Temperature of Equilibrium

In summary, the conversation discusses the equilibrium between N_2, H_2, and NH_3 gases at a temperature where each gas is maintained at a partial pressure of 1 atm. It is noted that at equilibrium, \Delta G is equal to 0. The equation \Delta G = \Delta H^{\circ} - T\Delta S^{\circ} is used to solve for the temperature, with the given values of \Delta H^{\circ} and \Delta G^{\circ}. However, it is questioned whether this relationship is true, as at that temperature, the pressures of the gases may not necessarily be 1 atm. It is also mentioned that at equilibrium, \Delta G^{\circ}
  • #1
breez
65
0
[tex]N_2 (g) + 3H2(g)[/tex] <--> [tex]2NH3(g)[/tex]

[tex]\Delta H^{\circ} of NH3 = -46.2 kJ/mol[/tex]
[tex]\Delta G^{\circ} of NH3 = -16.7 kJ/mol[/tex]

At what temperature can [tex]N_2, H_2, and NH_3[/tex] gases by maintained at equilibrium each with a partial pressure of 1 atm?

The solution my book uses is to solve for T in the equation [tex]\Delta G = \Delta H^{\circ} - T\Delta S^{\circ}[/tex] with [tex]\Delta G = 0[/tex]

Is this relationship true?

Also, how can you be sure that at that temperature, the pressures will all be 1 atm?

I thought [tex]\Delta G = \Delta G^{\circ} + RT \ln Q[/tex]?

If reactants/products are all 1 atm, then ln Q = 0, and [tex]\Delta G^{\circ}[/tex] must equal zero, which it clearly does not, thus there shouldn't exist a temperature where this is possible.
 
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  • #2
Careful, at equilibrium delta G is zero, not delta G naught

At equilibrium


delta G naught=-RT lnKeq

you are given delta G naught, you know R, what is Keq expression in terms of pressure and temperature?
 
  • #3


I can provide a response to the content provided. Firstly, the equilibrium temperature for a reaction is dependent on its enthalpy and entropy values. The equation \Delta G = \Delta H^{\circ} - T\Delta S^{\circ} is a valid relationship for calculating the equilibrium temperature. However, it is important to note that this equation assumes ideal conditions, which may not always be the case in real-world scenarios.

In the given reaction, \Delta H^{\circ} and \Delta S^{\circ} values are known, and the equilibrium temperature can be calculated by setting \Delta G = 0. This means that at equilibrium, the reaction has no net change in free energy, and the forward and reverse reactions occur at equal rates. This is the condition for thermodynamic equilibrium. Solving for T in the equation \Delta G = \Delta H^{\circ} - T\Delta S^{\circ} will give the temperature at which this equilibrium is achieved.

It is also important to mention that the partial pressures of the gases do not affect the equilibrium temperature. The equilibrium temperature is solely determined by the enthalpy and entropy values of the reaction. Therefore, at the calculated equilibrium temperature, the partial pressures of N_2, H_2, and NH_3 gases will be 1 atm, assuming ideal conditions.

As for the equation \Delta G = \Delta G^{\circ} + RT \ln Q, this is the relationship for calculating the free energy change of a reaction at any given temperature. Q represents the reaction quotient, which is the ratio of the concentrations of products and reactants at any given moment. At equilibrium, Q is equal to the equilibrium constant, and \Delta G^{\circ} is equal to 0. Therefore, at equilibrium, the equation becomes \Delta G = RT \ln K, where K is the equilibrium constant. This equation is essentially the same as \Delta G = \Delta H^{\circ} - T\Delta S^{\circ}, just in a different form.

In conclusion, the relationship \Delta G = \Delta H^{\circ} - T\Delta S^{\circ} is a valid way to calculate the equilibrium temperature of a reaction. At this temperature, the partial pressures of the gases will be 1 atm, assuming ideal conditions. However, it is important to consider other factors such as non-ideality and kinetic effects in
 

1. What is the definition of temperature of equilibrium?

The temperature of equilibrium is the temperature at which the rate of heat transfer between two objects is equal and there is no net flow of heat. This means that the temperature of both objects will remain constant.

2. How is the temperature of equilibrium calculated?

The temperature of equilibrium can be calculated using the formula Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the objects, c is the specific heat capacity, and ΔT is the change in temperature. The equilibrium temperature will be reached when Q = 0.

3. What factors affect the temperature of equilibrium?

The temperature of equilibrium is affected by factors such as the specific heat capacity of the objects, the mass of the objects, and the rate of heat transfer. Other factors that may affect the temperature of equilibrium include the surrounding environment and any external sources of heat or cold.

4. How does the temperature of equilibrium relate to the laws of thermodynamics?

The temperature of equilibrium is an important concept in the second law of thermodynamics, which states that heat will naturally flow from a hotter object to a colder object until they reach equilibrium. This means that the temperature of equilibrium is a result of the flow of heat and the tendency for systems to reach a state of maximum entropy.

5. Can the temperature of equilibrium be changed?

Yes, the temperature of equilibrium can be changed by altering the factors that affect it, such as the specific heat capacity or the rate of heat transfer. For example, adding more or less heat to a system can change its temperature of equilibrium. However, in a closed system, the temperature of equilibrium will remain constant once it is reached.

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