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Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Document Description: Ideal Gas Laws: Revision Notes for Chemistry 2022 is part of Theory of Gases for Physical Chemistry preparation. The notes and questions for Ideal Gas Laws: Revision Notes have been prepared according to the Chemistry exam syllabus. Information about Ideal Gas Laws: Revision Notes covers topics like Gaseous State, Measurable Properties of Gases, The Gas Laws, Ideal Gas Equation, Dalton’s Law of Partial Pressures:, Graham’s Law of Diffusion and Ideal Gas Laws: Revision Notes Example, for Chemistry 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Ideal Gas Laws: Revision Notes.

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Table of contents
Gaseous State
Measurable Properties of Gases
The Gas Laws
Ideal Gas Equation
Dalton’s Law of Partial Pressures:
Graham’s Law of Diffusion
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Gaseous State

In the gaseous state, the molecules are farthest apart as compared to solid and liquid states and the intermolecular forces are negligible so the particles move randomly. 

A given substance may occur in solid, liquid or gaseous phase depending upon the relative value of two tendencies namely Mutual Attraction (MA) and Escaping Tendency (ET)

  • If MA is greater than ET then substance will occur in solid state.

  • If MA is slightly greater than ET then substance will occur in liquid state.

  • If MA is very much less than ET then substance will occur in gaseous state

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Out of the three states of matter, the most simplest one is the gaseous state.

  • The state is characterized by sensitivity of volume change with change of pressure and temperature. 
  • It is due to large distance between molecules as compared to their own dimensions.
  • There exist weak Vander Waal’s forces, molecules move independently of each other with speed about 400 ms–1.

Gases show maximum equality in their behavior irrespective of their nature.

Measurable Properties of Gases

Mass

The gases possess mass. The mass of gas is generally used in the of form of number of moles which is related as

(i)  no. of moles = Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

     Two other useful formulae to calculate number of moles of gas are

(ii) number of moles = Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

(iii) no. of moles = Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

When a container contains more than one gas then the molecular mass of mixture is termed as effective molecular mass (EMM) which is intermediate between molecular masses of all the gases present in the container.

 Effective molecular mass = Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Volume

Volume of gas is nothing but volume of the container in which it is present.

Relation between different units of volume

            1m3 = 103 dm3 = 103 litre = 106 cm3 = 106 ml = 109 mm3

Temperature

Degree of hotness or coldness of a body is measured by temperature

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

C – Celcium scale, K – Kelvin scale,F – Fahrenheit scale

Pressure

Force acting per unit area

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry 

Unit:

CGS : dyne/cm2

 MKS : Newton/m2      (1N/m2 = 1 Pa)

 Relation : 1N/m2 = 10 dyne/cm2

Units of pressure:

            1 atm = 76 cm of Hg

                       = 760 mm of Hg

                       = 760 torr

                       = 1.01325 × 105 N/m2

                       = 101.325 kPa

                       = 1.01325 bar

                       = 14.7 lb/In2 (Psi)

                       = 10.33 meters of H2O

Density

Mass per unit volume

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Units:

             CGS= g/cm3

MKS = kg/m3

Relation : 1 kg/m3 = 10–3 g/cm3


Absolute density 

(mass per unit volume)

Relative density

(Relative to hydrogen turned as vapour density)

(i) Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

(ii)  unit : g/l

(ii) No unit

(iii) Function of temperature, pressure no. of moles

(iii) Independent of Pressure, Temperature

Note: Mass, volume and number of moles are extensive properties that depend on mass hence then all divertly additive

Note:  Density, Pressure and Temperature are intensive properties they does not depend on mass hence they are non-additive in nature.

The Gas Laws

Boyle’s Law:

It relates the volume and the pressure of a given mass of a gas at constant temperature. Boyle’s law states that, “at constant temperature, the volume of a sample of a gas varies inversely with the pressure.”

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry (when temperature and number of moles are kept constant)

The proportionality can be changed into an equality by introducing a constant k, i.e.,

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Boyle’s law can be verified by any one of the following three ways graphically.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry 

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Alternatively, Boyle’s law can also be stated as follows:

“Temperature remaining constant, the product of pressure and volume of a given mass of a gas is constant”. The value of the constant depends upon the amount of a gas and the temperature.

Mathematically, it can be written, as,

P1V1 = P2V2 = P3V3 = ………………..

Location of straight line and curve change with temperature in the isotherm shown in the following figure.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry 

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

According to Boyle’s law, PV = Constant at constant temperature

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Charles’ Law:

It relates the volume and  temperature of a gives mass of gas at constant pressure.

For each degree change of temperature, the volume of a sample changes by the fraction Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  of its volume at 0°C.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Let the volume of a given amount of gas be V0 at 0°C. The temperature is increased by t°C and the new volume becomes Vt

            Thus, Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

A new temperature scale was introduced known as Kelvin scale or absolute scale (named after the British physicist and mathematician Lord Kelvin). The lower limit of the scale is called absolute zero which corresponds to –273°C.

At absolute zero or –273°C, all molecular motions would stop and the volume of the gas would become zero. The temperature in absolute scale is always obtained by adding 273 to the temperature expressed in °C.

