P Chem Lab 6

Tompall Toone Nathaly Murillo Aaron Reinicker Physical Chemistry I Chem 445-021 Experiment 6 Vapor Pressure of a Pure Liquid Abstract In this experiment the vapor pressure of methanol was measured by means of a vacuumed isoteniscope in a stirred water bath. The heat of vaporization as calculated by the Clausius-Clapeyron equation was ∆Hvap = 33.104 + 0.968 kJ/mol, which is somewhat close to the literature value of ∆Hvap =35.21 kJ/mol. Using the Antoine equation the heat of vaporization was calculated to be ∆Hvap = 50.085 + 0.351 kJ/mol. The Antoine Equation provides a better fit for the experimental data since most of the residuals are 0 or extremely close to the experimental data when compared to the Clausius-Clapeyron equation. Two trials were performed. The second trial appeared to be more accurate since the values of its Antoine coefficients (A = 8.754, B = 2025.15, C = 280.549) were closer to the literature values (A = 8.07240, B = 1574.990, C = 238.870). The Antoine coefficients for trial 1 were calculated as: (A = 10.75, B=3926.05, C = 434.57).

Introduction In this experiment, the vapor pressure of methanol was measured. Vapor pressure of a pure compound is an intensive property that is independent of the amounts of the two phases (gas and liquid) as long as both are present. It is defined as the pressure of a system in which the gas of a substance is in dynamic equilibrium with its liquid form. Since vapor pressure strongly increases as a function of temperature and slightly increases as a function of applied pressure, it was necessary to record the vapor pressure. The vapor pressure of the system was measured using a MKS Baratron pressure gauge in which it increased strongly as a function of increasing temperature. The following equation relating the variation of vapor pressure with temperature was used to analyze the results: (1) The above equation is known as the Clausius-Clayeron equation and was used under the assumption that the heat of vaporization is independent of temperature. In equation 1, P represents the vapor pressure of the liquid, T represents the temperature in Kelvin, and ΔHvap stands for the molar heat of vaporization for methanol. Equation 1 will give an accurate fit to vapor pressure data over a wide range of temperatures, as long as the temperature is well below the critical temperature. This will cause compensating errors in the analysis, and therefore a more accurate equation is required to consider the variation of vapor pressure with temperature. Hence the following equation, the Antoine equation, was used to give a more elaborate method for finding vapor pressure as a function of temperature: (2)

A, B, and C in the Antoine equation are empirical constants obtained from a fit to the data.

Procedure Ice was packed around the glass trap. Next, the constant temperature bath was set to 24oC. Once the isoteniscope cooled from being in the oven, the bulb was filled approximately three-fourths of the way with methanol. The isoteniscope was clamped into the constant temperature bath and then connected to the vacuum pump. The vacuum pump was turned on and pressure was slowly reduced until the vaporization pressure. The vapor pressure was reached when the methanol boiled vigorously and after several evacuations, the pressure equilibrated back to the previous reading. No methanol was allowed to enter into the U-tube part of the isoteniscope during these evacuations. Once the vapor pressure was discovered, methanol was allowed to enter the U-tube of the isoteniscope. Methanol in the tube was leveled by increasing, opening the system to the atmosphere, or decreasing, turning on the vacuum, the pressure. The constant bath temperature was then increased by various increments. During the temperature increase the level of the methanol fluctuated, so; pressure was again increased or decreased as needed. After the temperature became constant and the methanol leveled, the pressure was recorded. Temperature was increased until methanol’s boiling point was reached, 64.7 oC and the pressure was then at atmospheric pressure, approximately 760 torr. The system was then returned to room temperature and pressure. Finally, the methanol was removed from the isoteniscope. This procedure was then

repeated for a second trial, however; the temperature of the constant temperature bath was increased at a different interval then the first trial.

