1

Real Gas Behavior: Gravimetric Determination of the Second Virial Coefficient of CO2

CHEM 457, 2 October 2015, Experiment 04

Faith Tran, Douglas Hiban, Torreh Parach, Daniel Borden

Results and Discussion

After obtaining the data shown in Table 1, the second virial coefficient was determined from this

experiment. The same vessel (mass of empty vessel = 443.743±0.001 g) was used throughout the

experiment, therefore volume (0.5612±0.0001 L) was kept constant. The vessel was kept at a

constant temperature (21.2±0.1 °C) as well. Pressure (varied from 9 to 4 bar) was deliberately

changed to determine the amount of CO2 in the vessel.

P (bar gauge) T (°C)

Mass of Vessel and

CO2 (g)

9.001±0.005 21.2±0.1 460.327±0.001

7.972±0.004 21.2±0.1 459.188±0.001

7.027±0.004 21.2±0.1 458.140±0.001

5.943±0.003 21.2±0.1 456.924±0.001

4.949±0.002 21.2±0.1 455.827±0.001

3.990±0.002 21.3±0.1 454.786±0.001

Table 1. Results obtained in units measured (pressure in bar gauge, temperature in Celsius, and

mass of vessel and CO2 in grams).

Figure 1 shows the calibration of the mass of the vessel with various balanced masses (integer

masses from 1 to 10 g).

2

Figure 1. Balance Calibration Check for Empty Vessel using various balanced masses.

The calibration is checked via the R2 value, which shows how linear data is. A linear plot would

mean good calibration. The R2 value is 1, which means that the graph is extremely linear and that

the balance is accurate enough for this experiment.

The amount of CO2 in moles was obtained by subtracting the measured mass of the empty vessel

from the measured mass of the vessel and CO2 and dividing by the molar mass, as shown in Eq.

(1).

𝑛𝐶𝑂2 =𝑚𝑐𝑔−𝑚𝑐

(𝑀𝑊𝐶𝑂2) (1)

𝑛𝐶𝑂2 = 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐶𝑂2

𝑚𝑐𝑔 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑎𝑛𝑑 𝑔𝑎𝑠

𝑚𝑐 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

𝑀𝑊𝐶𝑂2 = 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝐶𝑂2

The pressure was measured relative to the pressure of the atmosphere (gauge pressure), therefore

the absolute pressure would be the atmospheric pressure (726±1 torr) added to the measured gauge

pressure. Eq. (2) shows the interpolation of the pressure for the elevation above sea level.

𝑃𝑟 = 𝑃1 +ℎ−ℎ1

ℎ2−ℎ1(𝑃2 − 𝑃1) (2)

𝑃𝑟 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑟𝑜𝑜𝑚 𝑎𝑡 1261 𝑓𝑡 (𝑡𝑜𝑟𝑟)

y = 1x + 0.0131R² = 1

448

450

452

454

456

458

460

462

448 450 452 454 456 458 460 462

Pre

dic

ted

Mas

s V

alu

es (

g)

Obtained Mass Values (g)

Balance Calibration Check for Empty Vessel

3

𝑃1, 𝑃2 = 𝐼𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒𝑠 (𝑡𝑜𝑟𝑟)

ℎ = 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝑎𝑏𝑜𝑣𝑒 𝑠𝑒𝑎 𝑙𝑒𝑣𝑒𝑙 (𝑓𝑒𝑒𝑡)

ℎ1, ℎ2 = 𝐼𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛𝑠 (𝑓𝑒𝑒𝑡)

The interpolation was used as opposed to the reading of the mercury barometer because of the

drastic difference in pressure from literature value. According to the literature, the pressure of the

room was for an elevation of about 3500 ft above sea level.[1] The experiment was done at 1261

ft above sea level. This elevation leads to an 8.3% difference in pressure relative to the

interpolated value, which leads to significant difference in the values obtained. Because of this

large difference, it was concluded that the barometer was incorrect. The rest of this discussion

will be based on the interpolated value.

Table 2 shows the data obtained in units that are to be used in this discussion.

P (torr absolute) T (K) mols CO2

7474.3±3.7 294.4±0.1 0.24049±3E-5

6702.4±3.4 294.4±0.1 0.21461±3E-5

5993.6±3.0 294.4±0.1 0.19080±3E-5

5180.6±2.6 294.4±0.1 0.16317±3E-5

4435.0±2.2 294.4±0.1 0.13824±3E-5

3715.7±1.9 294.5±0.1 0.11459±3E-5

Table 2. Results obtained in units used in discussion (pressure in torr absolute, temperature in

Kelvin, and moles of CO2).

