Molecular Velocity and its Distribution PDF

MOLECULAR VELOCITY AND ITS DISTRIBUTION Dr. I.A. Akinbulu 1 Definition: Molecular velocity is defined as the velocity of an individual molecule in a particular sample of gas Distribution of molecular velocity Distribution of molecular velocities was investigated b...

MOLECULAR VELOCITY AND ITS DISTRIBUTION Dr. I.A. Akinbulu 1 Definition: Molecular velocity is defined as the velocity of an individual molecule in a particular sample of gas Distribution of molecular velocity Distribution of molecular velocities was investigated by Maxwell and Boltzmann It depends on temperature and molecular weight of a gas In three dimensions, the distribution is given by the equation 2 But k = R/NA But NAm = M f(v) is probability with a unit of reciprocal speed Molecular velocity distribution curve is represented graphically as a plot of probability versus velocity, at constant temperature 3 Typical Molecular Velocity Distribution Curve 4  Features of Molecular Velocity Distribution Curve o Probability increases with increasing velocity, reaches a maximum and begins to decrease o As temperature increases, the most- probable speed shifts to higher value, the curve becomes broader, but retains its shape o At the same temperature, the fraction of molecules with higher velocities increases as molecular weight decreases 5 Effect of Temperature on Molecular Velocity Distribution Curve 6 Effect of molecular weight on Molecular Velocity Distribution Curve 7  Velocities Associated with Molecular Velocities Distribution Curve o Most-probable velocity: It is the velocity possessed by maximum number of molecules of a gas at a particular temperature. It is the speed most likely to be possessed by any molecule (of the same mass) in the system o Mean velocity: Is the average of the various velocities possessed by the molecules 8 o Root-mean square velocity: Is the square root of the average of the square of the velocity of a large number of molecules of the same gas 9 Worked Example: Methane is a green house gas, associated with global warming. Calculate (a) the most-probable velocity, (b) the mean velocity and (the root-mean square velocity of methane at 40°C. [Molar mass of CH4 = 16 g/mol, Molar gas constant = 8.314 J/mol/K] Solution: Molar mass of CH4 = 16 g/mol = 0.016 kg/mol (a) vp = 570.34 m/s 1 0 (b) (c) 1 1 Kinetic Energy and Temperature 12  Deductions from equation 15 o Average kinetic energy is directly proportional to temperature o At zero Kelvin, molecular motion ceases N.B.: Average kinetic energy is limited to translational motion 1 3