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Title: Lab 2 Report- GAS THERMOMETRY Ideal Gas Law (Build Your Own Temperature Scale)

Purpose: To apply the physical concepts of temperature and absolute zero, define the relationship between pressure, volume, and temperature in gases using gas thermometry, and apply the Ideal Gas Law. Introduction: Temperature is the quantity that a thermometer measures. Temperature is correlated with the average kinetic energy of atoms and molecules in a system. Absolute zero is the temperature where molecules are not in motion (1). Any sample of gas contained in a fixed volume can be observed to have a relationship between temperature and pressure. The pressure of the gas increases in proportion to the increase in temperature on the Kelvin scale. Essentially, the volume of a gas is inversely proportional to its pressure and directly proportional to its temperature and the amount of gas (2). In general, a given volume of a confined gas at constant pressure is affected by temperature: The volume rises with rising temperature and falls with falling temperature. Volume and pressure are inversely correlated; as a gas's volume decreases, pressure rises, and as a gas's volume rises, the pressure falls. In actuality, the pressure reduces by the same factor as the volume increases, and vice versa. PV = nRT is the ideal gas equation's formula. The four variables stand for the following four properties of a gas: o (P) Pressure is frequently expressed as an amount expressed in atmospheres (atm), kilopascals (kPa), or millimetres mercury/torr (mm Hg, torr). o Volume (V), expressed as litres o The ideal gas constant, R , varies depending on which units are being used o the number of moles of gas (n) o the (T) temperature of the gas measured in degrees Kelvin (K) If three of these qualities stay constant, the ideal gas equation allows us to investigate the link between the non-constant properties of ideal gases (n, P, V, and T). A helpful tool, the ideal gas equation can provide a highly accurate approximation of gases at high temperatures and low pressures (3). Materials:  Thermometer  Arbitrary temperature scale  Burner  Tap  Jar  Manometer  Variac

 Lid  Release valve  Magnifying glass  Vacuum Pump  Dipper  Argon Tank  Boiling Nitrogen Reservoir  Ice Water Reservoir  Boiling Water Reservoir  Pressure-Temperature Graph Procedures: 1. Put on a lab coat, thick gloves, and protective eyewear 2. Look through a magnifying lens to observe the molecules of the gas 3. Look at the four components that could alter the gas's temperature inside the glass jar: the gas tank, the release valve, the burner, and the jar lid. 4. Turn on the vacuum pump 5. Change the tank's gas pressure with the dipper 6. Empty the tank of Valve A of residual gas from previous experiments and afterwards close Valve A 7. Insert gas into the tank of Valve B and choose the right amount of gas for the experiment 8. Select the initial pressure for the experiment 9. Put the dipper back on the stand and boil the water in the first reservoir using the variac. 10. Place the dipper in the boiling water reservoir to get the initial reference point and select the right pressure for the P-T graph from the PC screen 11. Place the dipper in the ice water reservoir to get the second reference point and check the PC screen to observe how the pressure changes as time passes 12. Place the dipper in the boiling nitrogen reservoir to get the third reference point and check the PC screen to see the pressure drop as the temperature reduces from that of ice water to that of boiling nitrogen 13. Place the dipper in the boiling water reservoir again to verify the measurement. Observation:  After creating a successful unique temperature scale, we observed that the arbitrary temperature scale had a boiling water temperature of 746. 4 Aw, room temperature of

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586 Aw, ice water temperature of 546.3 Aw, boiling nitrogen temperature of 154 Aw and absolute zero temperature of 0 Aw.  The temperature of the gas inside the jar could be changed by 4 separate components. The gas tank, the burner, the release valve, and the jar's lid. No matter how much magnification was applied to the molecules in the lab, the Ideal Gas Law was used to presume that they had no diameter.  A random number of gas molecules were placed in a tank, and we defined the pressure at three different temperatures for those molecules as well as the temperature at absolute zero. Results: The following equation can be used to demonstrate the connection between Aw and Kelvin: Aw = (P(absolute) / P(triple point))^(1/1.68) where P(triple point) is the triple point pressure of water, which is 0.006112 bar or 4.58 torr. The following is how we can translate the pressures into Aw values using the formula above: Aw (746.4) = (627 / 4.58)^(1/1.68) = 18.69 Aw (586) = (760/ 4.58)^(1/1.68) = 20.96 Aw (546.3) = (462/ 4.58)^(1/1.68) = 15.59 Aw (154) = (136 / 4.58)^(1/1.68) = 7.53 We must first determine the absolute pressure using the given relative pressure numbers to create a graph of pressure versus Aw temperature. The formula for converting relative pressure to absolute pressure is: P(relative) = P(absolute) - P(atm) where P(atm) is the atmospheric pressure, which in this instance is taken to be 760 torr. We may determine the absolute pressures with the provided dipper readings by using the formulas below: In boiling water reservoir: P(absolute) = 760 - (133) = 627 torr In ice water reservoir: P(absolute) = 760 - (298) = 462 torr In boiling nitrogen reservoir: P(absolute) = 760 - (624) = 136 torr Next, as seen below, we can plot the data points using the Aw temperature and pressure values: Aw Temperature Pressure (torr) 746.4 627 586 760 546.3 462 154 136

Conclusion: The physical ideas of temperature and absolute zero were first established with the creation of the distinctive temperature scale. We learned about the Ideal Gas Law using the glass jar and were able to use it in the experiment. Using gas thermometry, the experiment defined the link between pressure, volume, and temperature in gases. References: (1) Encyclopædia Britannica, inc. (2023, March 21). Absolute zero . Encyclopædia Britannica. https://www.britannica.com/science/absolute-zero (2) Libretexts. (2020a, July 17). 6.3: Relationships among pressure, temperature, volume, and amount . Chemistry LibreTexts. https://chem.libretexts.org/Courses/University_of_California_Davis/ UCD_Chem_002A/UCD_Chem_2A/Text/Unit_III%3A_Physical_Properties_of_Gases/ 06.03_Relationships_among_Pressure_Temperature_Volume_and_Amount#:~:text=The %20volume%20of%20a%20gas%20is%20inversely%20proportional%20to%20its,and %20the%20amount%20of%20gas. (3) Khan Academy. (n.d.). The ideal gas law (PV = NRT) (video) . Khan Academy. https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:interm olecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/ideal-gas-equation-

pv-nrt#:~:text=The%20ideal%20gas%20law%20(PV%20%3D%20nRT)%20relates%20the %20macroscopic,space%20(have%20no%20volume).

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