Lecture 4 CH101 Physical Chemistry PDF

LECTURE 4 Dalton’s Law cont. Problem A) Determine the mole fraction of each gas in a mixture containing 54.0 grams of CO2 and 33 grams of N2. C= 12 O= 16 N= 14 B) Determine the partial pressure of each gas above if the total pressure of the CO2 and N2 mixture is 101.3 kPa. Solution:...

LECTURE 4 Dalton’s Law cont. Problem A) Determine the mole fraction of each gas in a mixture containing 54.0 grams of CO2 and 33 grams of N2. C= 12 O= 16 N= 14 B) Determine the partial pressure of each gas above if the total pressure of the CO2 and N2 mixture is 101.3 kPa. Solution: 54.0g A) CO2 = 1.23 mol CO2 44.0 g 33.0 g N = 1.18 mol N2 28.0 g 2 Total moles = 1.23 + 1.18 = 2.41 mol 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒎𝒐𝒍𝒆𝒔 𝒐𝒇 𝑪𝑶𝟐 1.23 XCO2 = = = 0.51 𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒎𝒐𝒍𝒆𝒔 2.41 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒎𝒐𝒍𝒆𝒔 𝒐𝒇 𝑵𝟐 1.18 XN2 = = = 0.49 𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒎𝒐𝒍𝒆𝒔 2.41 PCO2 =XCO2. Pt = (0.51)(101.3 kPa) = 51.7 kPa PN2 = XN2. Pt = (0.49) (101.3 kPa) = 49.6 kPa At a fixed temperature, the average kinetic energy of all gases is the same, regardless of its identity: Graham’s Law states that “ the effusion rate of a gas is inversely proportional to the square root of its molecular mass”.  KINETIC MOLECULAR THEORY OF GASES The postulates of the kinetic molecular theory of gases are: 1. Gases consist of large number of identical particles (atoms or molecules) that are so small and so far apart on the average that the actual volume of the molecules is negligible in comparison to the empty space between them.. This assumption explains the great compressibility of gases. 2. There is no force of attraction between the particles of a gas at ordinary temperature and pressure. The support for this assumption comes from the fact that gases expand and occupy all the space available to them. 3. Particles of a gas are always in constant and random motion. If the particles were at rest and occupied fixed positions, then a gas would have had a fixed shape which is not observed. 4. Particles of a gas move in all possible directions in straight lines. During their random motion, they collide with each other and with the walls of the container. Pressure is exerted by the gas as a result of collision of the particles with the walls of the container. 5. Collisions of gas molecules are perfectly elastic. This means that total energy of molecules before and after the collision remains same (There may be exchange of energy between colliding molecules but the sum of their energies remains constant). If there were loss of kinetic energy, the motion of molecules will stop and gases will settle down. This is contrary to what is actually observed. 6. At any particular time, different particles in the gas have different speeds and hence different kinetic energies. This assumption is reasonable because as the particles collide, we expect their speed to change. Even if initial speed of all the particles was same, the molecular collisions will disrupt this uniformity. 7. If a molecule has variable speed, then it must have a variable kinetic energy. In kinetic theory it is assumed that average kinetic energy of the gas molecules is directly proportional to the absolute temperature  BEHAVIOUR OF REAL GASES: DEVIATION FROM IDEAL GAS BEHAVIOUR Two types of curves are seen: 1. In the curves for H2 and He, as the pressure increases the value of pV also increases. 2. The second type of plot like CO and CH4. First , the pV value decreases with increase in p and reaches to a minimum value. After that pV value starts increasing. Real gases follow ideal gas equation only under high-temperature and low-pressure conditions.  Real gases show deviations from ideal gas law because molecules interact with each other. At high pressures molecules of gases are very close to each other. Molecular interactions start operating and molecules do not strike the walls of the Container due to molecular attractive forces. This affects the pressure exerted by the molecules on the walls of the container. Thus, the pressure exerted by the gas is lower than the pressure exerted by the ideal gas. Preal = Pideal - an2 / V2 an2 Pideal = Preal + 2 V  The volume occupied by the molecules also becomes significant because instead of moving in volume V, these are now restricted to volume (V–nb) where nb is approximately the total volume occupied by the molecules themselves.