Ideal Gas Law

Ideal Gas Law Experiment 12 INTRODUCTION Thermodynamics is the study of energy transformations involving heat and mechanical work, and how they relate to the properties of matter. The matter that we encounter daily, such as solids, liquids, and gasses can be described using thermodynamics. In particular, the study of the gases is a very important area of thermodynamics. The object of this experiment is to use the ideal gas model, from which a simple relationship between the pressure, the volume, the temperature and the number of moles of a gas is obtained, to study the behavior of a real gas. THEORY In science, idealized models often help us understand how nature works. An ideal gas is a collection of particles moving randomly where the interaction between each other is negligible. If the density of a real gas is low enough, then it will behave approximately as an ideal gas. Therefore, even though ideal gases do not exist in nature, we can gain useful information from them. Imagine we have a container filled with gas, for example, air, as it will be the case in this experiment. Inside our container, the temperature, the volume, the pressure, and the amount of gas are related through the following equation known as the ideal gas law,












































































where the universal gas constant,









The variables
,
, and

are pressure, volume, and temperature of the gas, respectively, inside the container. The amount of gas is given by
, the number of moles. One mole of gas contains molecules; this number is better known as Avogadro’s number








 . In this experiment, you will study the physical properties of the gas before and after it is compressed. You will then use the ideal gas law to understand how
,
, and
are related to each other before and after compression. 83 EXPERIMENT NO. 12 For this experiment, you will use a syringe (piston) whose volume can be changed. Part A: Application of the ideal gas law for a gas at a constant temperature; i.e., the temperature inside the syringe before and after the compression is the same. 1. With the pressure coupling disconnected from the pressure sensor, push the plunger all the way in and record the volume reading on the syringe.



























This reading should be about 





2. Log in to the Student account. From the Start menu, open the 1122 folder and the Exp12Ideal Gas Law file. 3. Set the plunger for a volume of 





. Record the temperature. (The gas should be at room temperature.)




























4. To begin recording data, click the Start button and compress the plunger quickly all the way down. Hold this position until the temperature and pressure have stabilized. It will take 


to 



 for the temperature to return to room temperature. Record the temperature after it has stabilized.




























5. Release the plunger and allow it to expand back out. (It may not go back to 





.) Wait again until the temperature and pressure have stabilized and click Stop. Label the graph with your names and print it for all members of your group. 6. Highlight an area (click and drag) on the pressure graph at the beginning of the run before you compressed the air (volume at 





). You should see that data highlighted in the Data Table. Record the initial pressure (

) and volume of the gas in the syringe in Table 12.1. Highlight an area on the pressure graph at the point just before the plunger was released (volume still at 





). Note that the temperature should be back down to almost room temperature. Record the final pressure (

) and volume (

) of the gas in the syringe. This reading should be the same as that in Part 1 (around 





). 84 Table 12.1: Ideal Gas Law - Different States of Gas












Compare

and

. Are they approximately equal? This will allow you to compare different states of the gas at the same temperature. 7. Determine the relationship between
and
for the two states of the gas, before and after compression, at a constant temperature. Please write down symbolic equation for this relationship.



















































































8. Complete the Table 12.2 and show your calculations. Table 12.2: Ideal Gas Law – Relationship Between
and











 9. Please give an explanation for the small error in volume that was observed. The small error in the volume can be accounted for due to the fact that the volume scale on the syringe does not include the volume of air in the tubing connected to the sensors. Calling this unknown volume in the tubing

, modify the equation in Part 7. Please show all your work. 85

















































































Calculate

using the data in Table 12.1. Show your work.




























Part B: Application of the ideal gas law for a gas that is NOT at a constant temperature; i.e., the temperature inside the syringe before and after the compression is different. 10. Using the same graph, highlight an area on the graph at the beginning of the run before you compressed the air (volume at 





), as you did before, and record it in Table 12.3. Record the corresponding pressure for that temperature. Highlight the area on the temperature graph where it peaks. Pick the place where the temperature has peaked, not the pressure. It takes the temperature sensor about

second to respond. Record the peak temperature and the corresponding pressure for that time in Table 12.3. You want two values that occurred at the same time. Record the initial and final volumes; be sure to include the correction to the volume, Vo, found in Step 9. Table 12.3: Ideal Gas Law – Gas at Different Temperature












86




11. From the Ideal Gas law, we know that



. Calculate the ratios,













and complete Table 12.4. Table 12.4: Ideal Gas Law –

Ratios














 Part C: Determine how many moles of gas are inside the syringe plus the attached tubing using the ideal gas law. 12. Set the plunger for a volume of 





. Click Start and collect about





 of data to determine the room temperature.




























This should be the same as

in Part 3. 13. Compress the plunger in steps of






, each time waiting for the syringe to go back to room temperature before compressing any further. Record the volume and pressure at each step in Table 12.5. As the syringe is compressed it becomes harder to obtain new measurements; please be careful how you hold the syringe so that temperature of gas does not change. 87 Table 12.5: Ideal Gas Law – Volume and Pressure Measurements










14. Write the ideal gas law so it can be used to plot pressure versus volume in a linear relationship. Show your work and assume that the temperature is constant (room temperature).













































































Using Equation 4 and the measured data in Table 12.5, determine how many moles of gas are inside the syringe. (Note:

























).



























Before you leave, log out of the computer without saving data 88 QUESTIONS 1. What is an adiabatic process? 2. Is the system used in this experiment adiabatic? Support your answer with your observations. 3. Now consider that the syringe volume is suddenly cut in half and the pressure, initially 



, changes by more than a factor of
. (a) Why does it momentarily spike above 



? (b) When the plunger was released in Part 5, what happens to the temperature? Explain. 4. Suppose you repeat Part 13, but this time you do not compress the syringe in increments of






increments. Instead, you compress it very slowly so the temperature remains constant during the whole process. Using the equation







determine the work done by the gas? Show detailed work. 89