Boyle’s Law
A relationship of volume with external pressure was given by Boyle’s in the form of law. This law is known as Boyle’s Law which states,
For a given mass of a gas the volume of the gas is inversely proportional to its pressure provided the temperature is kept constant.
Mathematically it may be written as
V ∞ 1 / P
Or V = K / P
Or PV = K
On the bases of the relation, Boyle’s law can also be stated as
The product of the pressure and volume of a given mass of a gas is always constant at constant temperature.
Explanation
Consider for a given mass a gas having volume V1 at pressure P1, so according to Boyle’s Law we may write as
P1V1 = K1 (constant)
If the pressure of the above system is changed from P1 to P2 then the volume of the gas will also change from V1 to V2. For this new condition of the gas we can write as,
P2V2 = K2 (constant)
But for the same mass of the gas.
K1 = K2
P1V1 = P2V2
This equation is known as Boyle’s Equation.
Charle’s Law
We know that everything expand on heating and contract cooling. This change in volume is small in liquids and solids but gases exhibit enormous changes due to the presence of large intermolecular spaces.
Change of volume of a gas with the change of temperature at constant pressure was studied by Charles and was given in the form of a law. which states,
Statement
For a given mass of a gas the volume of the gas is directly proportional to its absolute temperature provided the pressure is kept constant.
Mathematically this law may be written as
V ∞ T
V = K T
OR
V / T = K
This relation shows that the ratio of volume of a given mass of a gas to its absolute temperature is always constant provided the pressure is kept constant. On this bases Charles Law may also be defined as,
If the pressure remains constant for each 1ºC change of temperature the volume of the gas changes to 1/273 of its original volume.
On the bases of this statement
V1 / T = K & V2 / T2 = K
V1 / T1 = V2 / T2
This equation is known as Charle’s equation.
The volume temperature relationship can be represented graphically. When volume of a given mass of gas is plotted against temperature, a straight line is obtained.
Graph Coming Soon
Absolute Scale Of Temperature
There are different scales for the measurement of temperature such as Celsius ºC and Fahrenheit ºC. Similarly another scale known as absolute scale or Kelvin scale is determined on the basis of Charle’s law.
On the basis of Charle’s law we known that the volume of the gas changes to 1/273 times of its original volume for each 1 ºC change of temperature. It suggests that the volume of a gas would theoretically be zero at -273ºC. But this temperature has never been achieved for any gas because all the gases condense to liquid at a temperature above this point. So the minimum possible temperature for a gaseous system is to be -273ºC. This temperature is referred as absolute zero or zero degree of the absolute scale or Kelvin scale.
To form an absolute scale thermometer if the equally spaced divisions of centigrade thermometer are extended below zero and when the point -273ºC is maked then this point is called as absolute zero and the scale is called as absolute scale. It shows that for the conversion of centigrade scale into Kelvin scale 273 is added to the degrees on the centigrade scale.
K = 273 + ºC
Avogadro’s Law
In 1811, a scientist Avogadro’s established a relationship between the volume and number of molecules of the gas, which is known as Avogadro’s law.
Statement
Equal volume of all gases contains equal number of molecules under the same condition of temperature & pressure.
Mathematically it may be represented as
V ∞ n
OR
V = K n
On the basis of the above statement we can say that
1 dm3 of O2 gas will contain the same number of molecules as 1 dm3 of H2 or N2 or any other gas at same temperature and pressure.
It was also observed that 22.4 dm3 of any gas at S.T.P contain 1 mole of that gas, so 22.4 dm3 volume at S.T.P is called as molar volume or the volume of 1 mole of the gas and the mass present in 22.4 dm3 of any gas will be equal to its molar mass or molecular mass. It can also be explained on the basis of following figures.
Determination of Unknown Molecular Mass of a Gas With the Help of Avogadro’s Law
Suppose we have two gases (i) Oxygen (ii) CO
The volume of these two gases are equal which are 1 dm3.
