[Mimic]

For the reaction

[tex]\ce{CO2 (g) + H2 = CO (g) + H2O (g)}[/tex]

he equilibrium constant [itex]K_p[/itex] has a value of 0.534 at [itex]{960 K}[/itex] and [itex]{1.571 K}[/itex]. Calculate the variation of the standard reaction enthalpy, assumed constant in the temperature range considered. Also calculate the [itex]K_p[/itex] value of the above reaction at standard conditions at [itex]{25 ^\circ C}[/itex].

My procedure:

[tex]K_c = K_p(RT)^{\Delta \nu (g)} = K_p(RT)^{0} = K_p \cdot 1 = K_P[/tex]

from the van't Hoff equation

[tex]\ln K_2 - \ln K_1 = - \dfrac{\Delta H^{°}_{r}}{R} \left[\dfrac{1}{T_2} - \dfrac{1}{T_1}\right][/tex]

[tex]\Delta H^{°}_{r} = + 36.177 \dfrac{kJ}{mol}[/tex]

Now, for [itex]K_p[/itex] at [itex]{25 ^\circ C}[/itex]

[tex]K_p = \exp^{-\dfrac{\Delta G^{°}_{r}}{RT}}[/tex]

which of the two equations should I use to calculate [itex]\Delta G^{°}_{r}[/itex]?

[tex]\Delta G^{°}_{r} = \Delta H^{°}_{r} - T\Delta S^{°}_{r}[/tex]

or

[tex]\Delta G^{°}_{r} = \sum_{products} \nu \Delta G^{°}_{f} - \sum_{reagents} \nu \Delta G^{°}_{f}[/tex]

Can you help me?

Thank you in advance

[mjc123]

What do you mean by

Kp has a value of 0.534 at 960K and 1.571K.

Do you mean a value of 0.534 at 960K and a value of 1.571 at some other temperature?

which of the two equations should I use to calculate ΔGr°?

Well, which do you have the information for?

Note that this is not as simple as it may appear (though, as a homework question, they may be expecting you to use the over-simplified approach). Over this range of temperature (950 to 298K), ΔH and ΔS will not be constant. Also, the standard state of water at 298K is liquid, not gas.