Determining the Molar Mass of a Gas using the Ideal Gas Law
Name: Olaoluwa Ajayi (H00242503) Group Number: 2 Experiment carried out on: 10/11/16 Report submitted on: 17/11/16 Supervisor’s Name: Graeme Collie
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Contents
Synopsis: ................................................................................................................................................. 3 Aim:......................................................................................................................................................... 4 Theory: .................................................................................................................................................... 4 Procedures and Techniques: .................................................................................................................. 5 Experiment 1: Determination of the Molar Mass of a Gas ................................................................. 5 Experimental Procedure ..................................................................................................................... 5 Results – Experimental and Derived:..................................................................................................... 7 Table of Results ................................................................................................................................. 7 Sample Calculation ............................................................................................................................ 8 Mean and Standard Deviation .......................................................................................................... 9 Discussion of Results: ........................................................................................................................... 10 Conclusion: ........................................................................................................................................... 10 References: ........................................................................................................................................... 11
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Synopsis: The purpose of this experiment was to determine experimentally the molar mass of gas. This was achieved by injecting a weighed amount of liquid into a gas syringe which was heated by the steam jacket surrounding it. Just before the liquid was injected, the atmospheric pressure was measured. As the liquid vaporised, the volume occupied by the mass of gas and its temperature were measured. Each measurement was noted down, which allowed the molar mass (M) to be calculated. This procedure was repeated 5 times. The results obtained are shown below:
Attempt Number 1 2 3 4 5 Mean molar mass (g/mol)
Molar mass (g/mol) 108.77 112.55 112.20 103.73 116.65 110.78
Mean molar mass = 110.78 g/mol Standard deviation of results = 4.32085 Calculated value for molar mass of gas: (111 ± 4.32) g/mol (3 significant figures)
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Aim: The aim of this experiment is to determine the molar mass (M) of an unknown liquid by measuring the volume occupied by a known amount of gas when vaporised at a known temperature and pressure.
Theory: The analysis of gas is a complicated process. These energetic gas particles move around in a confined space, which collide and interact with each other. Since it is difficult to describe a gas on a scientific basis, chemists came up with a theoretical concept of an “ideal gas” in which the behaviour of gases can be analysed without the limitation of real world conditions. An ideal gas is defined as a theoretical concept of gas, in which collision between molecules are perfectly elastic (kinetic energy is conserved), and each molecule has negligible volume and negligible intermolecular forces. Ideal gases have no intermolecular interactions such as real gases, so the explanation of ideal gas isn’t overcomplicated by such conditions. No gases in real life are considered to be an “ideal” but there are lots of gases that can relate similarly to this concept of an ideal gas provided that their pressure is relatively low. This enables the use of the concept of an ideal gas to better understand the behaviour of real gases
A visual representation of an ideal gas can be imagined as a collection of circular molecules in a really small container (negligible in volume) in which the molecules move randomly in straight lines and that the pressure in the container is only caused by the molecules colliding with the container walls. The ideal gas equation is given as: PV = nRT Where: P =Pressure, V =volume n= number of moles, R = gas constant and T = temperature. The ideal gas equation can be derived from the combination of 3 gas laws: Boyle’s law, Charles’s law and Avogadro’s Law.
Calculating Molar Mass (M) In order to calculate the molar mass of gas using the ideal gas equation we can incorporate the equation: n=w/M where w is the mass of gas. By replacing this in the above equation, molar mass is given by: M=
wRT pV
If the temperature, pressure, volume and mass of the gas are measured experimentally, the molar mass of the gas can be calculated.
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Procedures and Techniques: Experiment 1: Determination of the Molar Mass of a Gas Equipment 500ml round bottom flask Isomantle heater Thermometer gas syringe and jacket 2cm3 hypodermic syringe (with needle attached) Cork bung Self-sealing cap Electronic barometer
Chemicals Unknown liquid: sample 6
Experimental Procedure: 1. The 500ml round bottom flask was half filled with hot water which was put into an isomantle. A conical stopper was then placed onto the flask. The isomantle was then switched and the water in the flask heated until it reached its boiling temperature of 100°C. 2. The small wooden cork attached to the needle of the hypodermic syringe was first removed. The inside of syringe was then rinsed with the unknown liquid sample. Approximately 2cm3 of the unknown sample was extracted ensuring there were no air bubbles present inside the syringe. The syringe needle was dried using a paper towel and the cork bung was reattached onto the syringe needle. 3. The syringe along with its contents with cork bung attached to the needle were weighed using a 4-figure balance. Care was taken to ensure the balance was reset to zero before the syringe was placed onto the balance and also that the same value of weight was given successive times. This weight was noted and was found to be 5.2455g 4. The self-sealing cap located on the nozzle of the gas syringe was removed and its volume was set to approximately 5cm3 (of air) by adjusting the syringe barrel. This value was noted on the syringe and was found to be 6cm3. 5. The self-sealing cap was refitted back onto the gas syringe nozzle. Plastic tubing from the flask filled with water was connected to the gas syringe which allowed steam to pass through its surrounding jacket. After a few minutes The thermometer inside the steam jacket was noted and this value was found to be 99°C. (This value of temperature remained relatively constant for the duration of the experiment) 6. The cork bung was removed from the syringe needle and needle was then inserted slowly into the self-sealing cap of the gas syringe. Care was taken to ensure the needle tip was beyond the narrow nozzle before proceeding.