The mass of 1 dm3 of oxygen is 1.43 gm
The mass of 1 dm3 of Co is 1.25 gm
According to Avogadro’s law we know that 1 dm3 of CO at S.T.P contain the same number of molecules as 1 dm3 of O2 under similar condition. Hence a molecule of CO has 1.25 / 1.43 times as much as a molecule of O2 and we know that the molecular mass of oxygen is 32 so the molecular mass of CO would be
1.25 / 1.43 x 32 = 28 g / mole
General Gas Equation (Ideal Gas Equation)
To give a relation between the volume, pressure and number of moles of n gas, Boyle’s law, Charle’s law and Avogadro’s law are used.
According to Boyle’s law | V ∞ 1 / P
According to Charle’s law | V ∞ T
According to Avogadro’s law | V ∞ n
By combining these laws we get
V ∞ 1 / P x T x n
OR
V = R x 1 / P x T x P
OR
P V = n R T
This equation is known as general gas equation n is also known as equation of state because when we specify the four variables = pressure, temperature, volume and number of moles we define the state for a gas.
In this equation “R” is a constant known as gas constant.
Value of R
1. When Pressure is Expressed in Atmosphere and Volume in Litres or dm3
According to general gas equation
P V = n R T
OR
R = PV / nT
For 1 mole of a gas at S.T.P we know that
V = 22.4 dm3 or litres
T = 273 K (standard temperature)
P = 1 atm (standard pressure)
So,
R = PV / nT
= 1 atm x 22.4 dm3 / 1 mole x 273 K
= 0.0821 dm3 K-1 mol0-1
2. When Pressure is Expressed in Newtons Per Square Metre and Volume in Cubic Metres
For 1 mole of a gas at S.T.P
V = 0.0224 m3 ………. ( 1 dm3 = 10-3 m3)
n = 1 mole
T = 273 K
P = 101200 Nm-2
So,
R = PV / nT
= 101300 Nm-2 x 0.0224 m3 / 1 mole x 273 K
= 8.3143 Nm K-1 mole-1
= 8.3143 J K-1 mol-1
Derivation of Gas Equation
According to general gas equation
P V = n R T
For 1 mole of a gas n = 1
P V = R T
OR
P V / T = R
Consider for a known mass of a gas the volume of the gas is V1 at a temperature T1 and pressure P1. Therefore for this gas we can write as
P1 V1 / T1 = R
If this gas is heated to a temperature T2 due to which the pressure is changed to P2 and volume is changed to V2. For this condition we may write as
P2 V2 / T2 = R
P1 V1 / T1 = P2 V2 / T2 = R
P1 V1 / T1 = P2 V2 / T2
This equation is known as gas equation.
Graham’s Law of Diffusion
We know that gas molecules are constantly moving in haphazard direction, therefore when two gases are placed separated by a porous membrane, they diffuse through the membrane and intermix with each other. The phenomenon of mixing of molecules of different gases is called diffusion.
In 1881, Graham established a relationship between the rates of diffusion of gases and their densities which is known as Graham’s law of diffusion.
Statement
The rate of diffusion of any gas is inversely proportional to the square root of its density.
Mathematically it can be represented as
r ∞ 1 / √d
r = K / √d
Graham also studied the comparative rates of diffusion of two gases. On this basis the law os defined as
The comparative rates of diffusion of two gases under same condition of temperature and pressure are inversely proportional to the square root of their densities.
If the rate of diffusion of gas A is r1 and its density is d1 then according to Graham’s law
r1 ∞ 1 / √d1
OR
r1 = K / √d1
Similarly the rate of diffusion of gas B is r2 and its density is d2 then
r2 ∞ 1 / √d2
OR
r2 = K / √d2
Comparing the two rates
r1 / r2 = (K / √d1) / (K / √d2)
r1 / r2 = √d2 / d1 ………………. (A)
But density d = mass / volume
Therefore,
For d1 we may write as
d1 = m1 / v1
And for d2
d2 = m2 / v2
Substituting these values of d1 & d2 in equation (A)
r1 / r2 = √(m2 / v2) / (m1 / v1)
But v1 = v2 because both gases are diffusing in the same volume.
Therefore,
r1 / r2 = √m2 / m1
Hence Graham’s law can also be stated as,
The comparative rates of diffusion of two gases are inversely proportional to the square root of their masses under the same condition of temperature and pressure.
