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### Topic: [Homework] Gibbs energy reaction  (Read 752 times)

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#### Mimic

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##### [Homework] Gibbs energy reaction
« on: June 01, 2019, 03:32:30 PM »
For the reaction

$$\ce{CO2 (g) + H2 = CO (g) + H2O (g)}$$

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

My procedure:

$$K_c = K_p(RT)^{\Delta \nu (g)} = K_p(RT)^{0} = K_p \cdot 1 = K_P$$

from the van't Hoff equation

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

$$\Delta H^{°}_{r} = + 36.177 \dfrac{kJ}{mol}$$

Now, for $K_p$ at ${25 ^\circ C}$

$$K_p = \exp^{-\dfrac{\Delta G^{°}_{r}}{RT}}$$

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

$$\Delta G^{°}_{r} = \Delta H^{°}_{r} - T\Delta S^{°}_{r}$$

or

$$\Delta G^{°}_{r} = \sum_{products} \nu \Delta G^{°}_{f} - \sum_{reagents} \nu \Delta G^{°}_{f}$$

Can you help me?

#### mjc123

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##### Re: [Homework] Gibbs energy reaction
« Reply #1 on: June 03, 2019, 05:02:20 AM »
What do you mean by
Quote
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?

Quote
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.