You have been assigned the task of measuring the equilibrium constant for the reaction N₂O₄ 2NO₂ as a function of temperature. To do so, you obtain a rigid 2-liter vessel equipped with a pressure gauge evacuate and then fill the vessel with a mixture of NO₂ and N₂0₄, and heat the vessel to T₀ = 473 K, a temperature at which you know the gas is essentially pure NO₂. The gauge pressure at this point is noted to be 1.00 atm. You then decrease the temperature in stages, recording the equilibrium gauge pressure at each temperature. The data are as follows:

(a) How many gram-moles of NO₂ are in the vessel at 473 K?

(b) The reaction equilibrium constant is K_p = P²_NO2 / PN₂O₄ where and PN₂O₄ are the equilibrium partial pressures of NO₂ and N₂O₄. Derive an equation or a series of equations for calculating K_p (atm) from specified values of T and P _gauge. (Suggestion: Begin by defining a₁ and n₂ as the moles of NO₂ and N₂O₄ present at equilibrium.) Then calculate K_p for T = 350 K, 335 K. 315 K, and 300 K. (Suggestion: Use a spreadsheet program.)

(c) The equilibrium constant should vary with temperature according to the relation K_p = ae^–b/T use the results of part (b) to determine the values of a and b by a graphical curve-fitting procedure. [Suggestion: Use the spreadsheet program from part (b).]