exam
edited by: John J. Alexander
que/tion exchange
University of Cincinnati Cincinnati. Ohio 45221
An Example of States for the System N2 + 3H2
Le Chatelier’s Principle Kerro Knox Cleveland State University Cleveland, OH 44115
P
The challenge to constructors of multiple choice questions is to make up questions that are difficult without being ambiguous. The question presented here tests the students’ ability to reason beyond a superficial first impression. It is the kind of question that professors call “thought provoking,” and students call “tricky.”
rf n2
P X
c n
h2
P X
Question
c
A mixture of nitrogen, hydrogen, and ammonia gases is in equilibrium at a certain temperature and pressure:
n
N2 + 3H2
*=*
2NH3
If the total pressure on the system is increased at constant temperature, the partial pressure of nitrogen in the new equilibrium mixture compared to the old will be a) decreased
b) the
same
c) increased
Acceptable Solution and Discussion The correct answer is (c) increased. At the lowest level, one’s immediate reaction to the question is that an increase in total pressure increases the partial pressure of all the constituents of a gas mixture. Then Le Chatelier’s Principle comes to mind, and one realizes that a total pressure increase will shift the equilibrium in the direction of less nitrogen. Can, however, the shift be great enough actually to decrease the partial pressure of the nitrogen? Certainly not, dictates common sense, and it is right. Teachers always hope that an exam will be a learning experience as well as a testing mechanism. In explaining the answer to this question to students, a specific example will be of considerable help to understanding exactly how the various quantities describing the system change. Consider a mixture initially consisting of one mole of nitrogen and three moles of hydrogen at 800 K where the equilibrium constant, Tyr
nh3
PNH32
a
=
Initial State 200 atm
Equilibrium State 1 P = 200 atm
*=*
2NH3
Equilibrium State 2 P = 400 atm
1.000 50.0 0.250 0.762
0.527 34.5 0.173 0.526
0.402 57.3 0.143 0.873
3.000 150.0 0.750 2.285
1.582 103.6 0.518 1.578
1.205 172.0 0.430 2.619
0.950 61.9 0.310 0.943
1.197 170.7
1.003
0.460
P
0 0
X
0
c
0
V
1.313
0.427 2.601
See text for definitions of variables.
could have the numerical value of 10'4. In the table are given the variables of the system for two equilibrium states, the number of moles, n, partial pressure in atmospheres, p, mole fraction, xf and molarity in mol/L, c, for each constituent as well as, at the bottom, the volume in liters, V. For this simple example, it is assumed that the gases and the gas mixture are ideal. It is seen that indeed the partial pressure of the nitrogen does increase when the pressure increases, but it does not increase as much as it would have had the reaction not taken place; its new value is not double its old value. Le Chatelier’s Principle is thereby illustrated. The volumes illustrate the fact that Boyle’s Law is not obeyed by this reacting system because the total number of moles of gas changes.
Finally, consider the two equilibrium concentrations. The question would have been ambiguous if in it “partial pressure of nitrogen” had been replaced by “concentration of nitrogen,” because the method of expressing concentration is not specified. The molarity of the nitrogen increases as it must (but again not as much as it would have in the absence of the equilibrium reaction), yet its mole fraction decreases, as required by Le Chatelier’s Principle.
Volume 62
Number 10
October 1985
863