It means that a lighter gas will diffuse faster than the heavier gas. For example compare the rate of diffusion of hydrogen and oxygen.
Rate of diffusion of H2 / Rate of diffusion of O2 = √Mass of O2 / Mass of H2 = √32/ 2 = √16 = 4
It shows that H2 gas which is lighter gas than O2 will diffuse four times faster than O2.
Dalton’s Law of Partial Pressures
Partial Pressure
In a gaseous mixture the individual pressure oxerted by a gas is known as partial pressure.
When two or more gases which do not react chemically are mixed in the same container each gas will exert the same pressure as it would exert if it alone occupy the same volume.
John Dalton in 1801 formulated a law which is known as Dalton’s Law of partial pressure and stated as.
Statement
The total pressure of a gaseous system is equal to the sum of the partial pressures of all the gases present in the system.
Suppose in a system three gases A, B & C are present. The partial pressure of these gases are
PA = Partial pressure of gas A
PB = Partial pressure of gas B
PC = Partial pressure of gas C
Then Dalton’s law may be mathematically written as
PT = PA + PB + PC
Where PT is the total pressure of the system.
To calculate the individual pressures of gases in the above example suppose the number of moles of A, B & C in the container are nA, nB and nC. So the total number of moles in the container will be
n = nA + nB + nC
Apply the general gas equation
P V = n R T
PT = n R T / V
Since R, T and V are same for gases A, B and C, therefore the partial pressure of these gases are as follows.
Partial pressure of gas A | PA = n(A)RT / V ……… (2)
Partial pressure of gas B | PB = n(B)RT / V ……… (3)
Partial pressure of gas C | PC = n(C)RT / V ……… (4)
Now divide equation (2) by (1)
PA / PT = (nA RT/V) / (nRT/V)
OR
PA / PT = nA / nT
Therefore,
P(gas) = P1 x n(gas) / n(total)
Application of Dalton’s Law
In an inert mixture of gases the individual gas exerts its own pressure due to collision of its molecules with the walls of the container but the total pressure produced on the container wall will be the sum of pressure of all the individual gases of the mixture.
On this basis the number of moles formed during a chemical reaction can be measured. For this purpose a gas produced in a chemical reaction is collected over water. The gas also contains some of water vapours. So the pressure exerted by the gas would be the pressure of pure gas and the pressure of water vapours.
Therefore the pressure of the system may be represented as
P(moist) = P(dry) + P(water vapour)
So,
P(dry) = P(moist) – P(water vapour)
In this way we can obtain the pressure of the gas and by using general gas equation we can calculate the number of moles of the prepared gas.
Ideal Gas
A gas which obeys all the gas laws at all temperatures and pressures is known as ideal gas.
It means that the product of pressure and volume must be constant at all pressures.
Similarly the rate of V/T will remain constant for an ideal gas.
But there is no gas which is perfectly ideal because of the presence of the force of attraction or repulsion between the molecules.
Gas Laws on the Basis of Kinetic Theory
Boyle’s Law
According to Boyle’s law the volume of a given mass of a gas is inversely proportional to its pressure at constant temperature.
It means that when the volume of the gas is decreased the pressure of the gas will increase.
According to kinetic molecular theory of gases the pressure exerted by a gas is due to the collisions of the molecules with the walls of the container. If the volume of a gas is reduced at constant temperature, the average velocity of the gas molecules remains constant so they collide more frequently wit the walls which causes higher pressure.
Charle’s Law
According to Charles law the volume of a given mass of a gas is directly proportional to its absolute temperature at constant pressure.
According to kinetic molecular theory the average kinetic energy of gas molecules is directly proportional to its absolute temperature so if the temperature of the gas is increased the average kinetic energy of the gas molecules is also increased due to which the sample of the gas expanded to keep the pressure constant. It is accordance with the law.
