of all the molecules of the gas at any instant are not the same. Thus, we can obtain only average value of speed of molecules. If there are n number of molecules in a sample and their individual speeds are u1, u2,…….un, then average speed of molecules uav can be calculated as follows:…

## 5.6.2 Dalton’s Law of Partial Pressures

The law was formulated by John Dalton in 1801. It states that the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases i.e., the pressures which these gases would exert if they were enclosed separately in the same volume and under the same conditions of temperature. In a mixture of gases, the pressure exerted by the individual gas is called partial pressure. Mathematically, pTotal = p1+p2+p3+……(at constant T, V) where pTotal is the total pressure exerted by the…

## 5.6.1 Density and Molar Mass of a Gaseous Substance

Ideal gas equation can be rearranged as follows: n/V = p/RT Replacing n by m/M we get m/MV = p/RT d/M = p/RT (where d is the density) On rearranging the above equation we get the relationship for calculating molar mass of a gas. M= (d RT)/p

## 5.6 Ideal Gas Equation

The three laws which we have learnt till now can be combined together in a single equation which is known as ideal gas equation. R is called gas constant. It is same for all gases. Therefore it is also called Universal Gas Constant. Equation (5.17) is called ideal gas equation. Equation (5.18) shows that the value of R depends upon units in which p, V and T are measured. If three variables in this equation are known, fourth can be calculated. From this equation we can see that at constant…

## 5.5.4 Avogadro Law (Volume – Amount Relationship)

In 1811 Italian scientist Amedeo Avogadro tried to combine conclusions of Dalton’s atomic theory and Gay Lussac’s law of combining volumes (Unit 1) which is now known as Avogadro law. It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. This means that as long as the temperature and pressure remain constant, the volume depends upon number of molecules of the gas or in other words amount of the gas. The number of molecules in one mole of a…

## 5.5.3 Gay Lussac’s Law (Pressure-Temperature Relationship)

Pressure in well inflated tyres of automobiles is almost constant, but on a hot summer day this increases considerably and tyre may burst if pressure is not adjusted properly. During winters, on a cold morning one may find the pressure in the tyres of a vehicle decreased considerably. The mathematical relationship between pressure and temperature was given by Joseph Gay Lussac and is known as Gay Lussac’s law. It states that at constant volume, pressure of a fixed amount of a gas varies directly with the temperature. Mathematically, P/T =…

## 5.5.2 Charles’ Law (Temperature – Volume Relationship)

Charles and Gay Lussac performed several experiments on gases independently to improve upon hot air balloon technology. Their investigations showed that for a fixed mass of a gas at constant pressure, volume of a gas increases on increasing temperature and decreases on cooling. They found that for each degree rise in temperature, volume of a gas increases by 1/273.15 of the original volume of the gas at 0 °C. Thus if volumes of the gas at 0 °C and at t °C are V0 and Vt respectively, then At this…

## 5.5.1 Boyle’s Law (Pressure – Volume Relationship)

On the basis of his experiments, Robert Boyle reached to the conclusion that at constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume. This is known as Boyle’s law. Mathematically, it can be written as where k1 is the proportionality constant. The value of constant k1 depends upon the amount of the gas, temperature of the gas and the units in which p and V are expressed. On rearranging equation (5.2) we obtain  pV = k1 It means that…

## 5.5 The Gas Laws

The gas laws which we will study now are the result of research carried on for several centuries on the physical properties of gases. The first reliable measurement on properties of gases was made by Anglo-Irish scientist Robert Boyle in 1662. The law which he formulated is known as Boyle’s Law. Later on attempts to fly in air with the help of hot air balloons motivated Jaccques Charles and Joseph Lewis Gay Lussac to discover additional gas laws. Contribution from Avogadro and others provided lot of information about gaseous state.

## 5.4 The Gaseous State

This is the simplest state of matter. Throughout our life we remain immersed in the ocean of air which is a mixture of gases. We spend our life in the lowermost layer of the atmosphere called troposphere, which is held to the surface of the earth by gravitational force. The thin layer of atmosphere is vital to our life. It shields us from harmful radiations and contains substances like dioxygen, dinitrogen, carbon dioxide, water vapour, etc. Let us now focus our attention on the behaviour of substances which exist in…