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23 Nov 2019

Consider an ideal gasthermometer consisting of moles of gas ina
volume of liters.

a) When we place the thermometer in thermal contact with a blockofice we
measure a pressure of 2.24 atm. We associate this pressure withatemperature
of 0 degrees Centigrade (C). Next we place the thermometerinthermal contact
with boiling water and measure a pressure of 3.06 atm. Weassociatethis
pressure with a temperature of 100 degrees C. Now assume thatthepressure
varies linearly with temperature,
P(atm) = a + b T(C). Determine the values of the slope (b)andy-intercept (a).
Plot the pressure vs. temperature.

b) Using the equation from part a) solve for the temperature asafunction of
pressure. You can see how a pressure reading can betranslateddirectly to a
temperature reading.

c) From your equation in part a) or b) determine the temperatureatwhich the
pressure is zero. This should look familiar!

d) Now define a new temperature scale - the Kelvin scale,bysubtracting your
result from part c) from the temperature expressed inCentigrade.Rewrite the P
vs T equation from part a) in terms of the temperature inKelvin.What do you
notice? Why is the Kelvin temperature scale an absolutescale?

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Advanced Study Assignment in Lab Manual Gen Chem 1

Felder and Rousseau. "Elementary Principles of Chemical Processes". 4th Edition. Problem 4.66, parts A-F.

Methanol is formed from carbon monoxide and hydrogen in the gas-phrase reaction;

CO + 2H₂ = CH₃OH

(A) (B) (C)

The mole fractions of the reactive species at equilibrium satisfy the relation

(y_C * 1) / (y_a * y_b^2 * P^2) = K_e(T)

Where P is the total pressure (atm) , K_e the reaction equilibrium constant (atm^-2), and T the Temperature (K). The equilibrium constant K_e= 10.5 at 373 K, and 2.316x10^-4 at 573 K. A semilog plot of K_e (logarithmic scale) versus 1 / T (rectangular scale) is approximately linear between T = 300 K and T = 600 K.

(a.) Derive a formula for k_e(T), and use it to show that K_e(450 K) = 0.0548 atm^-2.

(b.) write expressions for n_A, n_B, and n_C (gram-moles of each species), then y_A, y_B, and y_C, in terms of n_A0, n_B0, n_C0, and Îµ, the extent of reaction. Then derive an equation involving only n_A0, n_B0, n_C0, P, T, and Îµ_e, where Îµ_e is the extent of reaction at equilibrium.

(c.) Suppose you begin with equimolar quantities of CO and H₂, and no CH₃OH, and the reaction proceeds to equilibrium at 423 K and 2.00 atm. Calculate the molar composition of the product (y_A, y_B, and y_C) and the fractional conversion of CO.

(d.) The conversion of CO and H₂ can be enhanced by removing methanol from the reactor while leaving unreacted CO and H₂in the vessel. Review the equations you derived in solving Part (c.) and determine any physical constraints on Îµ_e associated with n_A0 = n_B0 = 1. Now suppose that 90% of the methanol is removed from the reactor as it is produced; in other words, only 10% of the methanol formed remains in the reactor. Estimate the fractional conversion of CO and the total gram moles of methanol produced in the modified operation.

(e.) Repeat Part (d.), but now assume that n_B0 = 2 mol. Explain the significant increase in fractional conversion of CO.

(f.) Write a set of equations for y_A, y_B, y_C, and Æ_A(The fractional conversion of CO) in terms of y_A0, y_B0, T, and P (The reactor temperature and pressure at equilibrium). Enter the equations in an equation-solving program. Check the program by running it for the conditions of Part (c.), then use it to determine the effects on Æ_A (increase, decrease, or no effect) of seperately increasing, (i) the fraction of CH₃OH in the feed, (ii) temperature, and (iii) pressure.

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 ï¿½bï¿½, 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 ï¿½dï¿½ 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.

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