Answers to discussion questions

1 An equation of state is an equation that relates the variables that define the state of a system to each other. 

Charles, and Avogadro established these relations for gases at low pressures (perfect gases) by appropriate experiments. Boyle determined how volume varies with pressure (V x /p), Charles how volume varies with temperature (V o T ), and Avogadro how volume varies with amount of gas (V oc n). Combining all of these proportionalities into one we find 

Inserting the constant of proportionality, R, yields the perfect gas equation RnT 

5 The van der Waals equation corrects the perfect gas equation for both attractive and repulsive interactions between the molecules in a real gas. See Justification 1.1 for a fiiller explanation. 

The Bertholet equation accounts for the volume of the molecules in a manner similar to the van der Waals equation but the term representing molecular attractions is modified to account for the effect of temperature. Experimentally one finds that the van der Waals a decreases with increasing temperature. Theory (see Chapter 18) also suggests that inteimolecular attractions can decrease with temperature. 

The partial pressure of a gas in a mixture of gases is the pressure the gas would exert if it occupied alone the same container as the mixture at the same temperature, It is a limiting law because it holds exactly only under conditions where the gases have no effect upon each other. This can only be true in the limit of zero pressure where the molecules of the gas are very far apart, Hence, Dalton s law holds exactly only for a mixture of perfect gases for real gases, the law is only an approximation. 

The critical constants represent the state of a system at which the distinction between the liquid and vapor phases disappears. We usually describe this situation by saying that above the critical temperature the liquid phase cannot be produced by the application of pressure alone. The liquid and vapor phases can no longer coexist, though fluids in the so-called supercritical region have both liquid and vapor characteristics. (See Impaa 1.4.1 for a more thorough discussion of the supercritical state.) 

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Solutions to theoretical problems 170 Answers to discussion questions 268... 

Solutions lo theoretical problems 194 Answers to discussion questions 278... 

Answers to discussion questions 239 Solutions to numerical problems 3I7... 

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