A plot of absolute pressure vs. moles of CO2 was then plotted according to Table 2 (shown in

blue). A plot of absolute pressure vs. moles of CO2 was plotted on the same graph according to the

ideal gas law (Eq. 3), as shown in Figure 2.

𝑛𝐶𝑂2 =𝑃𝑉𝑐

𝑅𝑇 (3)

nCO2 is the moles P is the pressure is in atm, Vc is the volume of the vessel in liters, R is the gas

constant in atm L mol-1 K-1, and T is temperature in K.

The ideal gas law assumes that there are no interactions between the molecules and that the

molecules have no finite size. These assumptions are not true, but can be more closely achieved at

high temperatures, high molar volumes, and low pressures.[2]

4

Figure 2. Plot of pressure of vessel vs. moles of CO2 in the vessel.

The blue line shows the data collected from Table 2. The orange line shows the amount of CO2

that would be in the vessel at the given pressure and temperature according to Eq. (3).

The difference in slopes indicate that the data collected deviates from the ideal gas model. The

lower slope (29795±66 torr/mol) of the real data, compared to the slope assuming ideality

(32719±4.5 torr/mol) means that the amount of CO2 does not affect the pressure as much as

ideality. This can be contributed to a compression factor, Z, which is calculated in Eq. (4).[2]

𝑍 =𝑃𝑉𝑚

𝑅𝑇 (4)

This compression factor accounts for the non-ideality of a real gas, which can be contributed from

interactive forces and finite size of the molecules.[2] Figure 3 shows the Z values for each pressure.

y = 29795x + 310.38R² = 1

y = 32719x + 1.5311R² = 1

0

1000

2000

3000

4000

5000

6000

7000

8000

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

Pre

ssu

re o

f V

esse

l (to

rr a

bs)

anount of CO2 (moles)

Pressure vs. Moles

5

Figure 3. Compression factor, Z, with corresponding pressures.

From Figure 3, it can be seen that as pressure goes down, Z goes up. This supports the idea that

lower pressures move gases towards ideality. At lower pressures the molecules are not as close to

each other, so fewer interactions are taking place between the molecules.[2]

𝑃𝑉𝑚

𝑅𝑇= 𝑍 = 1 +

𝐵

𝑉𝑚+

𝐶

𝑉2𝑚

+ ⋯ (5)

The virial equation of state, shown in Eq. (5) accounts for these interactions between molecules.

The virial equation is a model for estimating deviations from ideal gas behavior.[2] The first term

of the right side denotes ideality, the second term denotes interactions between two molecules, the

third term denotes interactions between three molecules, etc. Typically, including for this

experiment, the third term and beyond are much smaller than the first two terms, so they can be

ignored.[2] Only finding the value of B, the second virial coefficient, is of interest.

y = -88240x + 90953R² = 0.9773

3000

4000

5000

6000

7000

8000

0.945 0.95 0.955 0.96 0.965 0.97 0.975 0.98 0.985 0.99 0.995

P(t

orr

ab

s)

Compression Factor, Z

Pressure vs. Compression Factor

6

Figure 4. Plot of Z-1 vs. 1/Vm.

From Figure 4, the slope of the line gives the second virial coefficient, B, -185.1±14.3 cm3/mol.

This is different from the calculated second virial coefficient, according to the literature value.

The calculated B value at 0 °C is -149.7 cm3/mol.[3] The literature B value is less negative than the

one determined from the data. At ideality, B would be 0. The temperature in which a particular gas

is most ideal is called Boyle’s Temperature. In the case of CO2, Boyle’s Temperature, TB, is 714.8

K.[3] Above this temperature, B would be positive. Below this temperature, B is negative. This

means that the more negative B is, the less ideal it is. Therefore the B value determined from Figure

4 indicates a lesser ideality. This should not be the case if no errors occurred with the experiment

because as temperature gets closer to Boyle’s temperature, ideality should increase. From the B

values, this does not follow the expectation. The value from the data is 23.65% higher than the

literature value.

The y-intercept of Figure 4 shows the deviation from ideality because an ideal gas would yield a

y-intercept of 0. The y-intercept here is 0.0258±0.00464, which shows a deviation from ideality.

If the gas were ideal, then the y-intercept would be 0. The compression factor would be 1, so Z-1

would be 0. This, however, shows that at infinitely large molar volumes, the Z value is above 1.

y = -0.185141x + 0.025855R² = 0.976700

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-0.1 0 0.1 0.2 0.3 0.4 0.5

Z-1

1/Vm (mol/L)

Z-1 vs. 1/Vm

7

This shows that at higher molar volumes, above the ideal molar volume, the repulsive forces

dominate.

