PHYSICS-15-10- 11th (PQRS) SOLUTION

https://docs.google.com/document/d/1xiz3Ikd1skcfT86xmlDh1iRAKJYiEUxd/edit?usp=share_link&ouid=109474854956598892099&rtpof=true&sd=true States of Matter (Gaseous & Liquid) C H A P T E R Gaseous State : Measurable properties of gases; Gas laws - Boyle's law, Charle's law, Graham's law of diffusion, Avogadro's law, Dalton's law of partial pressure; Concept of Absolute scale of temperature; Ideal gas equation, Kinetic theory of gases (only postulates); Concept of average, root mean square and most probable velocities; Real gases, deviation from Ideal behaviour, compressibility factor, van der Waals equation, liquefaction of gases, critical constants. Liquid State : Properties of liquid - vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only). GASEOUS STATE BOYLE’S LAW P ∝ 1 at constant n and T. V THIS CHAPTER INCLUDES Boyle's law Charle's law P = 1.0 atm Increase Pressure Decrease Pressure P = 2.0 atm V = 0.5 L Boyle's Law representing Pressure-Volume relation Avogadro's law Dalton's law of partial pressures Graham's law of diffusion Kinetic theory of gases Distribution of Graphical Representation V PV P P molecular speeds Deviation from ideal behaviour (van der Waal's equation) Liquid state 1/V logP P log1/V CHARLE’S LAW V ∝ T at constant n and P. V = ⎛ t ⎞ t V0 ⎜1 + 273 ⎟ ⎝ ⎠ V V/T –273°C 0°C T T log T 1/T AVOGADRO'S LAW V ∝ n (P and T constant); 1 mole of every gas at STP occupies volume = 22.4 lit. Ideal Gas Equation On combining the Boyle’s law, Charles law and Avogadro’s law we get an equation known as ideal gas equation which correlate P, V, T, of a gas. ideal gas equation where R is a constant known as universal gas constant or molar gas constant. Numerical value of R R = 0.0821 litre atm K–1 mol–1 = 8.314 J K–1 mol–1 = 1.987 ≈ 2 cal K–1 mol–1 Other form of ideal gas equation. ⇨ ⇨ DALTON’S LAW OF PARTIAL PRESSURE The total pressure exerted by a mixture of two or more non-reacting gases in a definite volume is equal to the sum of individual pressures which each gas would exert if it occupies the same volume at a constant temperature P = p1 + p2 + p3 , P = (n1 + n2 + .......) RT V Pgas = Mole fraction of gas × Total pressure. no. of moles of gas = Total no. of moles of all gases × Total pressure GRAHAM’S LAW OF DIFFUSION Diffusion is the ability of gas to spread and occupy the whole volume. Under identical conditions of temperature and pressure, the rate of effusion/diffusion of a gas is inversely proportional to square root of its density. Rate of diffusion/effusion for two gases are related as r1 = r2 V1 / t1 = = = V2 / t2 where V = volume , t = time, M = molar mass, d = density, n = number of moles KINETIC THEORY OF GASES The postualates The gaseous molecules are considered to be the point masses. The volume of a molecule is negligible as compared to total volume of the gas. The molecules do not posses appreciable attraction. The collisions are perfectly elastic i.e. there is no loss of energy during the molecular collisions. The average kinetic energy of molecules is directly proportional to the absolute temperature of the gas. The effect of gravity on molecular motion is negligible. Based on Kinetic-Molecular Theory PV = 1 mNu2 3 m = Mass of one molecule N = Number of molecules in the container u = Root mean square velocity KE of n moles = 3 nRT, for n = 1 2 Average KE per molecule = 3 RT = 3 kT , k = Boltzmann’s constant 2 N0 2 DISTRIBUTION OF MOLECULAR SPEEDS Root mean square velocity (μrms) = Average velocity(μav) = Most probable velocity (μ ) = mp DEVIATION FROM IDEALITY (van der Waal’s EQUATION) A plot of PV- P at constant temperature for a number of gases shows deviations from ideal behaviour. Therefore PV = nRT can not be applied to these gases. Thus another equation must be sought in order to correlate P,V, T for these gases; which is van der waal’s equation. ⎛ ⎜P + ⎝ n2a ⎞ V − nb = nRT V P Causes of Deviation There are two objectionable postulates in the kinetic theory of gases. The volume of a molecule is negligible as compared to total volume of the gas. Actually gases molecules do posses some volume which account for the deviation. There is no intermolecular force of attraction between gaseous molecules. (There exists force of attraction between gaseous molecules otherwise liquefaction of gases would be impossible). By correcting these two postulates, we get an equation which can be applied to the gases which deviate from ideal behaviour. The deviation of a gas from ideal behaviour can also be expressed in term of compressiblity factor (Z). Z = PV RT [for 1 mole] for ideal gas Z = 1 for real gas Z > 1 or Z < 1 LIQUID STATE A liquid is composed of molecules that are constantly moving about at random, each undergoing billions of collisions per second. However strong attractive forces of the dipole-dipole, H-bonds, prevent them from moving as freely and as far apart as in a gas. Viscosity : Liquids flows as if they were divided into layers flowing over one another. Resistance offered to this flow is due to friction between two liquid layers and is called viscosity. Reciprocal of viscosity is called fluidity. Viscosity of a liquid decreases with rise of temperature. Coefficient of viscosity : The force in newtons per square metre required to maintain a difference of velocity of one metre per second between two parallel layers of the liquid at a distance of one metre from each other. It is expressed in Kg m–1 s–1. Liquids having stronger attractive forces are more viscous. Surface tension : The force that acts at right angles to an imaginary line of unit length at the surface of the liquid at rest. It is expressed in J m–2 or N m–1. Surface tension generally decreases with the rise of temperature. Liquids exhibit capillary action and make spherical drops. This can be explained on the basis of surface tension. IMPORTANT POINTS Critical temperature (Tc) : It is the temperature above which a real gas can not be liquefied whatever applied pressure may be Tc = 8a 27Rb Critical pressure (Pc) : It is the minimum pressure required to liquefy the gas at critical temperature P = a C 27b2 Critical volume (Vc) : The volume occupied by 1 mole of the gas at critical temperature and critical pressure is known as critical volume. VC = 3b Vc = 3 × 4Vm = 12Vm (Since b = 4V ) m Critical coefficient of a gas : RTc It is ratio of Pc Vc which is equal to 2.66 and remain constant for all the gases. Boyle's temperature (TB) : The temperature at which a real gas obey ideal gas equation at very low pressure is known as Boyle’s temperature. T = a B Rb Boyle's temperature of a gas is always higher than its critical temperature (Tc) ❑ ❑ ❑