Consider the reaction for the synthesis of nitrogen dioxide:

$NO(g)+\frac{1}{2}{O}_2(g)N{O}_2(g),H^0=-56\mathrm{.}5k\frac{J}{m}ol$

This reaction is not spontaneous at $298K$ because

A$.$ this reaction is exothermic

B$.S<mn\; id="EditorElement\_10406109">0</mn>$

C$.S_{\text{s}\text{u}\text{r}\text{r}}>0$

D$.|S|<mi\; id="EditorElement\_10405998">|</mi><mi\; id="EditorElement\_10406000"></mi><msub\; id="EditorElement\_10406017"><mrow><mi\; id="EditorElement\_10406002">S</mi></mrow><mrow\; id="EditorElement\_10406016"><mtext\; id="EditorElement\_10406005">s</mtext><mtext\; id="EditorElement\_10406007">u</mtext><mtext\; id="EditorElement\_10406009">r</mtext><mtext\; id="EditorElement\_10406011">r</mtext><mtext\; id="EditorElement\_10406013"></mtext></mrow></msub><mi\; id="EditorElement\_10406019">|</mi>$

E$.|S|>|S_{\text{s}\text{u}\text{r}\text{r}}|$

The $2^{nd}$ Law of Thermodynamics:

$S_{\text{U}\text{n}\text{i}\text{v}}>0$ for spontaneous process

$S_{\text{U}\text{n}\text{i}\text{v}}=S+S_{\text{s}\text{u}\text{r}\text{r}}$ and $S_{\text{s}\text{u}\text{r}\text{r}}=-\frac{H}{T}$

$Rxn$ is not spontaneous $S_{\text{U}\text{n}\text{i}\text{v}\text{e}\text{r}\text{s}\text{e}}<mn\; id="EditorElement\_10405562">0</mn>$

$Rxn$ is exo $)<mi\; id="EditorElement\_10405483">(</mi><mn\; id="EditorElement\_10405477">0</mn>$

$1\mathrm{.}5$mol gas $1$ mol gas $S<mn\; id="EditorElement\_10405415">0</mn>$

$S_{\text{u}\text{n}\text{i}\text{v}\text{e}\text{r}\text{s}\text{e}}<mn\; id="EditorElement\_10405373">0</mn>$ when $|S|>|S_{\text{s}\text{u}\text{r}\text{r}}|$