The more negative B value from the experiment could come from a couple errors. The most likely

error is due to a leak in the vessel. A leak would mean that less pressure and less CO2 would be in

the vessel at the time of weighing, which would ultimately increase the Z value. This explains why

the y-intercept is very positive as opposed to being closer to 1. The difference in the literature

value from the experimental value could be attributed to two things. The first is the purging of the

vessel and CO2 lines. The second is a leak in the vessel. If the lines were not completely purged

correctly or a leak was present, then contaminant molecules, such as oxygen and nitrogen, could

cause error. Oxygen and nitrogen have a lower molar mass than CO2, so the calculation for 1/Vm

would decrease as well. This is more prone and has a higher impact at higher pressures due to the

pressure difference between atmospheric pressure and the pressure of the vessel system. Because

it would affect higher pressure more, it would shift the slope of Figure 4 to be more negative than

the literature value. The amount of time spent weighing the vessel varied, which could have caused

a change in temperature while outside of the water bath.

The significance of this work is that gas ideality can be used to calculate the desired amount of a

gas. If, for example, measuring quantities for ballistics, explosions pressure can be more accurately

determined. For certain loading pressures, the difference between ideal and non-ideal models are

more than 100% different.[4]

The experimental limitations of this experiment are from the inability to measure the temperature

inside the vessel (another possible source of error). The temperature just outside the vessel could

be different than inside the temperature, which means that the calculations for Z may be inaccurate.

Even within the vessel, temperature may differ from spot to spot. This is mostly kept constant with

the water bath.

One way to improve this experiment is possibly have a thermocouple placed inside the vessel and

sealed. This would make the temperature reading inside the vessel more accurate. Also having the

8

balance at the same site as the experiment could minimize slight temperature changes inside water

bath and in the room.

Because of the high error in the second virial coefficient, the experiment was not very successful.

The balance was calibrated well and the volume and temperature stayed fairly constant, but

pressure and the amount of CO2 in the vessel most likely decreased due to the leak in the vessel.

The high R2 value for all linear figures meant that there was certainly a trend that was noticeable

though.

References

[1] Air Pressure and Altitude above Sea Level. Engineering ToolBox.

[2] Milosavljevic, B. H., Lab Packet for Chem 457: Experimental Physical Chemistry, 2015, 4.1-

4.7.

[3] Atkins, P.; De Paula, J. Atkins’ Physical Chemistry 10th ed. W.H. Freeman and Company: New

York. 2014. 46-47.

[4] Volk, F.; Bathelt, H., Application of the Virial Equation of State in Calculating Interior

Ballistics Quantities. Propellants and Explosives. 1976, 1, 7-14.

9

Appendix

Calculations and Error Analysis

Regression for Calibration of Vessel Mass

Interpolation for Pressure of Room

𝑃𝑟 = 𝑃1 +ℎ − ℎ1

ℎ2 − ℎ1

(𝑃2 − 𝑃1)

𝑃𝑟 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑟𝑜𝑜𝑚 𝑎𝑡 1261 𝑓𝑡 (𝑡𝑜𝑟𝑟)

𝑃1, 𝑃2 = 𝐼𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒𝑠 (𝑡𝑜𝑟𝑟)

ℎ = 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝑎𝑏𝑜𝑣𝑒 𝑠𝑒𝑎 𝑙𝑒𝑣𝑒𝑙 (𝑓𝑒𝑒𝑡)

ℎ1, ℎ2 = 𝐼𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛𝑠 (𝑓𝑒𝑒𝑡)

𝑃𝑟 = 733 𝑡𝑜𝑟𝑟 +1261 𝑓𝑡 − 1000 𝑓𝑡

1500 𝑓𝑡 − 1000𝑓𝑡(720 − 733 𝑡𝑜𝑟𝑟)

