Lab Report 7 - Ideal Gas Law PDF

Preview

Summary

Lab Report 7...

Description

Julia Varricchio PHY 133 Section 31 Experiment 10: Ideal Gas Law Experiment performed on: November 16, 2020 with F  aith Jarzembowski Report submitted: November 30, 2020

Introduction In this lab, we analyzed the ideal gas law. The ideal gas law demonstrates properties of a gas in equilibrium through the equation PV=nRT. The properties of pressure, temperature, number of moles, and volume can be held constant to find varying variables. We also analyzed avogadro's and boyle’s law. Avogrado’s law states that a gas with V1 and n1, will have an equal ratio to V2 and n2. In other words V1/n1=V2/n2. Boyle’s law is similar, but focuses on different variables than avogadro's law. Boyle’s law states that P1V1=P2V2. We also studied the value of absolute zero through the relationship of temperature seen in the ideal gas law. The absolute value is equal to 0 K or -273.15℃. In summary, we focused on measuring different values of a gas and analyzed the relationship those measurements had with different variables.

Theory The ideal gas law shows the relationship between pressure, temperature, volume, and number of moles of a typical gas. It is represented by PV=nRT. Through this equation we can also study the change in variable of a typical gas where other variables are held constant. For example, in Boyle’s law, temperature and number of moles are held constant, so we can see the relationship between varying pressure and temperature. Similarly, avogrado’s law has pressure and temperature held constant so we can see the relationship between varying volume and number of moles.

Procedure In the first part of the experiment we studied boyle’s and avogadro's law by using the software Logger Pro. We connected the temperature and pressure probes to the LabPro box and recorded

the values given by the software. Then we took a syringe and set the volume to 10 mL, and connected it to a pressure sensor. We recorded the values of pressure and volume. We then expanded the syringe to 20 mL and recorded the values of pressure and volume. We repeated this with values of 30, 40, and 50 mL. After we were done with 50 mL, we disconnected the syringe from the pressure sensor, and set the syringe to 20 mL. We reattached the syringe to the pressure sensor, and recorded the pressure and volume values. After we recorded those values, we expanded the syringe to 30 mL, 40 mL, 50 mL, and 60 mL and recorded the associated pressure and volume values. For the second part, we wanted to determine the volume of the gas cell. So, we attached a syringe set at 0 mL to a T-piece connected to a gas cell, and pressure sensor. After that was setup we expanded the syringe to 10mL, 20mL, 30mL, and 40mL and recorded the pressure and the volume for each value. For the third part of the experiment we wanted to determine absolute zero, so we made a plot on LoggerPro with temperature on the Y-axis and pressure on the X-axis. We then boiled water and placed our gas cell and temperature sensor in the water. Once the temperature began to decrease, we started collecting data through the LoggerPro graph. After 3-5 minutes of collecting data, we autoscaled the axis of the graph and made a linear fit line. Me and my partner recorded the y-intercept and slope of the linear fit line. We then began recording again for another 2 times and repeated this process.

Discussion 1. Systematic Error: Uniformity of Temperature

In the last part ot the lab, we only submerged the container underwater. There was also a small amount of gas in the tube and pressure sensor, that may have been at a somewhat cooler temperature than the vapor. This may have altered our measurements of temperature. If the air in the tube was somewhat cooler, this may have altered the temperature we recorded to be a lower value than expected. In other words, our measurement of temperature may have not been accurate, and can be a systematic error in determining absolute zero from this experiment.

Results

From this experiment we can analyze the data to visualize the relationship between variables in the ideal gas law. In the first part of the experiment, we analyzed Boyle’s and Avogrado’s law. This is shown from the top 2 graphs. The slope is equal to V*P in these graphs, so looking at the ideal gas law equation we can obtain n, number of moles of gas for each initial volume. For the first graph, where the initial volume was 10mL +/- 2mL, we got a slope of 1187.41 +/- 21.4646. When we plug this slope into the ideal gas equation we get a value of 0.4832074269 +/0.0873632735 for the number of moles of gas. For the second graph, where the initial volume was 20 mL +/- 2mL, the slope was 2301.63 +/- 20.2944. When we plug this slope into the ideal gas equation we get a value of 0.936687071 +/- 0.008264997557 for the number of moles of gas. In order to test, avogrado’s law we divided the number of moles by the initial volume and compared the two ratios. For the first graph we got a ratio equal to 0.04832074269 +/0.009703556107, and for the second graph we got a ratio of 0.04683435355 +/0.004701631864. These ratios do agree within uncertainty with avogrado’s law, where the ratios of n/Vo are equal. For the second part of the experiment, we wanted to determine V0 and n. From the last graph we can extrapolate these values. The slope is equal to V*P, so similarly to the first part of the experiment, we plug the slope into the ideal gas law equation to get n. Doing this, we get n is equal to 2.999239745 +/- 0.02227109701 moles of gas. Also, the absolute value of the y-intercept is equal to V0, so V0 is 72.5506 +/- 0.728222. This value was also used in the third part of the experiment. In the third part of the experiment we wanted to compare our value of n to the value of n in the second part and also determine the value for absolute zero. To find n, we used the V0 from the second part of the experiment, and the average slope from the third part. The slope was equal to T/P, so rearranging the ideal gas law equation and plugging in the slope

and V0, we get a value of 2.410552785 +/- 0.06359930966 for n. Although this value is similar to the value of n in the second part, it is not in agreement given uncertainties. Finally we got the absolute zero value, by taking the average of the intercepts from the 3 temperature vs. pressure graphs. We got -292.9666667 +/- 31.04679264. This measured value is in agreement with the determined value of absolute zero, which is -273.15℃.

Error Analysis Although we calculated uncertainties in our data, there are other sources of error. For example the syringe may not have been completely sealed to the pressure sensor in the first part. This may have led to the number of moles not being completely constant. If the number of moles are not held constant, then temperature and pressure will not coincide with Boyle’s law. Another form of error was the air in the tube in part 3 of the experiment. The air in the tube may have been cooler than the vapor from the boiling water. This would have altered our temperature to be lower than expected, and altered our calculation of absolute zero.

Conclusion In this experiment we analyzed the relationship between the variables observed in the ideal gas law. We saw an agreement in our values of n/V0, where our ratio for an initial volume of 10 mL was equal to 0.04832074269 +/- 0.009703556107, and our ratio for an initial volume of 20 mL was equal to 0.04683435355 +/- 0.004701631864. We also had an accurate measurement in our value of absolute zero, which was -292.9666667 +/- 31.04679264. Although our n values for the last two parts were not equal, 2.999239745 +/- 0.02227109701 and 2.410552785 +/0.06359930966, they were similar. In order to perform this experiment with more accuracy, we can use a brand new syringe, and also have a vacuum sealed tube....