Question

Use the postulates of the kinetic moleclar theory (KMT) to explain why boyle's law, charles's law, avogadro's law, and dalton's law of partial pressures hold true for ideal gases. Use the KMT to explain the P versus n (at constant V and T) relationship and the P versus T (at constant V and n) relationship.

Answer 1

Let us see each law in light of Kinetic molecular theory

a) Boyle's Law: At constant pressure, for ideal gas, the volume of gas is inversely proportional to pressure of gas

As per KMT, at constant temperature the pressure of vessel is due to collision of gas molecules on the wall of vessel. Now if we decrease the volume it means there will be an increase in number of collision against the wall of vessel hence the pressure increases.

b) Charle's law: at constant pressure, the volume occupied by gas is directley proportional to the temperature of gas in kelvin.

As per KMT, on increasing the temperature of ideal gas the average kinetic energy of molecules will increase. Due to increase in kinetic energy the molecules will move faster and there will be more number of collision of molecules with vessel. Now in order to maintain the pressure constant, the gas molecules must have large distance between each other, which is possible by increasing the volume of gas. Hence the volume increases on increasing temperature.

c) Avagadro's law: At constant temperature and pressure, Equal volume of all ideal gases have equal number of molecules of gas.

It can be mathematically related to KMT as

According to kinetic theory of gases

Where n = number of moelcules , c = speed of molecules

P= pressure and V = volume of gas

Now for two ideal gas, we have assumed that the pressure and volumes are same

P1V1= P2V2

Therefore

Now for ideal gases at same temperature , The average kinetic energy will also be same

Hence n1= n2 [The number of molecules or moles are same]

d) Dalton's law:

The total pressure of mixture of gases is equal to the sum of partial pressure of each gas.

P = P1 + P2 + P3 .....

As per KMT, there is no force of attraction or repulsion between the gas molecules of an ideal gas

Hence in a mixture of gas each gas will have its own pressure (irrespective of other gas present)

So we can say that in a mixture of gases which are non reacting with each other, each gas will exert its own pressure on the wall of vessel, due to collision with the walls. So the total pressure of mixture of gases will be equal to sum of pressures exerted by each individual gas.

e) Relation between P and T:

Gay-Lussac's law: At constant volume, the pressure exerted by a given amount of ideal gas is directly proportional to the temperature of gas in kelvin

In light of KMT: on increaseing temperature of gas the Average kinetic energy of molecules will increase so molecule swill move faster. The pressure of gas is due to collision of gas molecules on the wall of vessel. If the molecules are moving faster they will collide more frequently with the wall and hence exert more pressure on the walls of container. Thus pressure increases.

f) At constant volume and temperature, the pressure of gas is directly proportional to number of molecules of gas

KMT: at constant volume and temperature if we increase the number of molecules of gas then there will more frequency of collision of gas molecules with the wall of container, The pressure of gas is due to collisoin of gas molecules with the wall of container. hence the pressure will increase on increasing the number of molecules in a gas.