In reversible chemical reactions, the position of equilibrium is influenced by changes in temperature. According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in temperature, the system will adjust itself to counteract that change and restore equilibrium.
The given reaction is:
[tex]\[ 2 NO_2(g) \rightleftharpoons N_2O_4(g) \][/tex]
We know from the information provided that the formation of nitrogen dioxide ([tex]\( NO_2 \)[/tex]) absorbs heat, which means it's an endothermic process. Conversely, the formation of dinitrogen tetroxide ([tex]\( N_2O_4 \)[/tex]) releases heat, marking it as an exothermic process.
If the temperature of the system increases, the equilibrium will respond by favoring the endothermic reaction in order to absorb the extra heat. In this case, the endothermic reaction is the formation of nitrogen dioxide ([tex]\( NO_2 \)[/tex]):
[tex]\[ N_2O_4(g) \longrightarrow 2 NO_2(g) \][/tex]
Therefore, when the temperature increases, the equilibrium will shift towards the production of more nitrogen dioxide. This means that option:
C. The equilibrium will shift so that there is more nitrogen dioxide.
is the correct answer.