# Laboratory Report: Ideal Gas Law and Determination of Relative Molecular Mass

Categories: Biology

In this laboratory experiment, we aim to investigate the relationship between the height of mercury in an open-ended tube and a closed-end tube. Specifically, we will explore the conditions under which the height of mercury in the open-ended tube is higher or lower than the closed-end tube. The experiment involves measuring the volume and pressure of gas in both scenarios and comparing the results.

Apparatus:

1. Mercury-filled open-ended tube
2. Mercury-filled closed-end tube
3. Pressure measuring device
4. Ruler or caliper for height measurements
5. Atmospheric pressure gauge

Procedure:

1. Set up the apparatus with the open-ended and closed-end tubes filled with mercury.

2. Measure the initial heights of mercury in both tubes using a ruler or caliper.
3. Record the atmospheric pressure using the atmospheric pressure gauge.
4. Conduct experiments where the open-ended tube's height is higher and lower than the closed-end tube.
5. Measure the final heights of mercury in both tubes for each experiment.
6. Record the data for further analysis.

Calculations: For the experiment where the height of mercury in the open-ended tube is higher: P=Patm​+(Px1​−Px2​) V=hg​

For the experiment where the height of mercury in the open-ended tube is lower: P=Patm​−(Py1​−Py2​) V=hg​

Table 1: Initial and Final Heights of Mercury

 Experiment Initial Height (cm) Final Height (cm) Pressure (P) 1 hx1 hx2​​ Patm​+(Px1​−Px2​)​​ 2 hy1 hy2 Patm​−(Py1​−Py2​)

Create a graph plotting pressure (P) against volume (V) for both experiments.

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This will help visualize the relationship between pressure and volume under different conditions.

Interpret the results in terms of Boyle's Law, which states that at constant temperature, the pressure of a gas is inversely proportional to its volume.

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Discuss how the height difference in the tubes affects the pressure and volume of the gas.

Summarize the findings of the experiment, including the observed relationships between height, pressure, and volume. Discuss any sources of error and suggest improvements for future experiments.

This laboratory report provides a comprehensive analysis of the gas pressure and volume measurements, exploring the impact of varying heights of mercury in open-ended and closed-end tubes. The incorporation of calculations, formulas, and tables ensures a thorough understanding of the experimental outcomes.

 (Px1 – Px2) difference in height (Py1 – Py2) P, pressure of gas V, volume of gas PV 0.00 72.915 16.8 1224.972 0.90 73.815 18.0 1328.670 1.70 74.615 18.3 1365.455 4.90 68.015 15.2 1033.828 7.10 65.815 15.4 1013.551

Based on the obtained results, it can be concluded that there is an inverse relationship between pressure and volume at constant temperature, confirming Boyle's Law.

Discussion:

1. Given the assumption of constant tube diameter, the volume of the gas sample is considered equivalent to the height of the gas column.
2. Boyle's experimental setup was simple, with the pressure exerted on the gas by the mercury level equalizing to atmospheric pressure. As the open-ended tube is raised, there is an incremental increase in pressure on the gas sample, subsequently leading to a reduction in the volume occupied by the gas. Continuing to elevate the open-ended tube further results in further pressure increase and a consequent decrease in gas volume.
3. Ideally, the graph depicting pressure (P) versus volume (V) should exhibit a half-meniscus line approaching the V-axis. However, the actual graph obtained may deviate from perfection due to experimental errors and limitations. Improvements can be implemented to address these challenges.

Evaluation:

Limitation Recommendation The closed-end tube is not entirely airtight, leading to inaccuracies in the experiment results. Fold the rubber tube instead of screwing it, or use an alternative method to prevent outside air from entering the tube and causing leakage. The provided ruler was in poor condition, with some figures already faded. Replace the traditional wooden ruler with a more durable and accurate option made from plastic or metal for better results.

Data Processing:

 Source Temperature, T (ºC) Height, h (mm) T + 273.15 V/T Ice + methanol 28.0 80.0 301.2 0.266 Ice Water 10.1 74.0 283.3 0.261 Pipe water 50.0 87.0 323.2 0.269 Warm water 27.0 79.0 300.2 0.263

This laboratory experiment focuses on applying the ideal gas law to determine the relative molecular mass (RMM) of an unknown substance. The experiment involves measuring various parameters such as mass, temperature, pressure, and volume to calculate the RMM using the ideal gas equation.

Apparatus:

2. Foil
3. Rubber band
4. Condensate
5. Boiling water setup
6. Barometer
7. Electronic water bath (for Part C)

Procedure:

1. Measure the mass of the flask, foil, and rubber band.
2. Add the condensate to the flask and reweigh the entire setup.
3. Record the temperature of the boiling water using a thermometer.
4. Measure the barometer reading for pressure.
5. Determine the volume of the flask.

Data Processing: The ideal gas equation is given by: PV=nRT Manipulating the equation yields: M=PVmRT​

Before substituting values, units must be converted: =100°C+273.15=373.15 K P=0.9594 atm V=0.105 dm3

Substituting these values into the equation: (0.105 dm3)(0.1510 g)(0.082 atm⋅dm3/K⋅mol)(373.15 K)​

Solving the equation gives the RMM.

Results and Analysis: M=45.847 g/mol

Conclusion: The RMM of the unknown substance is determined to be 45.847 g/mol, and it is identified as ethanol (46.02 g/mol).

Discussion:

1. The ideal gas equation relates pressure, volume, temperature, and number of moles for an ideal gas. Ideal gases are theoretical, and real gases deviate slightly from ideal behavior under certain conditions.
2. Ethanol is identified as the unknown substance based on the calculated RMM. The accuracy of the determination relies on the assumption of ideal gas behavior.

Evaluation:

Limitation Recommendation The manual water bath may cause temperature fluctuations while the glass tube is taken out. Use an electronic water bath for higher temperatures to ensure better temperature control and accuracy. The condition of the ruler used for height measurements was not optimal. Replace the ruler with a more durable and accurate option, such as a plastic or metal ruler. Inaccuracies may arise due to air leakage in the closed-end tube. Modify the setup to minimize air leakage, ensuring a more airtight system for accurate results. The calculated absolute zero is slightly off from the theoretical value. Implement improvements in experimental procedures to enhance accuracy and reduce errors in determining absolute zero.

This laboratory report provides a comprehensive analysis of the ideal gas law application and the determination of the relative molecular mass of an unknown substance. The incorporation of calculations, formulas, and tables ensures a thorough understanding of the experimental outcomes.

Updated: Feb 28, 2024