Nitrogen dioxide can dimerize to form dinitrogen tetroxide according to the reversible reaction
2 NO₂(g) ⇌ N₂O₄(g)
The dimerization is often modeled as the sum of two elementary equilibria:
Step 1 NO(g) + $
\frac{1}{2}O2(g)⇌NO2(g)K_{c1}=1.2\times10^{5}$
Step 2 2 NO(g) + O₂(g) ⇌ N₂O₄(g) Kc2=2.0×106
(a) Starting from Steps 1 and 2, construct the balanced overall equation that yields 2 NO₂(g) ⇌ N₂O₄(g). Show all intermediate algebraic manipulations required to reach the target stoichiometry.
(b) Determine Kcoverall numerically for the dimerization at the temperature specified, giving your answer in scientific notation.
(c) A sealed 5.00 L flask at this temperature is charged with 0.0200 mol of NO₂ and no N₂O₄. Calculate the value of the reaction quotient Qc for dimerization in the flask immediately after charging.
(d) Using your result from part (b), predict the direction in which the system will proceed to reach equilibrium. Quantitatively justify your prediction.
(e) Describe qualitatively how the magnitude of the equilibrium constant you obtained in part (b) influences the color change (brown to colorless) that would be observed as equilibrium is approached.