            K = (t°C + 273)

This new temperature scale may be used for deducing Charles’ law.

By substituting T for 273 + t and T0 for 273 in Eq. (i).

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  or Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry   

Or     Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry     pressure is kept constant

Alternatively, Charles’ law can be stated as follows:

“The volume of a given amount of a gas at constant pressure varies directly as its absolute temperature”.

          Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry (if pressure is kept constant)

Pressure-Temperature Law: (Gaylussac’s Law)

It relates the pressure and absolute temperature of a given mass of a gas at constant volume.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - ChemistryAn illustration describing the increase in pressure that accompanies an increase in the absolute temperature of a gas kept at a constant volume is provided above. Volumes remaining constant, the pressure of given mass of a gas increases or decreases by Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry of its pressure at 0°C per degree change of temperature.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry   Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry   (if volume and number of moles are kept constant)

At constant volume, the pressure of a given amount of a gas is directly proportional to its absolute temperature.

Avogadro’s Law

(i)  For Solid, liquid and gas

1 mole of any substance contains Avogadro’s number (NA) of molecules/atoms/particles etc.

                                                            NA = 6.023 × 1023

(ii) For gases:

In 1812, Amadeo Avogadro stated that samples of different gases which contain the same number of molecules (any complexity, size, shape) occupy the same volume at the same temperature and pressure. It follows from Avogadro’s hypothesis that  v  ∝ n (T and P are constant)

                                                     v  ∝ n (T, P constant) =  Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

            STP: 273.15 K            1 atm

            SATP: 298.15 K         1 bar

Ideal Gas Equation

Combining all these gas laws, a simple equation can be derived at, which related P, V, n and T for a gas

            PV = nRT                    (for n moles of gas)

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

       Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry     (Combined gas law)

P is the pressure of the gas and can be expressed in atm of Pa. Correspondingly, the volume must be expressed in litres or m3 respectively. n is the number of moles and T is the temperature in Kelvin. R is called the universal gas constant.

Numerical Values of R

(i)         In litre atmosphere = 0.0821 litre atm deg–1 mole–1

(ii)        In ergs = 8.314 × 107 erg deg–1 mole–1

(iii)       In jouls = 8.314 jouls deg–1 mole–1

(iv)       In calories = 1.937 cal deg–1 mole–1


Relation between Molecular Mass and Gas Densities

  • Actual density:  For an ideal gas PV = nRT or Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  where w = mass of the gas in gms and

M = Molecular wt. in gms.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry      or Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry = Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

(i)   Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry     Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

(ii)    Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry    Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

            (where d = density of gas)

  • Vapour Density:  for gases another term which is often used is vapour-density. Vapour density of a gas is defined as the ratio of the mass of the gas occupying a certain volume at a certain temperature and pressure to the mass of hydrogen occupying the same volume at the same temperature and pressure i.e. W

 .Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry           
Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry (Vapour density of gas)

Vapour density of a gas is same at any temperature, pressure and volume.


Dalton’s Law of Partial Pressures:

 The total pressure of a mixture of non-reacting gases is equal to the sum of their partial pressures.

By Dalton’s Law PT = P1 + P2 + ………………..

By the partial pressure of a gas in a mixture is meant, the pressure that the gas will exert if it occupies alone the total volume of the mixture at the same temperature.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Derivation: n = n1 + n2 + ……………..

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - ChemistryIdeal Gas Laws: Revision Notes Notes | Study Physical Chemistry - ChemistryIdeal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Assumption: Volume of all the gases is same as they are kept in same container.

Relationship between Partial Pressure and Number of Moles

Important formula

(i)Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - ChemistryIdeal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

(ii) Partial pressure of gas in the mixture = Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

Partial pressure and Aqueous Tension

Dalton’s law is used to calculate the pressure of a dry gas when it is collected over water at atmospheric pressure.

By Dalton’s law,

Graham’s Law of Diffusion

Diffusion is the tendency of any substance to spread throughout the space available to it. Diffusion will take place in all direction and even against gravity.

The steaming of gas molecules through a small hole is called effusion.

According to Graham, the rate of diffusion (or effusion) of a gas at constant pressure and temperature is inversely proportional to the square root of its molecular mass.

       Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  , at constant P and T

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  at constant P and T

Since molecular mass of gas = 2 × vapour density, Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry at constant P and T 

The rate of diffusion (or effusion) r of two gases under different pressure can be given by

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry    at constant T only.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - ChemistryIdeal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry   

Therefore, according to Graham’s law of diffusion (effusion) at constant P and T.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

d1 and d2 are the respective densities and V1 and V2 are volumes diffused (effused) in time t1 and t2.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry    

Where n1, n2 are modes diffused (effused) in time t1 and t2

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry

 Where x1 and x2 are distances travelled by molecules in a narrow tube in time t1 and t2.

Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry
Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry
Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry  

The document Ideal Gas Laws: Revision Notes Notes | Study Physical Chemistry - Chemistry is a part of the Chemistry Course Physical Chemistry.
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