Graham’s Law
According to Graham’s Law
r1 / r2 = √m2 / m1
The rate of diffusion of a gas is directly proportional to the velocity of the molecules so,
v1 / v2 = √m2 / m1
A relationship of volume with external pressure was given by Boyle’s in the form of law. This law is known as Boyle’s Law which states,
For a given mass of a gas the volume of the gas is inversely proportional to its pressure provided the temperature is kept constant.
Mathematically it may be written as
V ∞ 1 / P
Or V = K / P
Or PV = K
On the bases of the relation, Boyle’s law can also be stated as
The product of the pressure and volume of a given mass of a gas is always constant at constant temperature.
Explanation
Consider for a given mass a gas having volume V1 at pressure P1, so according to Boyle’s Law we may write as
P1V1 = K1 (constant)
If the pressure of the above system is changed from P1 to P2 then the volume of the gas will also change from V1 to V2. For this new condition of the gas we can write as,
P2V2 = K2 (constant)
But for the same mass of the gas.
K1 = K2
P1V1 = P2V2
This equation is known as Boyle’s Equation.
Charle’s Law
We know that everything expand on heating and contract cooling. This change in volume is small in liquids and solids but gases exhibit enormous changes due to the presence of large intermolecular spaces.
Change of volume of a gas with the change of temperature at constant pressure was studied by Charles and was given in the form of a law. which states,
Statement
For a given mass of a gas the volume of the gas is directly proportional to its absolute temperature provided the pressure is kept constant.
Mathematically this law may be written as
V ∞ T
V = K T
OR
V / T = K
This relation shows that the ratio of volume of a given mass of a gas to its absolute temperature is always constant provided the pressure is kept constant. On this bases Charles Law may also be defined as,
If the pressure remains constant for each 1ºC change of temperature the volume of the gas changes to 1/273 of its original volume.
On the bases of this statement
V1 / T = K & V2 / T2 = K
V1 / T1 = V2 / T2
This equation is known as Charle’s equation.
The volume temperature relationship can be represented graphically. When volume of a given mass of gas is plotted against temperature, a straight line is obtained.
Graph Coming Soon
Absolute Scale Of Temperature
There are different scales for the measurement of temperature such as Celsius ºC and Fahrenheit ºC. Similarly another scale known as absolute scale or Kelvin scale is determined on the basis of Charle’s law.
On the basis of Charle’s law we known that the volume of the gas changes to 1/273 times of its original volume for each 1 ºC change of temperature. It suggests that the volume of a gas would theoretically be zero at -273ºC. But this temperature has never been achieved for any gas because all the gases condense to liquid at a temperature above this point. So the minimum possible temperature for a gaseous system is to be -273ºC. This temperature is referred as absolute zero or zero degree of the absolute scale or Kelvin scale.
To form an absolute scale thermometer if the equally spaced divisions of centigrade thermometer are extended below zero and when the point -273ºC is maked then this point is called as absolute zero and the scale is called as absolute scale. It shows that for the conversion of centigrade scale into Kelvin scale 273 is added to the degrees on the centigrade scale.
K = 273 + ºC
Avogadro’s Law
In 1811, a scientist Avogadro’s established a relationship between the volume and number of molecules of the gas, which is known as Avogadro’s law.
Statement
Equal volume of all gases contains equal number of molecules under the same condition of temperature & pressure.
Mathematically it may be represented as
V ∞ n
OR
V = K n
On the basis of the above statement we can say that
1 dm3 of O2 gas will contain the same number of molecules as 1 dm3 of H2 or N2 or any other gas at same temperature and pressure.
It was also observed that 22.4 dm3 of any gas at S.T.P contain 1 mole of that gas, so 22.4 dm3 volume at S.T.P is called as molar volume or the volume of 1 mole of the gas and the mass present in 22.4 dm3 of any gas will be equal to its molar mass or molecular mass. It can also be explained on the basis of following figures.
Determination of Unknown Molecular Mass of a Gas With the Help of Avogadro’s Law
Suppose we have two gases (i) Oxygen (ii) CO
The volume of these two gases are equal which are 1 dm3.
