How Can You Calculate Equilibrium Temperature with Given Thermodynamic Values?

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Discussion Overview

The discussion revolves around calculating the equilibrium temperature of a chemical reaction using given thermodynamic values, specifically focusing on the relationship between Gibbs free energy, enthalpy, and entropy. Participants explore the implications of using standard conditions and the assumptions that must be made regarding thermodynamic properties at different temperatures.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents calculated values for K, ΔS0, ΔG0, and ΔH0, expressing concern about using ΔG0 at standard conditions to find the equilibrium temperature.
  • Another participant suggests that assumptions may be missing, such as the constancy of temperature during the reaction.
  • A participant provides the chemical reaction and reiterates the assumption that the aggregate states of the substances do not change when moving from standard temperature to equilibrium temperature.
  • One suggestion involves using the Van't Hoff equation to relate K at standard conditions to K at the desired equilibrium temperature.
  • Another participant questions the necessity of K, proposing instead to find T such that ΔG = ΔH - TΔS = 0.
  • A participant reflects on the challenge of assuming that ΔS and ΔH remain constant at different temperatures, indicating a lack of clarity in their understanding due to sleep deprivation.
  • An edit clarifies a previous mistake regarding the sign in the equation for ΔG0.

Areas of Agreement / Disagreement

Participants express uncertainty about the assumptions required for the calculations, particularly regarding the constancy of thermodynamic values at different temperatures. There is no consensus on the best approach to calculate the equilibrium temperature, with multiple competing views presented.

Contextual Notes

Participants note that the thermodynamic values provided are at standard conditions, raising questions about their applicability at different temperatures. The discussion highlights the complexity of relating these values under changing conditions.

Nikitin
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I'm supposed to find out the temperature of a reaction at equilibrium. I've calculated K=0.187, ΔS0=940J, and I know that ΔG0=1134kJ and ΔH0=1414kJ.

I'm supposed to use the R*T*ln(K)=ΔG0 formula, but my only problem is that ΔG0 is given for standard conditions,, ie where the temperature equals 298K.

But I am supposed to use it anyway in the assignment, ie I need to reform it into ΔG0=ΔH0 + T*ΔS0=T*R*ln(K), and calculate T.

However, ΔS and ΔH for the reaction are given at standard conditions. When the temperature changes they too change, so how is it possible to get a reliable answer?
 
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help?
 
Can you post the original question? You might be missing some kind of assumption, like the temperature remains constant for the reaction.
 
Here's the reaction. Ca3(PO4)2 (s) + 3 SiO2 (s) + 5 C (s) -> 3 CaSiO3 (s) + 1/2 P4 (g) + 5 CO (g)

I'm supposed to find the equilibrium temperature, with the data from the OP (all of which are at standard conditions). I am also to assume that none of the substances change their aggregate states (ie none of them turn into gases) going from standard temperature to the equilibrium temperature.
 
Can you find out K at standard conditions. Using this, relate K and T at standard conditions with K and T asked in the question by Van't Hoff equation.\mathrm{ln}\frac{K_2}{K_1}=\frac{-\Delta H^{\circ}}{R}\left ( \frac{1}{T_2}-\frac{1}{T_1} \right )
 
Do you really need K? Isn't it just a matter of finding T such that \Delta G = \Delta H - T \Delta S = 0?
 
AGNuke: I knew K at equil. temperature.. What I was struggling with was assuming that ΔS and ΔH are the same at 298K and 1500K for the reaction... Anyway I feel I understand allot more.

Borek said:
Do you really need K? Isn't it just a matter of finding T such that \Delta G = \Delta H - T \Delta S = 0?
The assignment wanted that the equilibrum temperature be calculated for K=0.187.. ugh I was probably unclear about this.. sorry I'm sleep deprived as heck.

EDIT: When I wrote that ΔG0=R*T*ln(K) in the OP, I meant ΔG0=-R*T*ln(K). I forgot the minus-sign infront of R*T*ln(K).
 
Last edited:

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