Chapter 3 Gases Dr.Imededdine Arbi Nehdi Chemistry Department, Science College, King Saud University © 2009, Prentice-Hall, Inc.

Characteristics of Gases Unlike liquids and solids, gases (H2, F2, O2,CO2, NH3, He, Ar, Xe, …) expand to fill their containers; are highly compressible; have extremely low densities. Gases form homogeneous mixtures with each other regadless of the identities or relative proportions of the component gases. © 2009, Prentice-Hall, Inc.

Pressure F P = A Pressure is the amount of force applied to an area. (N/m2) The SI unit of pressure is N/m2. It is given the name pascal (Pa). Atmospheric pressure is the weight of air per unit of area. © 2009, Prentice-Hall, Inc.

Units of Pressure SI unit is N/m2 (Pa) Bar 1 Pa = 1 N/m2 = kg/m.s2 non-SI unit: atm, bar, mmHg, Torr Atmosphere 1.00 atm = 760 mm Hg = 760 torr 1.00 atm = 1.01325 x105 Pa = 101.325 kPa Bar 1 bar = 105 Pa = 100 kPa © 2009, Prentice-Hall, Inc.

Standard Pressure Normal atmospheric pressure at sea level is referred to as standard pressure. It is equal to 1.00 atm 760 torr (760 mm Hg) 101.325 kPa © 2009, Prentice-Hall, Inc.

Standard temperature and pressure conditions (STP) The conditions 0C and 1 atm are referred to as the standard temperature and pressure (STP). © 2009, Prentice-Hall, Inc.

Units of Pressure mm Hg or torr These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury. Mercury barometer Atmosphere 1.00 atm = 760 mm Hg = 760 torr © 2009, Prentice-Hall, Inc.

Manometer This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel. Open-end manometer © 2009, Prentice-Hall, Inc.

Figure 1: cylinder and piston © 2009, Prentice-Hall, Inc.

The Gas Laws © 2009, Prentice-Hall, Inc.

Boyle’s Law (The Pressure-Volume relationship) Boyle`s law: The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. © 2009, Prentice-Hall, Inc.

As P and V are inversely proportional A plot of V versus P results in a curve. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line. PV = k © 2009, Prentice-Hall, Inc.

Charles’s Law (The Temperature- Volume relationship) The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. i.e., V T = k A plot of V versus T will be a straight line. © 2009, Prentice-Hall, Inc.

Avogadro’s Law (The Quantity- Volume relationship) The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. Mathematically, this means V = kn © 2009, Prentice-Hall, Inc.

Ideal-Gas Equation V  nT P So far we’ve seen that V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avogadro’s law) Combining these, we get V  nT P © 2009, Prentice-Hall, Inc.

Ideal-Gas Equation PV = nRT nT P V  nT P V = R or The relationship then becomes or PV = nRT ideal-gas equation An ideal gas is a hypothetical gas whole pressure, volume, and temperature behavior is completely described by ideal-gas equation. © 2009, Prentice-Hall, Inc.

Gas constant R The constant of proportionality is known as R, the gas constant. © 2009, Prentice-Hall, Inc.

The molar volume of an ideal gas at STP - The conditions 0C and 1 atm are referred to as the standard temperature and pressure (STP). Suppose we have 1.000 mol of an ideal gas at 1.000 atm and 0.00 C (273.15 K). Then , from the ideal-gas equation the volume of the gas is: V = nRT/P = (1.000 x 0.08206 x 273.15)/1.000 = 22.41 L - The volume occupied by 1 mol of ideal gas at STP, 22.41 L, is known as the molar volume of an ideal gas at STP. © 2009, Prentice-Hall, Inc.

Densities of Gases n P V = RT If we divide both sides of the ideal-gas equation by V and by RT, we get n V P RT = © 2009, Prentice-Hall, Inc.

Densities of Gases n   = m P RT m V = We know that moles  molar mass = mass n   = m So multiplying both sides by the molar mass ( ) gives P RT m V = © 2009, Prentice-Hall, Inc.

Densities of Gases P RT m V = d = Mass  volume = density So, Note: One only needs to know the molar mass (M), the pressure, and the temperature to calculate the density of a gas. © 2009, Prentice-Hall, Inc.

Molecular Mass P d = RT dRT P  = We can manipulate the density equation to enable us to find the molar mass (M) of a gas: P RT d = Becomes dRT P  = © 2009, Prentice-Hall, Inc.

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. In other words, Ptotal = Pt = P1 + P2 + P3 + … Pi (i= 1, 2, 3, …) = niRT/V © 2009, Prentice-Hall, Inc.