The mass of 1 dm3 of oxygen is 1.43 gm
The mass of 1 dm3 of Co is 1.25 gm
According to Avogadro’s law we know that 1 dm3 of CO at S.T.P contain the same number of molecules as 1 dm3 of O2 under similar condition. Hence a molecule of CO has 1.25 / 1.43 times as much as a molecule of O2 and we know that the molecular mass of oxygen is 32 so the molecular mass of CO would be
1.25 / 1.43 x 32 = 28 g / mole
General Gas Equation (Ideal Gas Equation)
To give a relation between the volume, pressure and number of moles of n gas, Boyle’s law, Charle’s law and Avogadro’s law are used.
According to Boyle’s law | V ∞ 1 / P
According to Charle’s law | V ∞ T
According to Avogadro’s law | V ∞ n
By combining these laws we get
V ∞ 1 / P x T x n
OR
V = R x 1 / P x T x P
OR
P V = n R T
This equation is known as general gas equation n is also known as equation of state because when we specify the four variables = pressure, temperature, volume and number of moles we define the state for a gas.
In this equation “R” is a constant known as gas constant.
Value of R
1. When Pressure is Expressed in Atmosphere and Volume in Litres or dm3
According to general gas equation
P V = n R T
OR
R = PV / nT
For 1 mole of a gas at S.T.P we know that
V = 22.4 dm3 or litres
T = 273 K (standard temperature)
P = 1 atm (standard pressure)
So,
R = PV / nT
= 1 atm x 22.4 dm3 / 1 mole x 273 K
= 0.0821 dm3 K-1 mol0-1
2. When Pressure is Expressed in Newtons Per Square Metre and Volume in Cubic Metres
For 1 mole of a gas at S.T.P
V = 0.0224 m3 ………. ( 1 dm3 = 10-3 m3)
n = 1 mole
T = 273 K
P = 101200 Nm-2
So,
R = PV / nT
= 101300 Nm-2 x 0.0224 m3 / 1 mole x 273 K
= 8.3143 Nm K-1 mole-1
= 8.3143 J K-1 mol-1
Derivation of Gas Equation
According to general gas equation
P V = n R T
For 1 mole of a gas n = 1
P V = R T
OR
P V / T = R
Consider for a known mass of a gas the volume of the gas is V1 at a temperature T1 and pressure P1. Therefore for this gas we can write as
P1 V1 / T1 = R
If this gas is heated to a temperature T2 due to which the pressure is changed to P2 and volume is changed to V2. For this condition we may write as
P2 V2 / T2 = R
P1 V1 / T1 = P2 V2 / T2 = R
P1 V1 / T1 = P2 V2 / T2
This equation is known as gas equation.
Graham’s Law of Diffusion
We know that gas molecules are constantly moving in haphazard direction, therefore when two gases are placed separated by a porous membrane, they diffuse through the membrane and intermix with each other. The phenomenon of mixing of molecules of different gases is called diffusion.
In 1881, Graham established a relationship between the rates of diffusion of gases and their densities which is known as Graham’s law of diffusion.
Statement
The rate of diffusion of any gas is inversely proportional to the square root of its density.
Mathematically it can be represented as
r ∞ 1 / √d
r = K / √d
Graham also studied the comparative rates of diffusion of two gases. On this basis the law os defined as
The comparative rates of diffusion of two gases under same condition of temperature and pressure are inversely proportional to the square root of their densities.
If the rate of diffusion of gas A is r1 and its density is d1 then according to Graham’s law
r1 ∞ 1 / √d1
OR
r1 = K / √d1
Similarly the rate of diffusion of gas B is r2 and its density is d2 then
r2 ∞ 1 / √d2
OR
r2 = K / √d2
Comparing the two rates
r1 / r2 = (K / √d1) / (K / √d2)
r1 / r2 = √d2 / d1 ………………. (A)
But density d = mass / volume
Therefore,
For d1 we may write as
d1 = m1 / v1
And for d2
d2 = m2 / v2
Substituting these values of d1 & d2 in equation (A)
r1 / r2 = √(m2 / v2) / (m1 / v1)
But v1 = v2 because both gases are diffusing in the same volume.
Therefore,
r1 / r2 = √m2 / m1
Hence Graham’s law can also be stated as,
The comparative rates of diffusion of two gases are inversely proportional to the square root of their masses under the same condition of temperature and pressure.
