Gas Law for Real Gases Van Der Waals Equation

Lecture 7 Real gases While the ideal gas law is the same for every gas, there are two effects in all real gases that are important at high gas densities due to temperatures close to condensation or very high pressures . • Real gases • Gas law for real gases: van der Waals equation Ch10: Solids, liquids and phase transitions • Intermolecular forces IMF : H-bond, dipole-dipole, London • IMFs determine relative boiling points 2 8 Real gases TP The density of H O 𝑔 is 0.0327 and the density of H O 𝑙 is 0.958 . Calculate how much space is taken up by the water molecules in 1 L of gaseous water at 100℃. The first effect is due to gas particles themselves taking up space. For example, we have seen that at 100℃, the density of H O 𝑔 is 0.0327 and the density of H O 𝑙 is 0.958 9 1. 2. 3. 4. 5. 6. . 0.0001 L 0.0006 L 0.001 L 0.006 L 0.01 L 0.06 11 1 Real gases Real gases The density of H O 𝑔 is 0.0327 and the density of H O 𝑙 is 0.958 the volume taken up by the gaseous water as a liquid would be 0.0327 mol 𝑉 . . More generally, the volume of the container is expressed as empty space 𝑉 plus that taken up by the molecules themselves, , so 𝑉 0.000614 L This means that . 100% 𝑉 𝑏𝑛 Here the parameter van der Waals 𝑏 is the volume taken up by one mole of the molecules of the substance. 0.06% of the 1-L volume is taken up by the water molecules, 1L 𝑉 𝑉 . 12 13 Real gases 𝑉 𝑉 Real gases 𝑏𝑛 The second effect is due to attraction of the gas particles for one another. At high pressures, the volume of the molecules of a gas 𝑏𝑛 is no longer negligible relative to the volume of the container 𝑉 . 14 This attraction lessens the impact of each particle with the container walls and so reduces the pressure. 15 2 Real gases Real gases The reduction in pressure is proportional to the number of particles hitting the wall and the number of neighboring particles lessening each particle’s impact with the wall, The ideal gas law relates 𝑃 𝑃 𝑃 Using the expressions 𝑉 ,𝑃 𝑏𝑛 and 𝑃 𝑉 𝑉 𝑛𝑅𝑇. 𝑃 𝑎 , we can rewrite the ideal gas law in terms of actual pressure and the actual container volume, 𝑎 𝑃 The parameter van der Waals 𝑎 is a measure of the intermolecular attraction exerted between particles of the gas. 16 and 𝑉 𝑎 𝑉 𝑏𝑛 𝑛𝑅𝑇 This is known as the van der Waal equation. 17 Real gases Working with the van der Waals equation Computations with the van der Waals equation are usually done by rearranging it for the observed pressure, 𝑃 𝑃 𝑎 and 𝑅 0.08314 L bar/ K mol For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What are the ideal and observed pressures of 3.00 mol of Cl2 confined in 4.00 L at 500. K? 𝑎 and using tabulated values of van der Waals 𝑎 and 𝑏. 18 19 3 Working with the van der Waals equation 𝑃 𝑎 and 𝑅 Working with the van der Waals equation 0.08314 L bar/ K mol 𝑃 For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What are the ideal and observed pressures of 3.00 mol of Cl2 confined in 4.00 L at 500. K? 𝑃 𝑎 0.08314 L bar/ K mol For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What are the ideal and observed pressures of 3.00 mol of Cl2 confined in 4.00 L at 500. K? 𝑃 31.3 bar confirm yourself 𝑃 20 and 𝑅 31.3 bar confirm yourself 𝑎 32.5 bar 3.7 bar 28.8 bar confirm yourself 21 Working with the van der Waals equation 𝑃 𝑎 and 𝑅 Working with the van der Waals equation 0.08314 L bar/ K mol 𝑃 For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What are the ideal and observed pressures of 3.00 mol of Cl2 confined in 4.00 L at 500. K? 𝑃 𝑃 𝑎 and 𝑅 0.08314 L bar/ K mol For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What are the ideal and observed pressures of 3.00 mol of Cl2 confined in 4.00 L at 3000. K? 31.3 bar confirm yourself 𝑎 32.5 bar 3.7 bar 28.8 bar confirm yourself Since the observed pressure is smaller than the ideal pressure, the effect of 𝑎 is more important than 𝑏 at 500. K. 22 23 4 Working with the van der Waals equation 𝑝 𝑎 and 𝑅 Working with the van der Waals equation 0.08314 L bar/ K mol 𝑃 For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What are the ideal and observed pressures of 3.00 mol of Cl2 confined in 4.00 L at 3000. K? 