Results and Analysis Table 1 includes temperature, in both Celsius and Kelvin, inverse of both temperature, pressure, and the natural log of the pressure for both runs. With this data, Figure 1 is produced showing the relationship temperature (in degrees Celsius) and pressure. This plot is used to determine if our data, though from different trials, are related. Ideally, the two trials will form one monotonically increasing curve. The data yields an acceptable trend. Figure 2 shows the linear relationship between the natural log of pressure and inverse temperature (in Kelvin). This relationship yields the parameters for the ClausiusClapeyron equation, the molar heat of vaporization is 33.104 +/- 0.968 kJ/mol, fairly close to the literature value of 35.21 kJ/mol, and a y-intercept, A’, of 8.0067+/- .049. Table 2 provides the temperature, the experimental pressure, the calculated pressure from the Clausius-Clapeyron equation, and the difference between the experimental pressure and the Clausius-Clapeyron calculated pressure. Next using equation 6, parameters for the Antoine Equation, A, B, and C, were calculated using Regression in Excel. The parameter for the Antoine Equation A, B, and C in the first trial were 10.75, 3926.05, and 434.57 respectively, for the second trial: A = 8.754, B = 2025.15, C = 280.549. Once the Antoine parameters for the trials were found, Table 2 includes the pressure calculated using the Antoine equation and the difference between the experiential pressure and the calculated Antoine pressure.

Figure 3a displays the first trials pressure differences, for both equations, verses the experimental pressure, a plot of the residuals. Figure 3b displays the same information only the data used in the second trial. No systematic error seems to be prevalent in the second trial. However, the first trial seems to show signs of clustering and an increasing trend in the later data points; these results indicate a bias. This bias also explains why Figure 1 is not a smoother curve. In general, the Antoine Equation yielded smaller residuals meaning the calculated value was more similar to the experimental values. This means that the Antoine Equation is a better model and fits the data closer. The calculated values for the Antoine Equation were compared to the literature value for methanol, A = 8.07240, B = 1574.990, C = 238.870. The second trial yielded results that are more accurate. The inaccuracy of the first trial is due to a systematic error as found in Figure 3a. The boiling point of methanol is 64.7 oC, found on the methanol bottle used in the experiment. The calculated boiling point, at 760 torr, using the Figure 2b, the ClausiusClapeyron method, is 64.4 oC. Using Antoine Equation parameters found: Trial 1 equals 64.3 oC and Trial 2 equals 64.3 oC. Both equations obtain reasonable results. This analysis was repeated for a set of given data and the Clausius-Clapeyron and Antoine equations were compared. Figure 4 shows the relationship between pressure and temperature in Celsius. The given data provides an extremely nice trend. Figure 5 is used to calculate the parameters for the Clausius-Clapeyron; Figure 5 plots natural log of pressure verses inverse temperature. The heat of vaporization is 50.085 + 0.351 kJ/mol and the y-intercept, A, equals 9.2709 + 0.0501. Table 3 calculates the residuals for both the Clausius-Clapeyron and Antoine Equation (found using equation 6). The Antoine

parameters were found to be A = 7.20976 + 0.06142, B =1329.233 + 23.217, C = 169.4521 + 2.362. Figure 6 plots these residuals. The Antoine Equation provides a better fit for the experimental data because the most of the residuals are 0 or extremely close to the experimental data. Data and Results Table 1a: Experimental Data Trial 1 Temp (C) 24.0 29.0 34.0 40.0 46.0 52.0 58.0 63.2

Temp (K) 297.15 302.15 307.15 313.15 319.15 325.15 331.15 336.35

1/T (C) 0.0417 0.0345 0.0294 0.0250 0.0217 0.0192 0.0172 0.01582

1/T (K^-1) 0.003365 0.00331 0.003256 0.003193 0.003133 0.003076 0.00302 0.002973

Pressure (torr) 156.6 191.6 235.3 300.9 384.2 489.2 620 730.4

Log{P} 2.195 2.282 2.372 2.478 2.585 2.690 2.792 2.864

Footnote: Vapor Pressure at air evaporation = 114.5 torr Table 1b: Experimental Data Trial 2 Temp (C) 31.0 36.0 41.0 47.0 53.0 57.0 62.0

