Consider the dimerization of nitrogen dioxide at room temperature: 2 NO2g⇌ N2O4g K_eq = 8 atm^-1If the equilibrium partial pressure of nitrogen dioxide in a container is 0.5 atm, what is the partial pressure of dinitrogen tetroxide?

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11ecba2d_11bd_83dd_a3bf_9b2fb79879f1_MD0008_00 The equilibrium constant for any chemical reaction is the molar ratio of products to reactants when the system is at equilibrium. The partial pressure of a gas is directly proportional to the number of moles of that gas according to the ideal gas law; therefore, partial pressure can be substituted for molar concentration. If more than one of a given molecule is involved in a reaction, each molecule involved is counted separately. Therefore, each product or reactant must be raised to the power of its stoichiometric coefficient to account for all molecules involved in the reaction. Nitrogen dioxide (NO₂) can combine with itself to form dinitrogen tetroxide (N₂O₄). The equilibrium constant for this reaction (K_p = 8 atm⁻¹) is the ratio of N₂O₄ to NO₂ when equilibrium is achieved. However, because two NO₂ molecules are required for each reaction, the NO₂ partial pressure must be squared. Therefore, the equilibrium partial pressures of NO₂ and N₂O₄ in the described scenario are related by the equation 11ecba2d_11bd_83de_a3bf_a964104b151f_MD0008_00 This equation can be rearranged and solved as follows: 11ecba2d_11bd_83df_a3bf_8dba30a1c4e7_MD0008_00 (Choice A) 0.03 atm would be correct if N₂O₄ were the reactant and NO₂ were the product, in which case N₂O₄ would be in the denominator of the equilibrium expression. (Choice B) 0.5 atm would be correct if "equilibrium" meant that all components are at equal concentration. Instead, equilibrium is the state in which the forward and reverse reactions occur at equal rates and no net change is observed. More stable compounds dominate at equilibrium. (Choice D) 4 atm would be correct if only one molecule of NO₂ were involved in the reaction and its partial pressure were not squared in the equilibrium expression. Educational objective: The equilibrium constant (K_p) of a reaction is the molar ratio of products to reactants when equilibrium is achieved. Each product or reactant must be raised to the power of its stoichiometric coefficient in the equilibrium expression.

Consider the Dimerization of Nitrogen Dioxide at Room Temperature