𝑃𝑟 = 726.214 = 726 𝑡𝑜𝑟𝑟

Uncertainty of Interpolation

𝜕𝑃𝑟 = 1 𝑡𝑜𝑟𝑟

Uncertainty of Temperature

𝜕𝑇 = 0.1 °𝐶 𝑜𝑟 0.1 𝐾

Uncertainty of Balance

𝜕𝑚 = 0.001 𝑔

10

Uncertainty of Pressure of Vessel for 9 bar

𝜕𝑃 = 9.001 × 0.005 = 0.045 𝑏𝑎𝑟

𝜕𝑃 = 0.045 𝑏𝑎𝑟 ×750.061683 𝑡𝑜𝑟𝑟

1 𝑏𝑎𝑟= 33.76 = 30 𝑡𝑜𝑟𝑟

Conversion of Pressure of Vessel (bar gauge to torr absolute) for 9 bar

𝑃 = 𝑃𝑔 + 𝑃𝑟

𝑃 = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑣𝑒𝑠𝑠𝑒𝑙 (𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒)

𝑃𝑔 = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑣𝑒𝑠𝑠𝑒𝑙 (𝑔𝑎𝑢𝑔𝑒)

𝑃 = 9.001 𝑏𝑎𝑟 𝑔 ×100,000 𝑃𝑎

1 𝑏𝑎𝑟×

0.0075006 𝑡𝑜𝑟𝑟

1 𝑃𝑎+ 723 𝑡𝑜𝑟𝑟 = 7474.29 = 7474 𝑡𝑜𝑟𝑟 𝑎𝑏𝑠.

Moles of CO2 for 9 bar

𝑛𝐶𝑂2 =𝑚𝑐𝑔 − 𝑚𝑐

(𝑀𝑊𝐶𝑂2)

𝑛𝐶𝑂2 = 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐶𝑂2

𝑚𝑐𝑔 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑎𝑛𝑑 𝑔𝑎𝑠

𝑚𝑐 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

𝑀𝑊𝐶𝑂2 = 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝐶𝑂2

𝑛𝐶𝑂2 =460.327 − 449.743 𝑔

44.0095 𝑔

𝑚𝑜𝑙

𝑛𝐶𝑂2 = 0.24049 = 0.240 𝑚𝑜𝑙

Uncertainty for moles of CO2

𝜕𝑛𝐶𝑂2 =√𝜕𝑚𝑐𝑔

2 + 𝜕𝑚𝑔2

(𝑀𝑊𝐶𝑂2)

𝜕𝑛𝐶𝑂2 =√(0.001 𝑔)2 + (0.001 𝑔)2

44.0095 𝑔

𝑚𝑜𝑙

𝜕𝑛𝐶𝑂2 = 3.213 × 10−5 = 3 × 10−5 𝑚𝑜𝑙

Uncertainty of Volume of Vessel

𝜕𝑉𝑐 = 0.0001 𝐿

Molar Volume of Vessel for 9 bar

11

𝑉𝑚 =𝑉𝑐

𝑛𝐶𝑂2

𝑉𝑚 = 𝑚𝑜𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒

𝑉𝑐 = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

𝑉𝑚 =0.5612 𝐿

0.24049 𝑚𝑜𝑙

𝑉𝑚 = 2.3336 𝐿

𝑚𝑜𝑙

Uncertainty of Molar Volume for 9 bar

𝜕𝑉𝑚 = 𝑉𝑚 × √(𝜕𝑉𝑐

𝑉𝑐)

2

+ (𝜕𝑛𝐶𝑂2

𝑛𝐶𝑂2)

2

𝜕𝑉𝑚 = 2.3336 𝐿

𝑚𝑜𝑙× √(

0.0001 𝐿

0.5612 𝐿)

2

+ (3 × 10−5 𝑚𝑜𝑙

0.240 𝑚𝑜𝑙)

2

𝜕𝑉𝑚 = 5.079 × 10−4 = 5 × 10−4𝐿

𝑚𝑜𝑙

Inverse Molar Volume for 9 bar

1

𝑉𝑚=

1

2.3336 𝐿

𝑚𝑜𝑙

= 0.4285 = 0.429 𝑚𝑜𝑙

𝐿

Uncertainty of Inverse Molar Volume for 9 bar

𝜕1

𝑉𝑚=

1

𝑉𝑚× |𝑞|

𝜕𝑉𝑚

𝑉𝑚

𝑞 = 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 (−1)

𝜕1

𝑉𝑚= 0.429

𝑚𝑜𝑙

𝐿× |−1|

5 × 10−4 𝐿𝑚𝑜𝑙

2.3336 𝐿

𝑚𝑜𝑙

𝜕1

𝑉𝑚= 9.1918 × 10−5

𝑚𝑜𝑙

𝐿

Compression Factor, Z, of CO2 at 9 bar

12

𝑍 =𝑃𝑉𝑚

𝑅𝑇

𝑍 = 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟

𝑅 = 𝑔𝑎𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 0.0821𝑎𝑡𝑚 𝐿

𝑚𝑜𝑙 𝐾

𝑇 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 (𝐾)

