Gaseous State : Ideal Gas laws

 

GASEOUS STATE

The state of matter in which the molecular forces of attraction between the particles of matter are minimum, is known as gaseous state. It is the simplest state and shows great uniformity in behaviour.

 

Characteristics of gases

(1)     Gases or their mixtures are homogeneous in composition.

(2)     Gases have very low density due to negligible intermolecular forces.

(3)     Gases have infinite expansibility and high compressibility.

(4)     Gases exert pressure.

(5)     Gases possess high diffusibility.

(6)     Gases do not have definite shape and volume like liquids.

(7)     Gaseous molecules move very rapidly in all directions in a random manner i.e., gases have highest kinetic energy.

(8)     Gaseous molecules are loosely packed having large empty spaces between them.

(9)     Gaseous molecules collide with one another and also with the walls of container with perfectly elastic collisions.

(10)  Gases can be liquified, if subjected to low temperatures (below critical) or high pressures.

(11)   Thermal energy of gases >> molecular attraction.

(12)   Gases undergo similar change with the change of temperature and pressure. In other words, gases obey certain laws known as gas laws.

 

Measurable properties of gases

(1)     The characteristics of gases are described fully in terms of four parameters or measurable properties :

(i)      The volume, V, of the gas.

(ii)     Its pressure, P

(iii)    Its temperature, T

(iv)    The amount of the gas (i.e., mass or number of moles).

 

(2)     Volume : (i) Since gases occupy the entire space available to them, the measurement of volume of a gas only requires a measurement of the container confining the gas.

(ii)     Volume is expressed in litres (L), millilitres (mL) or cubic centimetres (cm3) or cubic metres (m3).

(iii)    1L = 1000 mL ; 1 mL = 10–3L

          1L = 1 dm3 = 103 cm3

          1m = 103 dm3 = 106 cm3 = 106 mL = 103 L

 

(3)     Mass : (i) The mass of a gas can be determined by weighing the container in which the gas is enclosed and again weighing the container after removing the gas. The difference between the two weights gives the mass of the gas.

(ii)     The mass of the gas is related to the number of moles of the gas i.e.

                                moles of gas (n) =  \frac { Mass\quad is\quad grams }{ Molar\quad mass } =\frac { m }{ M }

(iii)    Mass is expressed in grams or kilograms, 1 Kg = 103 g

 

(4)     Temperature : (i) Gases expand on increasing the temperature. If temperature is increased twice, the square of the velocity (V2) also increases two times.

(ii)     Temperature is measured in centigrade degree (oC) or celsius degree with the help of thermometers. Temperature is also measured in Fahrenheit (Fo).

(iii)    S.I. unit of temperature is kelvin (K) or absolute degree.

                                         K = oC + 273

(iv)    Relation between F and oC is   \frac { ^{ o }C }{ 5 } =\frac { { F }^{ o }-32 }{ 9 }

 

(5)     Pressure :  (i) Pressure of the gas is the force exerted by the gas per unit area of the walls of the container in all directions. Thus, Pressure (P) =  \frac { Force\quad (F) }{ Area\quad (A) } =\frac { Mass(m)\times Acceleration(a) }{ Area(a) }

(ii)     Pressure exerted by a gas is due to kinetic energy  of the molecules. Kinetic energy of the gas molecules increases, as the temperature is increased. Thus, Pressure of a gas  Temperature (T).

(iii)    Pressure of a pure gas is measured by manometer while that of a mixture of gases by barometer.

(iv)    Commonly two types of manometers are used,

(a) Open end manometer;

(b) Closed end manometer

(v)     The S.I. unit of pressure, the pascal (Pa), is defined as 1 newton per metre square. It is very small unit.

            1Pa = 1Nm–2 = 1 kg m–1 kg m–1 s–2

(vi)    C.G.S. unit of pressure is dynes cm–2.

(vii)   M.K.S. unit of pressure is kgf/m2. The unit kgf/cm2 sometime called ata (atmosphere technical absolute).

(viii) Higher unit of pressure is bar, KPa or MPa.

            1 bar = 105 Pa = 105 Nm–2 = 100KNm–2 = 100KPa

(ix)    Several other units used for pressure are

Name

Symbol

Value

bar bar 1bar = 105Pa
atmosphere atm 1 atm = 1.01325 × 105Pa
Torr

Torr

 1 Torr =  \frac { 101325 }{ 760 } Pa = 133.332 Pa
millimetre of mercury

mm Hg

1 mm Hg = 133.322 Pa

 

(x)     The pressure relative to the atmosphere is called gauge pressure. The pressure relative to the perfect vacuum is called absolute pressure.

            Absolute pressure = Gauge pressure + Atmosphere pressure.

(xi)    When the pressure in a system is less than atmospheric pressure, the gauge pressure becomes negative, but is frequently designated and called vacuum. For example, 16 cm vacuum will be

                                      \frac { 76-16 }{ 76 }   × 1.013 = 0.80 bar

(xii)   If ‘h’ is the height of the fluid in a column or the difference in the heights of the fluid columns in the two limbs of the manometer d the density of the fluid (Hg = 13.6 × 103 Kg/m3 = 13.6 g/cm3) and g is the gravity, then pressure is given by, Pgas = Patm + h dg 

 

(xiii) Two sets of conditions are widely used as ‘standard’ values for reporting data.

Condition

T

P

Vm (Molar volume)
S.T.P./N.T.P. 273.15 K 1 atm 22.414 L
S.A.T.P*. 298.15 K 1 bar 24.800 L

 

Standard Ambient temperature and pressure.

 

Boyle’s law

(1)     In 1662, Robert Boyle discovered the first of several relationships among gas variables (P, T, V).

(2)     It states that, “For a fixed amount of a gas at constant temperature, the gas volume is inversely proportional to the gas pressure.”

                                      Thus, P ∝  \frac { 1 }{ V }   at constant temperature and mass

                                      or P = \frac { K }{ V }   (where K is constant)

                                      or  PV = K                                                                  

                   For two or more gases at constant temperature and mass.

                                      P1V1 = +2V2 = …… = K

                   Boyle’s law can also be given as,   \left( \frac { dV }{ dP } \right) _{ T }=-\frac { K }{ { V }^{ 2 } }

 

(3)     Graphical representation of Boyle’s law : Graph between P and V at constant temperature is called isotherm and is an equilateral (or rectangular) hyperbola. By plotting P versus  \frac { 1 }{ V } , this hyperbola can be converted to a straight line. Other types of isotherms are also shown below,

 

Note :  The isotherms of CO2 were first studied by Andrews.

(4)     At constant mass and temperature density of a gas is directly proportional to its pressure and inversely proportional to its volume.

                   Thus, d ∝ P ∝  \frac { 1 }{ V }       [∴ V =  \frac { Mass }{ d } ]

                   or   \frac { { d }_{ 1 } }{ { d }_{ 2 } } =\frac { { P }_{ 1 } }{ P_{ 2 } } =\frac { { V }_{ 2 } }{ V_{ 1 } } ……. = K  

(5)     At altitudes, as P is low d of air is less. That is why mountaineers carry oxygen cylinders.

(6)     Air at the sea level is dense because it is compressed by the mass of air above it. However the density and pressure decreases with increase in altitude. The atmospheric pressure at Mount Everest is only 0.5 atm.