How Can You Calculate Equilibrium Temperature with Given Thermodynamic Values?

[Nikitin]

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?

 

[Nikitin]

help?

 

[AGNuke]

Can you post the original question? You might be missing some kind of assumption, like the temperature remains constant for the reaction.

 

[Nikitin]

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.

 

[AGNuke]

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 )

 

[Borek]

Do you really need K? Isn't it just a matter of finding T such that \Delta G = \Delta H - T \Delta S = 0?

 

[Nikitin]

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.

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).