Question

onsider the following exergenic reaction:

2NO2 (gas) →N2O4 (gas)

At constant pressure, which of the following statements is true?
1)
The reaction is never spontaneous.


2)
The reaction is only spontaneous at temperatures below 10K but not at higher temperatures.


3)
The reaction is always spontaneous.


4)
The reaction is only spontaneous in the presence of enzymes.

Answer 1

@aaronq

Answer 2

In order for a reaction to be spontaneous, the gibb's free energy \(\sf (\Delta G)\) associated with it must be negative.

The equation that you should be aware of is: \(\Large \sf \Delta G=\underbrace{\Delta H}_{\small Enthalpy}- T\underbrace{\Delta S}_{\small Entropy}\)

The question tells you that the reaction is exergonic, meaning that it releases energy,\(\sf \Delta G<0\). This indicates that it is spontaneous. But since number of gas molecules decreases (2 on the left and 1 one on the right), we know that the process is entropically unfavourable and thus the reaction is NOT spontaneous above a certain temperature.

We need the thermodynamic parameters to find the actual temperature at which we achieve the condition of \(\sf \Delta G<0\).
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\(\Delta H=-57.2 ~kJ\)
\(\Delta S= -175.83~ J/K\)
http://chemed.chem.purdue.edu/demos/demosheets/21.1.html
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We use the equation i wrote above, and impose the condition that \(\sf \Delta G=0\), to find the temperature at which the spontaneity of the reaction changes.

\(\Large \sf 0=\Delta H- T\Delta S \rightarrow T=\dfrac{\Delta H}{\Delta S}=\dfrac{-57200 J}{-175.83 J/K}=325 K\)

\(\sf \Large 325 K-273K=52 ~C^o\)

Above \(\sf 52 ~C^o, ~or~325 K,\) the reaction is not spontaneous.

It doesn't seem that any of your options match this, so i would go with C