At a certain temperature, K for the reaction 2NO₂ N₂O₄
Is 7.5 L/mol. If 2.0 mol of NO₂ is placed in a 2.0-liter container and permitted to react at this temperature, calculate the concentration of N₂O₄ at equilibrium.

Question

At a certain temperature, K for the reaction 2NO₂

At a certain temperature, K for the reaction 2NO<sub>2</sub> N<sub>2</sub>O<sub>4</sub> Is 7.5 L/mol. If 2.0 mol of NO<sub>2</sub> is placed in a 2.0-liter container and permitted to react at this temperature, calculate the concentration of N<sub>2</sub>O<sub>4</sub> at equilibrium. A) 0.39 mol/L B) 0.82 mol/L C) 7.5 mol/L D) 0.65 mol/L E) none of these

N₂O₄
Is 7.5 L/mol. If 2.0 mol of NO₂ is placed in a 2.0-liter container and permitted to react at this temperature, calculate the concentration of N₂O₄ at equilibrium.

Quizplus · Accepted Answer

The balanced equation for the reaction is: 2 NO₂ (g) ⇌ 2 NO (g) + N₂O₄ (g) The initial concentration of NO₂ is 1.0 mol/L (calculated by dividing 2.0 mol by 2.0 L). Since there are no products initially, their concentrations are zero. At equilibrium, let the concentration of N₂O₄ be x mol/L. Then the concentrations of NO will each be (2.0 - x) mol/L, since the stoichiometry of the reaction shows that for every 2 mol of NO₂ that react, 2 mol of NO are formed. Using the equilibrium constant expression: K = ([NO]2[N₂O₄])/([NO₂]2) Substitute the equilibrium concentrations in terms of x: 7.5 = ((2.0 - x)2(x))/((1.0)2) Simplifying: 7.5 = (4.0x - 2.0x2) 2.0x2 - 4.0x + 7.5 = 0 Using the quadratic formula: x = (4.0 ± sqrt((4.0)2 - 4(2.0)(7.5)))/(2(2.0)) x = 0.39 or x = 1.93 Since the concentration of N₂O₄ cannot be greater than 2.0 mol/L (the total pressure in the container), the only valid answer is x = 0.39 mol/L. Therefore, the concentration of N₂O₄ at equilibrium is 0.39 mol/L. The correct answer is choice A.

At a Certain Temperature, K for the Reaction 2NO2

At a Certain Temperature, K for the Reaction 2NO₂