In the Laboratory
A Simple Determination of the NO2 Dimerization Equilibrium Constant Qingjiang Yu* Department of Chemistry, Liaocheng Teacher’s College Shandong, China Hongxia Gao (Attached Middle School of Liaocheng Teacher’s College) Theory of Determination
Experimental Determination
There exist two chemical equilibria in the system if NO is mixed with O 2 in a closed container:
CAUTION: The oxides of nitrogen generated in this experiment are irritating and noxious even in small quantities. Have a beaker of 1 M KOH handy and bubble the nitrogen oxide gases through it for disposal. With MnO2 as catalyst, O2 is generated from H2O2 and gathered into a gas storage bottle. NO is generated from Cu and 2 M HNO3. After being rinsed with 1 M KOH, NO is gathered into a storage bottle. This experiment is carried out at different temperatures by mixing 8 mL of NO with 4 mL of O2. Based on the ideal gas equation, we should estimate the volume of NO and O2 at room temperature so that the initial volume at different designated temperatures can be determined. Therefore, it is necessary to correct the gas volume. With the estimated volume of gas, pump NO and O2 with two 10-mL glass syringes, and place them in a thermostated water bath at a designated temperature to see the difference between the volume and the set volume. Repeat the experiment until the set volume is obtained. Record the corrections. Link the exit at the bottom of the syringe to the conduit of the gas storage bottle with a thin emulsion tube. According to the corrected volume, pump NO and O2 respectively and grip the emulsion tube with the watercontrol clip. Place it upright in a water bath and keep it at the designated temperature for 10 min. Take the syringes containing NO and O2 from the water bath, clean the water on the inner wall of the emulsion tube with absorbent paper, and pull out the emulsion tube at the exit of the syringe containing O2. Meanwhile, block the exit with your index finger and accurately link it to the emulsion tube at the exit of the syringe containing NO. Then, open the water-control clip, push and pull the pin of the syringe containing O2 two or three times to gather the mixed gas totally into one syringe, grip the water-control clip, and place the syringe containing the mixed gases (NO2 and N 2O 4) into the water bath again
893–423K
2NO(g) + O2 (g)
413–294.2K
2NO2(g)
colorless
red-brown
N2O4(g) (1) colorless
Under normal pressure (1 atm) and temperature in the range of 413–423 K, the quantity of N2O4 within this system is negligible and two volumes of NO react with one volume of O2 to produce two volumes of NO2. When the temperature is low, the generated NO2 dimerizes into colorless N2O4. If N2O 4 gas doesn’t liquify (its boiling point is 294.2 K), some of the NO2 produced will dimerize. (Two volumes of NO 2 give 1 volume of N2O 4.) When the temperature is within the range of 294.2–413 K, NO2 and N2O4 coexist in the system; thus the volume of gas in the system is larger than 1 volume but smaller than 2 volumes. If the total volume of gas in the reaction system at a certain temperature is measured by experiment, the actual volume of N2O4 and NO 2 in the system can be obtained. For example, if 2 of volumes NO is mixed with 1 volume of O2 in a closed container and allowed to reach chemical equilibrium under 1 atm at some specified temperature, the total volume of gas in the system can be measured by experiment. Represent this experimental volume by Vm. Let 2V represent the volume of NO2 before any dimerization and x the volume of NO2 after equilibrium is reached. Then the volume of N2O4 is V – x/2. From this the following can be derived: x + (V – x/2 ) = Vm x = 2(Vm – V) V – x/ 2 = 2V – Vm Under a pressure of 1 atm, the total pressure of the mixed gas (NO2 and N2O4) is 1 atm. According to Dalton’s law of partial pressure, the dimerization equilibrium constant K p of NO2 can be expressed as follows:
Kp=
P N 2O 4 P NO 2
2
P⋅ = P⋅
2V – V m Vm
2(V m – V ) Vm
*Corresponding author.
2
=
(2V – V m) ⋅ V m 4(V m – V )
2
(2)
Table 1. Total Volume After 8 mL NO Mixed with 4 mL O2 at Different Temperatures Serial Number of the Experiment Temperature Vm (K) 1 2 3 298.4
4.8
4.7
4.8
299.8
4.8
4.8
4.8
4.77 4.80
310.0
5.1
5.2
5.1
5.13
313.2
5.3
5.3
5.2
5.27
317.0
5.4
5.5
5.3
5.40
322.8
5.6
5.7
5.7
5.67
Vol. 74 No. 2 February 1997 • Journal of Chemical Education
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In the Laboratory
to keep it at the designated temperature. After the volume of the gas remains constant for 5 min, record the total volume of the mixed gas at that temperature. Data Determined
Table 2. Polymerization Equilibrium Constant of NO2 at Different Temperatures Temperature (K)
Kp
Log Kp Determination value
Literature value
298.4
6.50
0.81
0.82
NOTE : The literature value is obtained from the following calculation (1):
299.8
6.00
0.78
0.77
310.0
2.88
0.46
0.45
log K p = 2692/T – 1.75 log T – 4.83 × 10 T
313.2
2.23
0.35
0.35
+ 7.144 × 10{6T 2 – 3.062
317.0
1.79
0.25
0.24
322.8
1.18
0.07
0.07
{3
Conclusion With a glass syringe as the reaction container, we use a water bath to maintain a constant temperature for the determination of the dimerization equilibrium constant of NO2. The result of our determination tallies with the documented value. This experiment has been used in our physical chemistry laboratory for three semesters, and both the instructors and the students are satisfied with the experimental result. The relative error between the experimental result and the documented value is ±5%. Literature Cited 1. Yin, Y.-j. College Chemical Handbook; Shandong Science and Technology Press: Shandong, China, 1985; 830.
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