Prove boyels law , charles law and dalton law of partial pressure on the basis of kmtg
Answers
Boyle’s Law
It states that under a constant temperature when the pressure on a gas increases its volume decreases. In other words according to Boyle’s law volume is inversely proportional to pressure when the temperature and the number of molecules are constant.
p ∝ 1/V
p = k1 1/V
k1 here is a proportionality constant, V is the Volume and p is the pressure. On rearranging, we get: k1= pV. Now, if a fixed mass of gas undergoes an expansion at constant temperature then the final volume and pressure shall be p2 and V2. The initial volume and initial pressure here is p1 and V1 then according to Boyle’s law: p1×V1 = p2×V2 = constant (k1)
p1/p2 = V2/V1
So according to Boyle’s law, if the pressure is doubled then at constant temperature the volume of that gas is reduced to half. The reason being the intermolecular force between the molecules of the gaseous substance. In a free state, a gaseous substance occupies a larger volume of the container due to the scattered molecules.
When a pressure is applied to the gaseous substance, these molecules come closer and occupy a lesser volume. In other words, the pressure applied is directly proportional to the density of the gas. Boyle’s law can be graphically represented as follows:
Charles law-
According to his findings, at constant pressure and for constant mass, the volume of a gas is directly proportional to the temperature.
This means that with the increase in temperature the volume shall increase while with decreasing temperature the volume decreases. In his experiment, he calculated that the increase in volume with every degree equals 1/273.15 times of the original volume. Therefore, if the volume is V0 at 0° C and Vt is the volume at t° C then,
Vt = V0 +t/273.15 V0 ⇒ Vt = V0 (1+ t/273.15 )
⇒ Vt = V0 (273.15+ t/273.15 )
For the purpose of measuring the observations of gaseous substance at temperature 273.15 K, we use a special scale called the Kelvin Temperature Scale. The observations of temperature (T) on this scale is 273.15 greater than the temperature (t) of the normal scale.
T= 273.15+t
while, when T = 0° c then the reading on the Celsius scale is 273.15. The Kelvin Scale is also called Absolute Temperature Scale or Thermodynamic Scale. This scale is used in all scientific experiments and works. In the equation [ Vt = V0 (273.15+ t/273.15 ) ] if we take the values Tt = 273.15+t and T0 = 273.15 then:
Vt = V0 ( Tt / T0 )
which implies Vt/V0= ( Tt / T0 ), which can also be written as:
V2/V1= T2/ T1
or V1 /T1 = V2 / T2
V/T = constant = k2
Therefore, V= k2 T
The graphical representation of Charles law is shown in the figure above. Its an isobar graph as the pressure is constant with volume and temperature changes under observation.
Dalton law of partial pressure-
Dalton's law of partial pressures states that the total pressure of a mixture of gases is the sum of the partial pressures of its components:
\text {P}_{\text{Total}} = \text P_{\text {gas 1}} + \text P_{\text {gas 2}} + \text P_{\text {gas 3}} ...P
Total
=P
gas 1
+P
gas 2
+P
gas 3
...
where the partial pressure of each gas is the pressure that the gas would exert if it was the only gas in the container. That is because we assume there are no attractive forces between the gases.
