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Behaviour Of Gases: Charle's Law,Boyle's law,Ideal Gas Law,Dalton's law of partial pressures




Gas Laws


    Gas laws are study of any two of quantities like pressure, volume and temperature, when the third is kept constant

    A. Boyle's law

  • "At constant temperature, the volume of a given mass of gas is inversely proportional to pressure." Thus
                   V ∝ 1/P
    Or,                PV = constant               (1)
  • If P1, V1are initial pressure and volumes and P2, V2be final values then,               
         P1V1= P2V2                    
  • Graph between P and V at temperature T1 and T2 such that T1<T2 are shown below,

    Boyle's law
  • Graph above shows that Boyle's law is strictly not obeyed by gases at all values of P and T but it obeys this law only at low pressure and high temperature i.e., at law density
B. Charle's Law
  • Charle's Law is stated as follows :
    "When pressure of a gas is constant the volume of a given mass of gas is directly proportional to its absolute temperature".
                   V/T = Constant               (2)
  • Graph between V and T is

    Charle's Law
    This graph shows that experimental graph deviates from straight line. Theoretical and experimental graphs are in agreement at high temperature.



Ideal gas equation


  • We can combine Boyle' law eqn (1) and Charle's' law eqn (2) in to a single eqn i.e.,
         PV/T = Constant          (3)
    If n moles is the mass of gas then we write
         PV = nRT               (4)
    where, n is number of moles of gas, R=NAKB is the universal constant known as gas constant and T is the absolute temperature.
  • A gas satisfying eqn (4) at all values of pressures and temperatures is said to be an ideal gas
    now no of moles of gas
         n = m/M = N/NA
    where
         m - mass of gas containing N molecules
         M - molar mass
         NA - Avogadro' number.
    From this,
         P = ρRT/M
         ρ - mass density of gas.

Concept Map of Ideal Gas

Dalton law of partial pressures :


  • Consider a mixture of non-interacting ideal gases with n1 moles of gas 1,n2 of gas 2 and so on
  • Gases are enclosed in an enclosure with volume V, temperature T and pressure P.
  • Equation of state of mixture
         PV = (n1+ n2)RT
    or     P = n1RT/V + n2RT/V + - - - -
          = P1 + P2 + - - --
    where,
         P1 = n1RT/V
    is pressure the gas 1 would exert at same V and T if no other gases were present in the enclosure. This is know as law of partial pressure of the gases.
  • The total pressure of mixture of ideal gases is sum of partial pressures of individual gases of which mixture is made of.


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