You have been assigned the task of measuring the equilibrium constant for the re

Question

You have been assigned the task of measuring the equilibrium constant for the reaction N2 O4 2NO2 as a function of temperature. To do so, you evacuate a rigid 2-liter vessel equipped with a pressure gauge, fill the vessel with a mixture of NO2 and N2O4, and then heat it 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

Kp = p2NO2 / pN2O4

where pNO2 and pN2O4 are the equilibrium partial pressures of NO2 and N2O4.

Derive an equation or a series of equations for calculating Kp (atm) from specified values of T and Pgauge. (Suggestion: Begin by defining n1 and n2 as the moles of NO2 and N2O4 present at equilibrium.) Then calculate Kp for T = 350 K, 335 K, 315 K, and 300 K. (Suggestion: Use a spreadsheet.)

(c) The equilibrium constant should vary with temperature according to the relation:

Kp = aeb/T

Use the results of Part (b) to determine the values of a and b by curve-fitting. [Suggestion: Use the spreadsheet from Part (b).].

Explanation / Answer

(a). Volume of vessel = 2 L

Guage pressure = 1.0 atm

Total pressure in the vessel = Guage pressure + atmospheric pressure

= 1.0 + 1.0

= 2 atm

Temperature = 473 K

Using Ideal gas equation:

PV = nRT

2 * 2 = n * 0.0821 * 473

4 = n * 38.83

n = 4 / 38.83

n = 0.103 moles

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