𝑍 = 7474 𝑡𝑜𝑟𝑟 ×1 𝑎𝑡𝑚

760 𝑡𝑜𝑟𝑟× 0.429

𝐿

𝑚𝑜𝑙×

1

0.0821𝑎𝑡𝑚 𝐿𝑚𝑜𝑙 𝐾

×1

298 𝐾

𝑍 = 0.9497 = 0.950

Uncertainty of Compression Factor, Z, CO2 for 9 bar

𝜕𝑍 = 𝑍 × √(𝜕𝑃

𝑃)

2

+ (𝜕𝑉𝑚

𝑉𝑚)

2

+ (𝜕𝑇

𝑇)

2

𝜕𝑍 = 𝑍 × √(3.73 𝑡𝑜𝑟𝑟

7474.3 𝑡𝑜𝑟𝑟)

2

+ (5 × 10−4

𝐿𝑚𝑜𝑙

0.2405 𝐿

𝑚𝑜𝑙

)

2

+ (0.1 𝐾

294.35 𝐾)

2

𝜕𝑍 = 0.00206 = 0.002

Regression for Pressure (torr) vs. moles of CO2 (from Data)

13

Regression for Pressure (torr) vs. moles of CO2 (from Ideal Gas Assumption)

Regression for Z-1 vs. 1/Vm

Calculated virial coefficient

𝐵 = 𝑏 − (𝑎

𝑅𝑇)

𝑎 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑖𝑛𝑡𝑒𝑟𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑓𝑜𝑟𝑐𝑒𝑠 (𝑎𝑡𝑚 𝐿2

𝑚𝑜𝑙2)

𝑏 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑓𝑖𝑛𝑖𝑡𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑠𝑖𝑧𝑒 (𝐿

𝑚𝑜𝑙)

14

𝐵 = 𝑠𝑒𝑐𝑜𝑛𝑑 𝑣𝑖𝑟𝑖𝑎𝑙 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

𝐵 = 4.29 × 10−2𝐿

𝑚𝑜𝑙−

3.610 𝑎𝑡𝑚 𝐿2

𝑚𝑜𝑙2

(0.0821𝑎𝑡𝑚 𝐿𝑚𝑜𝑙 𝐾

) (273.15 + 21.2 𝐾)

𝐵 = −0.10648𝐿

𝑚𝑜𝑙= −106.48

𝑐𝑚3

𝑚𝑜𝑙

Error in literature value

𝜎 =|𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑎𝑐𝑡𝑢𝑎𝑙|

𝑎𝑐𝑡𝑢𝑎𝑙× 100%

𝜎 = |−185.1 − (−149.7)

−149.7| × 100% = 23.65%

Report Questions

1. It is important to account for atmospheric pressure when completing data analysis because

the gas it effected by the absolute pressure within the vessel, not just the pressure relative

to the atmosphere. If the outside pressure is not accounted for, then the compression factor

calculated as pressure goes down goes down as well, which is not what the expectation is.

Less pressure would mean less interaction and would be more ideal.

2. The literature value states that the second virial coefficient is -149.7 cm3/mol. The

calculated second virial coefficient from this experiment was calculated to be -185.14

cm3/mol. The calculated coefficient from the experiment is lower than the calculated

literature value. The second virial coefficient is temperature dependent and the literature

shows this value at 273 K. The experiment was conducted at 21.2 °C. This, however, does

not account for the more negative value. A temperature closer to Boyle’s temperature

should denote a B value that is closer to zero. Since this is further away from zero, which

is where Boyle’s temperature would be and where a gas is most ideal,[1] then this means

that this is less ideal than expected. This may be due to errors in the experiment. There was

a leak in the vessel, which would make the mass, and therefore calculated amount of the

CO2 lower than what it should be. This would cause the compression factor and second

15

virial coefficient to go down. Another possible source of error could come from having a

lower pressure in the room measured than what the actual pressure is. There was concern

with the pressure reading on the mercury barometer due to the large difference from 1

atmosphere. Based on literature value, it would mean that the experiment was completed

at about 3000 ft above sea level, but the experiment was completed 1261 ft above sea level.

Because of this, the elevation was taken and interpolated based on literature. This is still

only an estimate, so it still may be inaccurate.

3. Ideal behavior assumes that there are no interactions between the molecules. This does not

occur with a real gas, however. A real gas will interact with other molecules because

molecules have interactive forces and a finite size. These two factors are taken into account

when using van der Waals equation.