Pt = n1RT/V + n2RT/V + n3RT/V + …. Pt = P1 + P2 + P3 + … Pi (i= 1, 2, 3, …) = niRT/V Pt = n1RT/V + n2RT/V + n3RT/V + …. Pt = (n1+ n2+ n3 + ….)RT/V = nt RT/V ntotal = nt = n1+ n2+ n3 + …. © 2009, Prentice-Hall, Inc.

Partial pressures and Mole Fractions Pi/Pt = (niRT/V)/ (ntRT/V) = ni/nt ni/nt is called the mole fraction of gas i, which denote Xi X 1 + X2 +X3 + ….. = 1 Pi = Xi Pt © 2009, Prentice-Hall, Inc.

Partial Pressures When one collects a gas over water, there is water vapor mixed in with the gas. To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure. © 2009, Prentice-Hall, Inc.

Kinetic-Molecular Theory This is a model that aids in our understanding of what happens to gas particles as environmental conditions change. The pressure of a gas is caused by collisions of the gas molecules with the walls of their container. © 2009, Prentice-Hall, Inc.

Main Tenets of Kinetic-Molecular Theory (Five statements) 1)Gases consist of large numbers of molecules that are in continuous, random motion. 2)The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. 3) Attractive and repulsive forces between gas molecules are negligible 4) Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant. 5) The average kinetic energy of the molecules is proportional to the absolute temperature © 2009, Prentice-Hall, Inc.

Main Tenets of Kinetic-Molecular Theory The individual molecules move at varying speeds. At any instant some of them are moving rapidly, others more slowly. The molecules in a sample of gas have an average kinetic energy and hence an average speed. © 2009, Prentice-Hall, Inc.

Main Tenets of Kinetic-Molecular Theory - This figure illustrates the distribution of molecular speeds for nitrogen gas at 0C and at 100C. - The curve shows the fraction of molecules moving at each speed. At higher temperatures a larger fraction of molecules is moving at greater speeds. u0 < u100 © 2009, Prentice-Hall, Inc.

Main Tenets of Kinetic-Molecular Theory This figure also shows the value of the root-mean-square(rms) speed, u, of the molecules at each temperature. The average speed  u The average kinetic energy of the gas molecules,, is related directly to u2 :  = ½ m u2 ( m – mass of molecule) The average kinetic energy of the molecules is proportional to the absolute temperature. At any given temperature the molecules of all gazes have the same average kinetic energy T u and  u =  3RT/M M- molar mass M u © 2009, Prentice-Hall, Inc.

Effusion Effusion is the escape of gas molecules through a tiny hole into an evacuated space. © 2009, Prentice-Hall, Inc.

Graham's Law: The effusion rate of a gas is inversely proportional to the square root of its molar mass. Assume that we have two gases at the same temperature and Pressure in containers with identical pinholes. If the rate of effusion of the two substances are r1 and r2, and their respective molar masses are M1 and M2, Graham`s law states: r1/r2 =  M2/M1 r1/r2 = u1/u2 =  3RT/M1 =  M2/M1 3RT/M2 This equation indicates that under identical condition, the lighter gas effuses more rapidly © 2009, Prentice-Hall, Inc.

Effusion The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster. © 2009, Prentice-Hall, Inc.

Diffusion -Diffusion is the spread of one substance throughout a space or throughout a second substance. Diffusion, like effusion, is faster for light molecules than heavy ones. The relative rates of two gases under identical conditions is approximated by Graha`s law. Molecules collisions make diffusion more complicated than effusion Schematic illustration of the diffusion of a gas molecule. The path of the molecule of interest begins from the dot. Each short segment of line represents travel between collisions. The blue arrow indicates the net distance traveled by the molecule.

Real Gases -In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure. - At high pressures the deviation from ideal behaviour (PV/RT =1) is large. PV/RT versus pressure for 1 mol of several gases at 300 K. © 2009, Prentice-Hall, Inc.

Real Gases Even the same gas will show wildly different behavior under high pressure at different temperatures. PV/RT versus pressure for 1 mol of nitrogen gas at three temperatures. As temperatures increases, the gas more closely approaches ideal behavior.

Deviations from Ideal Behavior The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature. © 2009, Prentice-Hall, Inc.

Corrections for Nonideal Behavior The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. The corrected ideal-gas equation is known as the van der Waals equation. © 2009, Prentice-Hall, Inc.

The van der Waals Equation ) (V − nb) = nRT n 2a V 2 (P + - a, b: the van der Walls constants © 2009, Prentice-Hall, Inc.