**Deviations from Ideal Behavior**

*All real gasses fail to obey the ideal gas law to varying degrees*

The ideal gas law can be written as:

For a sample of 1.0 mol of gas, n = 1.0 and therefore:

- The deviation from ideal behavior is large at high pressure
- The deviation varies from gas to gas
- At lower pressures (<10 atm) the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error

- As temperature increases the deviation from ideal behavior decreases
- As temperature decreases the deviation increases, with a maximum deviation near the temperature at which the gas becomes a liquid

- The gas molecules themselves occupy no appreciable volume
- The gas molecules have no attraction or repulsion for each other

*Real molecules, however, do have a finite volume and do attract one another*- At high pressures, and low volumes, the intermolecular distances can become quite short, and attractive forces between molecules becomes significant
- Neighboring molecules exert an attractive force, which will minimize the interaction of molecules with the container walls. And the apparent pressure will be less than ideal (PV/RT will thus be less than ideal).
- As pressures increase, and volume decreases, the volume of the gas molecules becomes significant in relationship to the container volume
- In an extreme example, the volume can decrease below the molecular volume, thus PV/RT will be higher than ideal (V is higher)
- At high temperatures, the kinetic energy of the molecules can overcome the attractive influence and the gasses behave more ideal
- At higher pressures, and lower volumes, the volume of the molecules influences PV/RT and its value, again, is higher than ideal

**The van der Waals Equation**

- The ideal gas equation is not much use at high pressures
- One of the most useful equations to predict the behavior of real gases was developed by Johannes van der Waals (1837-1923)
- He modified the ideal gas law to account for:
- The finite volume of gas molecules
- The attractive forces between gas molecules

- The van der Waals constants
*a*and*b*are different for different gasses - They generally increase with an increase in mass of the molecule and with an increase in the complexity of the gas molecule (i.e. volume and number of atoms)

Substance | a (L^{2} atm/mol^{2}) | b(L/mol) |

He | 0.0341 | 0.0237 |

H_{2} | 0.244 | 0.0266 |

O_{2} | 1.36 | 0.0318 |

H_{2}O | 5.46 | 0.0305 |

CCl_{4} | 20.4 | 0.1383 |

Example

Use the van der Waals equation to calculate the pressure exerted by 100.0 mol of oxygen gas in 22.41 L at 0.0°C

V = 22.41 L

T = (0.0 + 273) = 273°K

*a*(O

_{2}) = 1.36

**L**

^{2}atm/mol

^{2}

*b*(O

_{2}) = 0.0318

**L /mol**

*P*= 117

*atm*- 27.1

*atm*

*P*= 90

*atm*

- The pressure will be 90 atm, whereas if it was an ideal gas, the pressure would be 100 atm
- The 90 atm represents the pressure correction due to the molecular volume. In other words the volume is somewhat less than 22.41 L due to the molecular volume. Therefore the molecules must collide a bit more frequently with the walls of the container, thus the pressure must be slightly higher. The -27.1 atm represents the effects of the molecular attraction. The pressure is reduced due to this attraction.

good guide

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