Temp (K) 304.15 309.15 314.15 320.15 326.15 330.15 335.15

1/T (C) 0.0323 0.0278 0.0244 0.0213 0.0189 0.0175 0.0161

1/T (K^-1) 0.003288 0.003235 0.003183 0.003124 0.003066 0.003029 0.002984

Pressure (torr) 181.8 224.6 286.4 372.9 482.3 567.1 693.9

Footnote: Vapor Pressure at air evaporation = 128.1 torr

Log{P} 2.260 2.351 2.457 2.572 2.683 2.754 2.841

Figure 1a : Pvap vs Temperature Separate Trials Temperature vs Pvap 800 700 Pressure (torr)

600 500

Trial 1

400

Trial 2

300 200 100 0 0

20

40

60

80

Temperature (C)

Figure 1b : Pvap vs Temperature Combined Temperature vs Pvap combined

y = 9E-05x 3 + 0.2729x 2 - 9.7997x + 234.46 R2 = 0.9955

800 700 Pvap (torr)

600 500 400

Poly. (Series1)

300 200 100 0 0

10

20

30

40

Temperature (C)

50

60

70

Figure 2a: Log(P) vs 1/T Separate Trials log(P) vs 1/T 3.5 3

2

Trial 1

1.5

Trial 2

1 0.5 0 0.00295 0.003 0.00305 0.0031 0.00315 0.0032 0.00325 0.0033 0.00335 0.0034 1/T (K^-1)

Figure 2b: Log(P) vs 1/T Combined log(P) vs 1/T Combined

log(P)

log(P)

2.5

3 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 0.0029

y = -1729.3x + 8.0067 R2 = 0.9995

Series1 Linear (Series1)

0.003

0.0031

0.0032

0.0033

0.0034

1/T (K^-1)

A’ = 8.0067 + 0.049 ∆Hvap = 33.104 + 0.968 kJ/mol

Table 2: Differences Between Experimental and Calculated Values T (C) 24 29 31 34 36 40 41 46 47 52 53 57 58 62 63.2

P(exp) (torr) 156.6 191.6 181.8 235.3 224.6 300.9 286.4 384.2 372.9 489.2 482.3 567.1 620.0 693.9 730.4

P(calc, eq2) {|P (Exp) – P(calc) {P(exp)-P(calc)} (torr) P(Calc)|} (torr) Antoine (torr) Antoine (torr) 153.8 2.8 155.3228622 1.277137833 192.0 0.4 192.1225483 -0.52254834 209.4 27.6 208.9104465 -27.11044647 238.0 2.7 236.5650336 -1.26503363 258.8 34.2 256.7803004 -32.18030041 305.1 4.2 301.9141984 -1.014198431 317.7 31.3 314.2528034 -27.85280336 387.5 3.3 382.9758062 1.224193832 402.9 30 398.2316235 -25.33162353 487.8 1.4 482.960722 6.239278023 506.5 24.2 501.7193341 -19.41933413 587.2 20.1 583.4231056 -16.3231056 609.0 11 605.6169807 14.38301927 702.9 9 702.1059655 -8.2059655 733.4 3 733.6059297 -3.205929664 Footnotes: Hvap = 33.104 + 0.968 kJ/mol Antoine Coefficients (A = 10.75, B=3926.05, C = 434.57)

Figure 3a: {P (Exp) – P(Calc)} vs. P{Exp} Combined 20

{P (Exp) – P(Calc)}

10 0 0

100

200

300

400

-10

500

600

700

800 Clausius Clapyron

-20

Antoine

-30 -40 P{Exp}

Figure 3b: {Pexp - Pcalc} vs. Pexp Trial 2 3 2

Pexp

1 0 -1

Antoine Trial 2 0

100

200

300

400

500

600

700

800

Clausius Trial 2

-2 -3 -4 {Pcalc - Pexp}

Footnote: Antoine Coefficients Trial 2: A = 8.754, B = 2025.15, C = 280.549 Trial 1: A = 10.75, B=3926.05, C = 434.57

Sample Data of Unknown Substance (Provided in Lab) Figure 4: Temperature vs Pressure (Data Given)

y = 0.0011x 3 - 0.1751x 2 + 10.927x - 227.85 R2 = 0.9999

Pressure (mmHg)

