Question

2. Solve the following related problems involving the equilibrium between dinitrogen tetroxide and nitrogen dioxide.

N₂O₄ <==> 2 NO₂

The equilibrium constant for this reaction is K_p = 0.60 at 350 degrees Kelvin. A 1.0 L vessel contains the above two gases in equilibrium at 350 K. The total pressure of the two gases, P_(NO2) + P_(N2O4), in the vessel is 0.50 atm. From this information, calculate the equilibrium partial pressure for each gas. This is the initial equilibrium position for the reaction, which you will use to consider the effects of the following perturbations.

This equilibrium mixture is subjected to the following four perturbations:

a. addition of N₂O₄ gas to the vessel (which had been at the above equilibrium) to give a total concentration (before readjustment of the equilibrium position) of 0.375 atm in the reactant gas;

b. decreasing the total volume of the vessel to 0.50 L (in answering b-d, go back to the initial equilibrium mixture before then applying the perturbation);

c. increasing the total pressure inside the vessel to 1.5 atm by adding 1.0 atm of N₂ gas;

d. increasing the temperature of the gas mixture to 700 degrees K, a temperature at which the equilibrium constant is 2.40.

3. Hints: Note that the equilibrium constant is a K_p value and that reactant and product concentrations are given in terms of partial pressures.

For each of these perturbations, you can solve for the equilibrium partial pressures of the two gases. To do this you may have to set up an ICE table. Note that in �b�, the inverse relationship between P and V in the ideal gas law allows you to easily determine the partial pressures of the reactant and product gases immediately after the volume increase. Then you can calculate the final equilibrium concentrations following this perturbation.

Finally, the exact solution to part �d� is challenging. You should first consider the effect, on the partial pressures of the reactant and product gases, of an increase in temperature from 350 to 700 degrees K. (Remember that the ideal gas law indicates a direct proportionality of P and T.) Then you should consider a shift in the equilibrium concentrations, along with the new equilibrium constant for the higher temperature.

Even if you are not able to determine numerical values for the equilibrium positions following the perturbations, you still should understand the concepts and be able to prepare the following written response.

4. Now, prepare an explanation: Attempt to solve for the extent and direction of the shift in the equilibrium as a result of the above four perturbations. If you are unable to solve for numerical values of the final equilibrium partial pressures, you should still know the predicted directions of the shifts.

After studying and solving the above problem, write an explanation of the Le Chatelier Principle. This explanation should give a general statement of the principle and then should explain how the above four types of perturbations are rationalized in terms of this principle.