Lecture No. 3: Properties of Gases (2) PDF

Lecture No. 3 Properties of Gases (2) 1 Difference between Diffusion and Effusion Diffusion is the complete spreading out and intermingling of the molecule of one gas among those of another gas, e.g., spreading of perfume molecule among the air molecules. Effusi...

Lecture No. 3 Properties of Gases (2) 1 Difference between Diffusion and Effusion Diffusion is the complete spreading out and intermingling of the molecule of one gas among those of another gas, e.g., spreading of perfume molecule among the air molecules. Effusion is the movement of gas molecules through an extremely tiny hole into a region of lower pressure. 2 6. Graham’s law of effusion Graham’s law: the rates of effusion of gases are inversely proportional to the square roots of their densities (d) when compared at identical pressures and temperatures. i.e., Effusion rate α 1/√d (at constant P and T) so, Effusion rate × √d = C* where C* is proportional constant and is virtually identical for all gases. If we have two gases, A and B, so: effusion rate(A) ´ da = effusion rate(B) ´ db = C * effusion rate(A) db = effusion rate(B) da 3  Kinetic Energy: is the energy of motion, every moving object and particles have kinetic energy. K. E = ½ m. V2 m : mass V : velocity or speed Speed is the Effusion rate. 4  If we have a container with two gases A and B. the kinetic energy for the two gases is the same at constant pressure and temperature. ½ ma. V2a = ½ mb. V2b m = molecular weight (mass), V = effusion rate ( speed) Mw1 ( Rate 1 )2 = Mw2 ( Rate 2 )2 ( Rate 1 )2 = Mw 2 ( Rate 2 )2 Mw 1 ( Rate 1 ) = √ Mw 2 ( Rate 2 ) √ Mw 1 Density ( d) = m / Vl Effusion Rate α 1/√Mw α 1/√d 5  Because the density of a gas is directly proportional to its formula mass, so effusion rate(A) db FM b = = effusion rate(B) da FM a where FMa and FMb are the formula masses of gases A and B. FM = Mwt 6 Problem Which effuses more rapidly and by what factor, ammonia or hydrogen chloride? Solution FM NH3 = 17.03 FM HCl = 36.46 effusion rate(NH 3 ) dHCl FM HCl 36.46 = = = = 1.463 effusion rate(HCl) d NH 3 FM NH 3 17.03 So, the effusion rate of Ammonia is 1.463 times faster than the rate effusion of Hydrogen Chloride 7 Kinetic Molecular Theory: [ KMT ] The kinetic theory of gases explains the macroscopic properties of gases, such as volume, pressure, temperature, and number of moles. KE = ½ mѴ2 So, KMT can be explain the macroscopic behavior of ideal gases, also the properties of gases as described by various gas laws. 8 Kinetic Molecular Theory: Assumptions of the Kinetic Molecular Gas: A gas consists of extremely small particles called Molecules. Gas molecules are in constant Random Motion in straight lines The distance between the molecules are very large which make the molecules moved in individual shape and no interaction between molecules and each other. All collisions between molecules are perfectly Elastic collision, that’s mean no loss of Kinetic Energy 9  The average Kinetic Energy of the particles depends on the Kelvin Temperature. If the Elastic Collision is occur on the wall of the gas container, it will be called the Pressure of the gas. Due to the distance between molecules is very large, the volume of particles is negligible compare to the volume of gas container. 10 7. Kinetic theory and the gas law Kinetic theory and gas temperature The peaks of the curves represent the most frequently experienced values of KE. The average value of the KE lies slightly to the right of the peak of each curve (because the curves are not symmetrical). Calculations based on the model of an gas showed that the product of pressure and volume, PV, is proportional to the average kinetic energy, KE, , i.e., PV α average KE From the ideal gas law, PV α T So, we can say, T α average KE 11 7. Kinetic theory and the gas law Kinetic theory and the pressure-volume law Using the model of an gas, it was able to show that gas pressure is the net effect of innumerable collisions made by the gas particles on the walls. Suppose that one wall of the gas container is moveable piston that we can push in (or pull out) and so change the gas volume. If we make the volume smaller without changing the temperature, no change would occur in the average kinetic energy of the molecules. But now there would be more gas particles per unit volume. 12 7. Kinetic theory and the gas law Kinetic theory and the pressure-volume law If we reduce the volume by one-half, we double the number of molecules per unit volume. This would double the number of collisions per second with a unit area and so double the pressure. PV = K as a constant at constant Temp. P α 1/V or V α 1/P (Boyle’s law) 13 7. Kinetic theory and the gas law Kinetic theory and the pressure-temperature law The kinetic theory tells us that an increase in gas temperature increases the average velocity of gas particles. At higher velocities, the particles must strike the container’s walls more frequently and with greater force. But at constant volume, the area being struck is still the same, so the force per unit area (i.e., pressure) must therefore increase, i.e., P α T or T α P (Gay-Lussac’s law) 14 7. Kinetic theory and the gas law Kinetic theory and the temperature-volume law The kinetic theory tells us that an increase in gas temperature increases the average kinetic energy of its particles, which tends to increase the pressure of the gas. The only way to keep pressure constant is to allow the gas to expand. Therefore, the gas expands with increasing temperature to keep the pressure constant, i.e., V α T or T α V (Charles’s law) 15 7. Kinetic theory and the gas law Kinetic theory and the law of effusion The conditions of Graham’s law are that the rates of effusion of two gases with different formula masses must be compared at the same pressure and temperature. Thus, when two gases have the same temperature, their particles have identical average kinetic energies, i.e., 16 Ideal and Real Gas In the several slides, we have talked about the ideal gas law, which tell us that P. V = n.R.T. The volume of gas is negligible to the volume of the container. The molecules of the gas don’t interact with each other. The term ‘Real Gas’ usually refers to a gas that does not behave like an ideal gas. Their behavior can be explained by the interactions between the gaseous molecules. These intermolecular interactions between the gas particles is the reason why real gases do not be the ideal gas law 17  Real gases (also known as non-ideal gases) are gases that do not follow the Kinetic molecular theory, so they deviate from being an ideal gas. The factors that make them real gases instead of ideal gases are: Real gases do occupy some volume. Real gases have some intermolecular (attractive) forces present. Real Gas Law The Van der Waal real gas equation is given below: æ n2 a ö ç P + 2 ÷ (V - nb) = nRT è V ø 18  This equation can be used for ideal gases as well as for real gases. The ideal gas law cannot be used for real gases because the volume of gas molecules is considerable when compared to the volume of the real gas, and there are attraction forces between real gas molecules (ideal gas molecules have a negligible volume compared to the total volume, and there are no attraction forces between gas molecules). The Van der Waal equation can be given as below. 19 20 21