10.1: The Concept of Equilibrium Reactions

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Pure dinitrogen tetroxide (\(\ce{N2O4}\)) is a colorless gas that is widely used as a rocket fuel. Although \(\ce{N2O4}\) is colorless, when a container is filled with pure \(\ce{N2O4}\), the gas rapidly begins to turn a dark brown. A chemical reaction is clearly occurring, and indeed, chemical analysis tells us that the gas in the container is no longer pure \(\ce{N2O4}\), but has become a mixture of dinitrogen tetroxide and nitrogen dioxide; \(\ce{N2O4}\) is undergoing a decomposition reaction to form \(\ce{NO2}\). If the gaseous mixture is cooled, it again turns colorless and analysis tells us that it is again, almost pure \(\ce{N2O4}\); this means that the \(\ce{NO2}\) in the mixture can also undergo a synthesis reaction to re-form \(\ce{N2O4}\). Initially, only \(\ce{N2O4}\) is present. As the reaction proceeds, the concentration of \(\ce{N2O4}\) decreases and the concentration of \(\ce{NO2}\) increases. However, if you examine the figure, after some time, the concentrations of \(\ce{N2O4}\) and \(\ce{NO2}\) have stabilized and, as long as the temperature is not changed, the relative concentrations of the two gasses remain constant.

The reversible reaction of one mole of \(\ce{N2O4}\), forming two moles of \(\ce{NO2}\), is a classic example of a chemical equilibrium. We encountered the concept of equilibrium in Chapter 9 when we dealt with the autoprotolysis of water to form the hydronium and hydroxide ions, and with the dissociation of weak acids in aqueous solution.

\[\ce{2 H2O <=> H3O^{+} + HO^{–}} \nonumber\]

When we wrote these chemical equations, we used a double arrow to signify that the reaction proceeded in both directions. Using this convention, the dissociation of dinitrogen tetroxide to form two molecules of nitrogen dioxide can be shown as:

\[\ce{N2O4 ⇄ 2 NO2} \nonumber\]

If the temperature of our gas mixture is again held constant and the total pressure of the gas in the container is varied, analysis shows that the partial pressure of \(\ce{N2O4}\) varies as the square of the partial pressure of \(\ce{NO2}\). The Ideal Gas Laws tell us that the partial pressure of a gas, P_gas, is directly proportional to the concentration of that gas in the container). Mathematically, the relationship between the partial pressures of the two gasses can be expressed by the equation below:

\[\frac{(P_{NO_{2}})^{2}}{P_{N_{2}O_{4}}}=K \nonumber \]