𝑃 𝑃 𝑎 and 𝑅 0.08314 L bar/ K mol In general, the effect of 𝑏 is muted at low 𝑇 and so the effect of 𝑎 dominates there, while for high 𝑇 the effect of 𝑏 dominates. 187.1 bar confirm yourself 𝑎 195.3 bar 3.7 bar 191.6 bar confirm yourself Since the observed pressure is larger than the ideal pressure, the effect of 𝑏 is more important than 𝑎 at 3000. K. 24 25 Working with the van der Waals equation 𝑃 𝑎 and 𝑅 Working with the van der Waals equation 0.08314 L bar/ K mol 𝑃 𝑎 and 𝑅 0.08314 L bar/ L mol For Cl2, 𝑎 6.58 bar L2/mol2 and 𝑏 0.0562 L/mol. What is the observed and ideal pressures of 8.00 mol of Cl2 confined in 4.00 L at 27 ℃? Use In general, the effect of 𝑏 is muted at low 𝑇 and so the effect of 𝑎 dominates there, while for high 𝑇 the effect of 𝑏 dominates. For 3.00 mol of Cl2 confined in 1 versus 𝑇. 4.00 L, here is 𝑃 𝑃 49.9 bar 𝑎 56.2 bar 26.3 bar 29.9 bar Since the observed pressure is smaller than the ideal pressure, the effect of 𝑎 is more important than 𝑏 at 27 ℃ 26 27 5 Why intermolecular forces (IMF)? 𝑎 𝑏 L2bar/mol2 3.640 0.04267 L/mol 28 We know from the van der Waals equation that gases attract one another. Indeed, if they did not, they would not liquify. 29 Intermolecular forces: electrical stickiness! Molecules attract one another, because of the attraction of opposite electrical charges. Hydrogen bonding The most specific and strongest IMF is “hydrogen bonding”: X—H ∙ ∙ ∙ Y More common and of intermediate strength IMF is “dipole-dipole attraction”: Always present and weakest IMF is “temporary dipole attraction” “London force” : 30 31 6 Ice and water 32 Ice and water 33 Hydrogen bond angle is 180° 34 Hydrogen bonds are longer than typical bonds 35 7 TP Which of the following cannot form H-bonds between themselves? 1. 2. 3. 4. 5. 6. 7. 8. Dipole-dipole attraction Ammonia, NH3 Methanol, CH3OH Ethanol, CH3CH2OH Dimethyl ether, CH3OCH3 1 and 3 1 and 4 2 and 4 All of the above can form hydrogen bonds with themselves 36 Molecules must be “polar” What makes a molecule polar is unequal sharing of electron clouds. Sharing tendency is proportional to electronegativity difference. The greater the difference of electronegativities, the more unequal the sharing, the more polar the shared electron cloud. 37 TP Which of the following has dipole-dipole IMFs. 1. 2. 3. 4. 5. 6. 38 Instantaneous dipoles → London forces BFCl2, whose shape is trigonal-planar, like that of BF3 SCl2, which is a bent molecule, like H2O NH2Cl, whose shape is trigonal-pyramidal, like that of NH3 OCS, which is a linear molecule, like CO2 All of the above None of the above When one atom encounters another closely, the electrical repulsion between the electron clouds is similar to mismatched off-resonance interaction of light and matter. The result is the electron clouds of all atoms always quiver slightly. 40 8 Instantaneous dipoles → London forces Instantaneous dipoles → London forces This quivering means that electron clouds are momentarily lopsided, with the result that atom have momentary electrical dipoles. Should another atom pass nearby, the momentary dipole will induce a dipole in the neighboring atom. 41 42 Instantaneous dipoles → London forces Relative boiling points The net result is that electron clouds on neighboring atoms and molecules attract one another, due to the London force. Boiling means particles overcome attraction to their neighbors and depart the liquid. Relative boiling points reflect relative strength of intermolecular forces … London dispersion Dipole-dipole interaction Hydrogen bonding 43 44 9 Why is SnH4 < SbH3 < TeH2? 46 Why is CH4 < SiH4 < GeH4 < SnH4? 47 10