# 10.1: The Concept of Equilibrium Reactions

Pure dinitrogen tetroxide (N2O4) is a colorless gas that is widely used as a rocket fuel. Although N2O4 is colorless, when a container is filled with pure 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 N2O4, but has become a mixture of dinitrogen tetroxide and nitrogen dioxide; N2O4 is undergoing a decomposition reaction to form NO2. If the gaseous mixture is cooled, it again turns colorless and analysis tells us that it is again, almost pure N2O4; this means that the NO2 in the mixture can also undergo a synthesis reaction to re-form N2O4. Initially, only N2O4 is present. As the reaction proceeds, the concentration of N2O4 decreases and the concentration of NO2 increases. However, if you examine the figure, after some time, the concentrations of N2O4 and 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 N2O4, forming two moles of 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.

2 H2O ⇄ H3O+ + HO

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:

N2O4 ⇄ 2 NO2

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 N2O4 varies as the square of the partial pressure of NO2. The Ideal Gas Laws tell us that the partial pressure of a gas, Pgas, 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:

$\frac{(P_{NO_{2}})^{2}}{P{N_{2}O_{4}}}=K$

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