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7. The atmospheric pressure obtained by the electronic barometer was noted before inserting the syringe needle. This value was found to be 29.26inHg. 8. This value was converted to mmHg by multiplying the obtained value by 25.4. Using the unit conversion factor of 760mmHg = 101325 Pa the atmospheric pressure in Pascal (Pa) can calculated. This was calculated to be 99085.18 Pa. This value was noted. 9. The liquid from the hypodermic syringe was slowly injected into the steam syringe. As the liquid vaporized, the pressure inside the gas syringe would build up as more gas molecules are introduced into gas chamber, causing the syringe barrel to move downwards. A sufficient amount of liquid was injected to give a final volume of approximately 80cm3. The value obtained from the gas syringe was found to be 78cm3. 10. The hypodermic syringe was withdrawn from the self-sealing cap and the cork bung was placed onto the needle securely. 11. The volume of vapour occupied in the gas syringe was found by the difference between the volume of air plus the vapour in the gas syringe and the initial volume of air in the gas syringe. The volume of vapour occupied in the gas syringe was found to be 72cm3. This value was noted. 12. The hypodermic needle as then reweighed on the 4-figure balance and the value obtained was 4.9946g. This value was noted. 13. The mass of liquid injected into the gas syringe was calculated using difference between the initial and final mass of the hypodermic needle. The mass of liquid injected into the gas syringe was found to be 0.2509g. This value was noted 14. The self-sealing cap was removed from the nozzle of the gas syringe and the volume of air in the syringe was rest to a volume of approximately 5cm3. The Molar Mass of the vapour was determined using the formula: M=
wRT PV
Where M = Molar mass (g/mol) w = mass of vapour (g) R = Gas constant (8.314 J K-1 mol-1) T = Temperature (K) P = Atmospheric Pressure (Pa) V = volume of vapour (m3) The value of M obtained was calculated to be 109g/mol. This value was noted down.
15. This procedure was repeated a further 4 times, ensuring the hypodermic needle was reweighed and the atmospheric pressure was checked before each injection.
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Results - Experimental and Derived: Table of Results Attempt 1 Mass of liquid used (g)
Temperature (K)
Atmospheric Pressure (Pa)
0.2509
372
99085.18
Mass of liquid used (g)
Temperature (K)
Atmospheric Pressure (Pa)
0.2784
371
99085.18
Mass of liquid used (g)
Temperature (K)
Atmospheric Pressure (Pa)
0.2624
372
99085.18
Mass of liquid used (g)
Temperature (K)
Atmospheric Pressure (Pa)
0.2784
373
99085.18
Mass of liquid used (g)
Temperature (K)
Atmospheric Pressure (Pa)
0.2616
372
99085.18
Initial volume of air (m3) 0.6 × 10-5
Final volume of air + gas (m3) 7.8 × 10-5
Volume of vapour used (m3)
Molar Mass (g/mol)
7.2 × 10-5
108.77
Initial volume of air (m3) 0.7 × 10-5
Final volume of air + gas (m3) 8.4 × 10-5
Volume of gas used (m3)
Molar Mass (g/mol)
7.7 × 10-5
112.55
Initial volume of air (m3) 0.8 × 10-5
Final volume of air + gas (m3) 8.1 × 10-5
Volume of vapour used (m3)
Molar Mass (g/mol)
7.3 × 10-5
112.20
Initial volume of air (m3) 0.5 × 10-5
Final volume of air + gas (m3) 8.9 × 10-5
Volume of vapour used (m3)
Molar Mass (g/mol)
8.4 × 10-5
103.73
Initial volume of air (m3) 0.6 × 10-5
Final volume of air + gas (m3) 7.6 × 10-5
Volume of vapour used (m3)
Molar Mass (g/mol)
7.0 × 10-5
116.65
Attempt 2
Attempt 3
Attempt 4
Attempt 5
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Sample Calculation: (Attempt 1) Initial Mass of hypodermic syringe = 5.2455g Final Mass of hypodermic syringe = 4.9946g Mass of liquid used (w) = 0.2509g Temperature (T) = 99°C (372K) Atmospheric Pressure (p) = 29.26inHg × 25.4 = 743.2mmHg (99085.18 Pa) Initial volume of gas syringe = 6cm3 = 6.0 × 10-5 m3 Final volume of air + gas = 78cm3 = 7.8 × 10-5 m3 Volume of gas used (V) = 72cm3 = 7.2 × 10-5 m3
Converting mmHg to Pa 760mmHg → 101325 Pa 1mmHg → 101325/760 743.2mmHg → (101325/760) × 743.2 = 99085.18 Pa
Calculating Molar mass (M)
M=
M=
𝑤𝑅𝑇 𝑝𝑉
0.2509 × 8.314 × 372 99085.18 × 7.2 ×10−5
M = 108.77 g/mol (2 decimal places)
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Mean and Standard Deviation:
Attempt Number 1 2 3 4 5 Mean molar mass (g/mol)
Molar mass (g/mol) 108.77 112.55 112.20 103.73 116.65 110.78
