Gaseous States of Matter Semester-1 : ICY-101: CHEMISTRY-I, Unit III Dr. Tapta Kanchan Roy Assistant Professor Department of Chemistry & Chemical Sciences Central University of Jammu 1
The simplest state of matter is gaseous state Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa. Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m 3. A more common and convenient unit is the liter, L. Temperature is the measurement of heat or how fast the particles are moving. Amount of substance is tricky. Counting molecules is a daunting task. But counting in terms of mole is easy.. Using molecular weight of the gas one can easily convert measured mass (in g or kg) to the number of moles, n. 2
The simplest state of matter is gaseous state Physical Characteristics Volume, V Pressure, P Temperature, T Number of atoms or molecules, n Typical Units liters (L) Pascal 1 Pa= 1 N m 2, 1 kg m 1 s 2 Atmosphere (1 atm = 1.015x10 5 N/m 2 ) Kelvin (K) mole (1 mol = 6.022x10 23 atoms or molecules) Each substance can be described by an equation that interrelates four variables: pressure, temperature, volume and number of moles of gas. This equation is called equation of state 3
Boyle s Law Pressure and volume are inversely proportional at constant temperature. PV = constant.. hence P 1 V 1 = P 2 V 2 Charles Law Volume of a gas is directly proportional to the absolute temperature at constant pressure. V = KT hence V 1 / T 1 = V 2 / T 2 Avogadro s Law The volume of a gas is directly proportional to the number of moles at constant temperature and pressure. V = K n hence. V 1 / n 1 = V 2 / n 2 4
Combining all equations. The equation of state for ideal/perfect gas : pv = nrt The value of R (gas constant) ---------------------------------------------------- 8.314 J K 1 mol 1 8.205 10 2 dm 3 atm K 1 mol 1 8.314 10 2 dm 3 bar K 1 mol 1 8.314 Pa m 3 K 1 mol 1 1 62.364 dm 3 Torr K 1 mol 1 1.987 cal K 1 mol 1 5
Gas laws: The perfect gas law: pv = nrt increasing T decreasing P decreasing V Pressure, p increasing T Pressure, p Volume, V Pressure, p Inverse of volume, 1/V P-V isotherm Pressure-volume dependence of a fixed amount of perfect gas at different T. It is a Hyperbolic curve and is called isotherm. Along a line the T is constant Inverse of volume, 1/V Temperature, T Temperature, T Isotherm Isobars Isochores Isotherm: Straight lines are obtained when P is plotted against 1/V at constant T 6
Mixture of gases: Dalton s Law of partial pressure : The total pressure of a gas mixture of gases is equal to the sum of the partial pressure of the constituents gases OR The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. P Total = P 1 + P 2 + P 3 + P 4 + P 5. p j = partial pressure, x j = mole fraction 7
Real Gases The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases. Most real gases deviate from ideal behaviour at low temperature high pressure Differences Between Ideal and Real Gases Ideal Gas Real Gas Obey PV=nRT Always Only at very low P and high T Molecular volume Zero Small but nonzero Molecular attractions/repulsion Zero Present (depends on intermolecular distances) 8
Real Gases The variation of the potential energy of two molecules on their separation. Short distance repulsive force assist expansion Long/intermediate distance a rac ve force assist compression Very large distance no interaction between the molecules. Ideal gas Real gas 9
Real Gases The compression factor Z PV RT Compressible factor of a gas is the ratio of its measured molar volume (V m = V/n) to the molar volume of a perfect gas (V m0 ) at the same pressure and temperature m Z For perfect gas Z = 1, p/atm For real gas : i) At low pressure: z 1 ii) At high pressure z > 1 (repulsion force are dominant, larger molar volume than perfect gas) i) At intermediate pressure, z< 1 (attractive forces are reducing the molar volume) C 2 H 4 10
Real Gases Virial coefficients: the small difference between ideal gas law and real gas suggests that the first term in an expression of the form p/atm -- a more convenient form : V m / dm 3 mol -1 - The coefficient B, C.. etc depends on temperature. Experimental isotherm of water at several temp. It is important to note that, the equation of state of real gas may coincide with prefect gas law as p 0. not all its properties necessarily Coincide with those of a perfect gas as p 0 Check for : dz/dp Condensation is one phenomenon that observed along the line through by the points M, W 11
Critical Constants Real Gases Critical temperature (T c ) - the temperature above which a gas cannot be liquefied Critical pressure (P c ) the minimum pressure that needs to be applied at T c to bring about liquefaction The van der Waal's Equation of State Real molecules do take up space and do interact with each other (especially polar molecules). So, we need to add correction factors to the ideal gas law to account for these. Real gas molecules posit molecular interactions: (P ideal = P obs + constant) Real gas molecules are not point masses but occupy some volume: (V ideal = V obs - constant) 12
Real Gases V id = V obs - nb : b is a constant for different gases P id = P obs + a (n / V) 2 : a is also different for different gases combining together: The van der Waal's Equation Boyle temperature - for a van der Waal's gas, the Boyle temperature (T B ) is written as At this temperature the properties of the real gas do coincide with those of a perfect gas as p 0 T B a Rb Critical Constants for Van der Waals s Gases At the critical point T c V c 8a ; 27Rb a Pc 27b PV c c Z c RT 3 b; 2 c 0. 375 13
Real Gases Reduced Variables The reduced state variables are defined as: V r V V c T ; r T T P c r P P c The Law of Corresponding States All substances obey the same equation of state in terms of the reduced variables So, Real gases at he same reduces volume and reduced temperature exerts the same reduced pressure is called the principle of corresponding states Z Reduced pressure 14
Suggested reading Atkin s Physical Chemistry, 10 th ed. By P. W. Atkins and J. de Paula, Oxford (2014) Physical Chemistry by I. N. Levine, McGraw-Hill Higher Education; 6 edition (2008) 15