It means that a lighter gas will diffuse faster than the heavier gas. For example compare the rate of diffusion of hydrogen and oxygen.
Rate of diffusion of H2 / Rate of diffusion of O2 = √Mass of O2 / Mass of H2 = √32/ 2 = √16 = 4
It shows that H2 gas which is lighter gas than O2 will diffuse four times faster than O2.
Dalton’s Law of Partial Pressures
Partial Pressure
In a gaseous mixture the individual pressure oxerted by a gas is known as partial pressure.
When two or more gases which do not react chemically are mixed in the same container each gas will exert the same pressure as it would exert if it alone occupy the same volume.
John Dalton in 1801 formulated a law which is known as Dalton’s Law of partial pressure and stated as.
Statement
The total pressure of a gaseous system is equal to the sum of the partial pressures of all the gases present in the system.
Suppose in a system three gases A, B & C are present. The partial pressure of these gases are
PA = Partial pressure of gas A
PB = Partial pressure of gas B
PC = Partial pressure of gas C
Then Dalton’s law may be mathematically written as
PT = PA + PB + PC
Where PT is the total pressure of the system.
To calculate the individual pressures of gases in the above example suppose the number of moles of A, B & C in the container are nA, nB and nC. So the total number of moles in the container will be
n = nA + nB + nC
Apply the general gas equation
P V = n R T
PT = n R T / V
Since R, T and V are same for gases A, B and C, therefore the partial pressure of these gases are as follows.
Partial pressure of gas A | PA = n(A)RT / V ……… (2)
Partial pressure of gas B | PB = n(B)RT / V ……… (3)
Partial pressure of gas C | PC = n(C)RT / V ……… (4)
Now divide equation (2) by (1)
PA / PT = (nA RT/V) / (nRT/V)
OR
PA / PT = nA / nT
Therefore,
P(gas) = P1 x n(gas) / n(total)
Application of Dalton’s Law
In an inert mixture of gases the individual gas exerts its own pressure due to collision of its molecules with the walls of the container but the total pressure produced on the container wall will be the sum of pressure of all the individual gases of the mixture.
On this basis the number of moles formed during a chemical reaction can be measured. For this purpose a gas produced in a chemical reaction is collected over water. The gas also contains some of water vapours. So the pressure exerted by the gas would be the pressure of pure gas and the pressure of water vapours.
Therefore the pressure of the system may be represented as
P(moist) = P(dry) + P(water vapour)
So,
P(dry) = P(moist) – P(water vapour)
In this way we can obtain the pressure of the gas and by using general gas equation we can calculate the number of moles of the prepared gas.
Ideal Gas
A gas which obeys all the gas laws at all temperatures and pressures is known as ideal gas.
It means that the product of pressure and volume must be constant at all pressures.
Similarly the rate of V/T will remain constant for an ideal gas.
But there is no gas which is perfectly ideal because of the presence of the force of attraction or repulsion between the molecules.
Gas Laws on the Basis of Kinetic Theory
Boyle’s Law
According to Boyle’s law the volume of a given mass of a gas is inversely proportional to its pressure at constant temperature.
It means that when the volume of the gas is decreased the pressure of the gas will increase.
According to kinetic molecular theory of gases the pressure exerted by a gas is due to the collisions of the molecules with the walls of the container. If the volume of a gas is reduced at constant temperature, the average velocity of the gas molecules remains constant so they collide more frequently wit the walls which causes higher pressure.
Charle’s Law
According to Charles law the volume of a given mass of a gas is directly proportional to its absolute temperature at constant pressure.
According to kinetic molecular theory the average kinetic energy of gas molecules is directly proportional to its absolute temperature so if the temperature of the gas is increased the average kinetic energy of the gas molecules is also increased due to which the sample of the gas expanded to keep the pressure constant. It is accordance with the law.
Graham’s Law
According to Graham’s Law
r1 / r2 = √m2 / m1
The rate of diffusion of a gas is directly proportional to the velocity of the molecules so,
v1 / v2 = √m2 / m1
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