Standard deviation
∑ni=1 (xi — x̄ ) 2 √ σ= n
Where: xi = calculated molar mass x̄ = mean molar mass n = number of repeats
2 2 2 2 2 σ = √((108.77 − 110.78) + (112.55 − 110.78 ) + (112.20 − 110.78) + (103.73 − 110.78 ) + (116.65 − 110.78 ) )
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σ = 4.32085
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Discussion of Results: The experiment was carried out in an efficient and systematic manner with no unusual events occurring that would’ve introduced error. Overall, the molar mass obtained for each attempt of the unknown liquid didn’t vary considerably. Although, the molar mass obtained in attempt 4 was significant different from the other 4 results. Despite having the same mass as attempt 2 (with a slight difference in temperature), the volume occupied by the gas during this attempt was much larger than anticipated. A possible reason for this could have been due to a decrease in atmospheric pressure the moment the syringe was injected. Since the atmospheric pressure was checked before the syringe was injected, this would’ve been undetected. This would result in the gas molecules colliding with the container walls as frequently which is accompanied by a larger volume occupied by the gas. Another possibility could have been a decrease in temperature the moment the syringe was injected. This would lead to the gas molecules having less kinetic energy to move around in comparison to their previous temperature. This would result to less collisions of gas molecules with each other and the container walls. This also could have been the reason a larger volume of gas was occupied in attempt 4. This change temperature may have been too small to alter the obtained value shown on the thermometer. There is a possibility that the equipment used in the experiment may have been faulty. This would lead to inaccurate measurements being made caused by systematic errors occurring. This results in the molar masses obtained to alter significantly from the true value. The experimental error for the mean molar mass was given as the standard deviation. The standard deviation formula took into account the mean molar mass, the number of repeats taken and individual molar masses obtained. When choosing which formula to use in calculating the standard deviation, the population formula was chosen over the sample formula. This is because the population standard deviation formula is more suited to laboratory experiments. This also resulted in a smaller value for the standard deviation in comparison to using the sample formula. For our experiment, we were given an unknown chemical in liquid form in which we had to determine its molar mass. The molar mass of the chemical is an important value in chemistry in determining what the chemical actually is. If the experiment also required us to find out what this liquid was, the molecular formula of the chemical can be determined by elemental analysis. Using this analysis would enable mass percentage of each element present in the unknown chemical to be obtained. From this information, the empirical formula of the chemical can be calculated in from which the molecular formula can also be calculated. Further analysis of the chemical could also be done such as IR spectroscopy. This would help to identify various functional group present in the unknown chemical.
Conclusion: The calculated value for the molar mass of gas obtained from the experiment was found to be: (111 ± 4.32) g/mol (3 significant figures)
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References: Websites: Chemistry LibreTexts (2013) The Ideal Gas Law [online], available: http://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Physical_Properties_of_Matte r/States_of_Matter/Gases/Gas_Laws/The_Ideal_Gas_Law [accessed 12 November 2016].
Clark, J. (2010) Ideal Gases and the Ideal Gas Law [online], available: http://www.chemguide.co.uk/physical/kt/idealgases.html [accessed 12 November 2016].
Blaber, M. (1996) The Ideal Gas Equation [online], available: http://www.mikeblaber.org/oldwine/chm1045/notes/Gases/IdealGas/Gases04.htm [accessed 14 November 2016].
Books: Blackman, A., Bottle, S. and Schmid, S. (2011) Chemistry, 2nd ed., Canberra: John Wiley & Sons Australia.
School of Engineering & Physical Sciences 2016, Laboratory Manual for Year 1 Chemical Engineering Academic Year 2016-17
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