Gases positional entropy

The earliest hint that physics and information might be more than just casually related actually dates back at least as far as 1871 and the publication of James Clerk Maxwell s Theory of Heat, in which Maxwell introduced what has become known as the paradox of Maxwell s Demon. Maxwell postulated the existence of a hypothetical demon that positions himself by a hole separating two vessels, say A and B. While the vessels start out being at the same temperature, the demon selectively opens the hole only to either pass faster molecules from A to B or to pass slower molecules from B to A. Since this results in a systematic increase in B s temperature and a lowering of A s, it appears as though Maxwell s demon s actions violate the second law of thermodynamics the total entropy of any physical system can only increase, or, for totally reversible processes, remain the same it can never decrease. Maxwell was thus the first to recognize a connection between the thermodynamical properties of a gas (temperature, entropy, etc.) and the statistical properties of its constituent molecules. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

More recently, a number of reports dealing with 1,3-sulfonyl shifts which proceed by other mechanisms have been published. For example, Baechler and coworkers suggested that the higher activation enthalpy observed for the isomerization of the deuterium labeled methallyl sulfone 72 in nitrobenzene at 150°C as compared to the corresponding sulfide, together with the positive entropy of activation may be taken as evidence for a homolytic dissociation mechanism (equation 44). A similar mechanism has also been suggested by Little and coworkers for the gas-phase thermal rearrangement of deuterium labelled allyl sec-butyl sulfone, which precedes its pyrolysis to alkene and sulfur dioxide. 

The reaction is producing 3 mole of gas from 2 moles of gas. The entropy is increasing and the change in entropy is expected to be positive. 

A reversible adiabatic expansion of an ideal gas has a zero entropy change, and an irreversible adiabatic expansion of the same gas from the same initial state to the same final volume has a positive entropy change. This statement may seem to be inconsistent with the statement that 5 is a thermodynamic property. The resolution of the discrepancy is that the two changes do not constitute the same change of state the final temperature of the reversible adiabatic expansion is lower than the final temperature of the irreversible adiabatic expansion (as in path 2 in Fig. 6.7). 

This positive entropy change means that there is greater disorder in the product (HjO gas) than the reactant (HjO liquid). In terms of just entropy, the increase in entropy drives the reaction to the right, toward a condition of higher entropy. 

Reactions with a large, positive entropy change also favor product formation (large Kp). For example, a reaction with a net increase in the number of moles of gas-phase species has a very positive A S°, from the translational entropy gain associated with the additional species. If AS° > 0, high temperatures increase Kp and drive the reaction toward completion (toward the products). If A5° < 0, Kp will increase as the temperature goes down. 

As you might expect, there is a large positive entropy change, corresponding to a large increase in randomness, on converting water from a liquid to a gas. 

A is correct. Since the number of moles of gas is decreasing with the forward reaction, positional entropy is decreasing. This almost always means that overall system entropy is decreasing. Since the MCAT doesn t distinguish between positional entropy and any other kind of entropy, you can always view a reaction with decreasing number of gas particles as decreasing in entropy and vice versa. 

We predict this reaction has a positive entropy change because the number of moles of gas increases in fact, AS = 165 J/K. Furthermore, because the reaction is nonspontaneous at lower temperatures, it must have a positive AH (58.1 kJ). As the —TAS term becomes more negative at higher temperatures, it will eventually outweigh the positive AH term, and the reaction will occur spontaneously. 

Positional probability is also illustrated by changes of state. In general, positional entropy increases in going from solid to liquid to gas. A mole of a substance has a much smaller volume in the solid state than it does in the gaseous state. In the solid state, the molecules are close together, with relatively few positions available to them in the gaseous... 

To understand the pressure dependence of free energy, we need to know how pressure affects the thermodynamic functions that comprise free energy, that is, enthalpy and entropy (recaii that G = H - TS). For an ideal gas, enthalpy is not pressure-dependent. However, entropy does depend on pressure because of its dependence on volume. Consider 1 moie of an ideai gas at a given temperature. At a volume of 10.0 L, the gas has many more positions avaiiable for its molecules than if its volume is 1.0 L. The positional entropy is greater in the iarger volume. In summary, at a given temperature for 1 mole of ideal gas... 

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