900 800 700 600

Given Data

500 400

Poly. (Given Data)

300 200 100 0 0

50

100 Temperature (C)

150

Figure 5: log(P) vs. 1/T Given Data y = -2616.4x + 9.2709 R2 = 0.9991

3.5 3

log(P)

2.5 2

Given Data Linear (Given Data)

1.5 1 0.5 0 0.002

0.0022

0.0024

0.0026

0.0028

0.003

0.0032

0.0034

1/T (K^-1)

A = 9.2709 + 0.0501 ∆Hvap = 50.085 + 0.351 kJ/mol Table 3: Differences Between Experimental and Calculated Values of Given Data T (C)

Pexp (torr)

Pcalc Clausius (torr)

{Pexp – Pcalc} Clausius (torr)

45 50 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 131.6 135 140

10.2 14.1 26.0 34.5 45.4 58.9 75.7 96.4 121.5 151.8 188.2 231.4 282.4 342.2 412 492.9 586.1 627.93 692.9 814.8

11.15 14.94 26.15 34.16 44.28 56.98 72.80 92.38 116.5 145.9 181.7 224.9 276.9 339.0 413.0 500.6 604.0 640.7 725.3 867.1

0.9456703 0.839993551 0.144513468 -0.34098393 -1.11607989 -1.91658342 -2.89684891 -4.019353 -5.04351836 -5.91379742 -6.54703556 -6.51914055 -5.55109117 -3.19432458 0.98445244 7.718977445 17.85961595 12.78193879 32.38995449 52.3437392

Pcalc Antoine (torr) 10.20129881 14.12540212 25.95394561 34.50241545 45.32416619 58.87914104 75.68958079 96.3435099 121.4978445 151.8810803 188.2955285 231.6190726 282.8064324 342.8899252 412.9797226 494.2636108 588.0062639 620.8520501 695.5480508 818.3033945

{Pexp-Pcalc} Antoine (torr) 0.001298806 0.025402123 -0.046054391 0.002415447 -0.075833814 -0.020858959 -0.010419213 -0.0564901 -0.002155538 0.081080347 0.095528495 0.219072553 0.406432418 0.689925209 0.979722649 1.363610759 1.906263913 -7.077949863 2.64805079 3.503394454

Footnote: Antoine Coefficients: A = 7.20976 + 0.06142 , B =1329.233 + 23.217 , C = 169.4521 + 2.362

Figure 6: (Pcalc – Pexp) vs Pexp for Clausius and Antoine Given Data

{Pcalc - Pexp} vs. {Pexp} Given Data

{Pcalc - Pexp} (mm Hg)

60 50 40 30 Clausius

20

Antoine

10 0 -10

0

100

200

300

400

500

600

700

800

900

{Pexp} (mm Hg)

Conclusion: The literature value for ∆Hvap of methanol is 35.21 kJ/mol and our calculated value was ∆Hvap = 33.104 + 0.968 kJ/mol. I think that the difference in this data was due to the fact that we calculated two different Room Temperature Vapor Pressures when we evacuated all the air from the system. For Trial 1 the Vapor Pressure at 24C was 114.5 torr while for Trial 2 our Vapor Pressure at 23.9C was 128.1 torr. I performed an additional analysis on the second trial by graphing its {Pexp – Pcalc} vs. Pexp. The second trial appears to be more accurate because the values of its Antoine coefficients (A = 8.754, B = 2025.15, C = 280.549) are closer to the literature values (A = 8.07240, B = 1574.990, C = 238.870) then for trial 1 (A = 10.75, B=3926.05, C = 434.57) which means that we may have brought the pressure down too low in that trial. Even with this error, the Antoine equation still appears to be a better fit then the Clausius Clapeyron Equation for both our experiment and the unknown data provided.

References: 1. NIST Chemistry Webbook. “Methyl Alcohol” U.S. Secretary of Commerce. 4 April 2008. 2. Wang, Nam Sun. Bubble Point /w Antoine Equation. “Computer Methods in Chemical Engineering” 4 April 2008.