Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Physical Chemistry

Created by: Asf Institute

Chemistry : Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

The document Ideal Gas Laws - Gaseous Chemistry Notes | EduRev is a part of the Chemistry Course Physical Chemistry.
All you need of Chemistry at this link: Chemistry

GASEOUS STATE

Introduction: 

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

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 independent 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

Def. The gases of 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 - Gaseous Chemistry Notes | EduRev

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

(ii) number of moles = Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

(iii) no. of moles = Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

When container contains more than one gas then 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 - Gaseous Chemistry Notes | EduRev

  • Volume

Def. 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

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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

  • Pressure

Def. Force acting per unit area

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev 

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

Def. Mass per unit volume

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Units:

             CGS= g/cm3

MKS = kg/m3

Relation : 1 kg/m3 = 10–3 g/cm3

Density of gases

Absolute density 

(mass per unit volume)

Relative density

(Relative to hydrogen turned as vapour density)

(i) Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

(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

(i) 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 - Gaseous Chemistry Notes | EduRev (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 - Gaseous Chemistry Notes | EduRev

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev 

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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 - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev 

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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 - Gaseous Chemistry Notes | EduRev  of its volume at 0°C.

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 - Gaseous Chemistry Notes | EduRev  Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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 - Gaseous Chemistry Notes | EduRev  or Ideal Gas Laws - Gaseous Chemistry Notes | EduRev   

Or     Ideal Gas Laws - Gaseous Chemistry Notes | EduRev     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 - Gaseous Chemistry Notes | EduRev (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.

Volumes remaining constant, the pressure of given mass of a gas increases or decreases by Ideal Gas Laws - Gaseous Chemistry Notes | EduRev of its pressure at 0°C per degree change of temperature.

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev   Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev   (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 - Gaseous Chemistry Notes | EduRev

            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 - Gaseous Chemistry Notes | EduRev     (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 - Gaseous Chemistry Notes | EduRev  where w = mass of the gas in gms and

M = Molecular wt. in gms.

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev      or Ideal Gas Laws - Gaseous Chemistry Notes | EduRev = Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

(i)   Ideal Gas Laws - Gaseous Chemistry Notes | EduRev     Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

(ii)    Ideal Gas Laws - Gaseous Chemistry Notes | EduRev    Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

            (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 - Gaseous Chemistry Notes | EduRev

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev           
Ideal Gas Laws - Gaseous Chemistry Notes | EduRev (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.

Derivation: n = n1 + n2 + ……………..

Ideal Gas Laws - Gaseous Chemistry Notes | EduRevIdeal Gas Laws - Gaseous Chemistry Notes | EduRevIdeal Gas Laws - Gaseous Chemistry Notes | EduRev

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 - Gaseous Chemistry Notes | EduRevIdeal Gas Laws - Gaseous Chemistry Notes | EduRev

(ii) Partial pressure of gas in the mixture = Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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 - Gaseous Chemistry Notes | EduRev  , at constant P and T

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev  at constant P and T

Since molecular mass of gas = 2 × vapour density, Ideal Gas Laws - Gaseous Chemistry Notes | EduRev 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 - Gaseous Chemistry Notes | EduRev    at constant T only.

Ideal Gas Laws - Gaseous Chemistry Notes | EduRevIdeal Gas Laws - Gaseous Chemistry Notes | EduRev   

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev    

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

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

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev
Ideal Gas Laws - Gaseous Chemistry Notes | EduRev
Ideal Gas Laws - Gaseous Chemistry Notes | EduRev  

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!
77 videos|83 docs|32 tests

Dynamic Test

Content Category

Related Searches

past year papers

,

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

,

Viva Questions

,

study material

,

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

,

Extra Questions

,

Ideal Gas Laws - Gaseous Chemistry Notes | EduRev

,

Semester Notes

,

Exam

,

Sample Paper

,

video lectures

,

Summary

,

Previous Year Questions with Solutions

,

Important questions

,

ppt

,

Objective type Questions

,

MCQs

,

practice quizzes

,

mock tests for examination

,

pdf

,

Free

,

shortcuts and tricks

;