Ideal Gases-Microscope Definition We define an ideal gas to have the following properties: 1- There are no atomic interactions among the molecules or atoms comprising the gas, therefore, there is no internal potential energy P.E resulting from such interactions, only kinetic energy 2- The sizes of the atoms or molecules is extremely small compared with their separations. 3- when the basic particles collide, they do so in a perfectly elastic way

T constant (isothermal)P constant (isobaric) V constant (isochoric) parabolas Straight line

Combinig these three relationships we get PV=nRT or PV=RT n= numper of moles N=numper of molecules NA= Avogadro cnstant m= mass of gas M W = molar weight of gas R= gas constant

Kinetic Theory of Gases Kinetic theory of gases was built on several assumption which are:

Calculate the pressure of an ideal gas from Kinetic Theory We consider a gas in a cubical vessel whose walls are perfectly elastic. Let each edge be of length L. call the faces normal to the x-axis A 1 and A 2 each of area L 2. Consider a molecule which has a velocity v which resolve into components v x, v y, and v z. If particle collides with A 1, it rebound with its x- component of velocity reversed. ∆P= mv x -(-mv x ) =2mv x Average force

Pressure of gas equal in all direction The root-mean square speed of the molecules is Units of pressure 1- dyne/cm 2 if ρ = g/cm 3 and C = cm/s 2- N/m 2 if ρ = kg/m 3 and C = m/s 3- 1 pascal (Pa) = 1 N/m atom = ρ g h = 1.01 ᵡ 10 5 N/m 2 5- Bar

If V=1 The relationship between the kinetic energy and temperature:, n=N

The ideal gases laws from the kinetic energy theory of gases. 1-Boyle's law 2-charle's law If T is constant,C also constant M= m N If P is constant

Van der Waals Equation The Ideal Gas Law is based on the kinetic molecular theory assumptions that gases are composed of point masses that undergo perfectly elastic collisions, gas particles are much smaller than distance between particles, therefor the volume of a gas is mostly empty space and the volume of the gas molecules themselves is negligible, and there is no force of attraction between gas particles or between the particles and the walls of the container. However, real gases deviate from those assumptions at low temperatures or high pressures. The van der Waals equation is: where P is the pressure, V is the volume, R is the universal gas constant, n is number of moles and T is the absolute temperature. The constants a and b represent the magnitude of intermolecular attraction and excluded volume respectively, and are specific to a particular gas.

1-To calculate volume of real gas: Approximate V → nR/TP 2-To calculate pressure of real gas: Diviation are greater if: 1- intermolecular attractive forces are greater. 2- mass and subsequently volume of gas molecules is greater High T and low P Low T and high P Conditions are (Ideal) at Conditions are (Real) at

3- Calculation the temperature of Boyle T B : At T=T B

If T< TB b≈ 0 PV< RT Decreases the pressure increases PV> RT And increases with pressure