Experiment 11 PDF

Preview

Summary

practical lab report for EXPERIMENT 11: EXPERIMENTING WITH GAS LAWS
...

Description

EXPERIMENT 11: EXPERIMENTING WITH GAS LAWS

Table of Contents 1.1.1. Prelab 1.1.2. Purpose 1.1.3. Introduction 1.1.4 Safety Information 1.1.5 Experimental Raw Data and Observations 1.1.6 In-Lab 1.1.7 Results and Discussion 1.1.8 Lab Report Date: March 8th, 2017

References: ScienceLab, compiler. 2003 May 21. Water MSDS [Internet]. Houston, Texas: Sciencelab; cited 2007 January 31. Available from: http://www.sciencelab.com/msds.php?msdsId=9927321 University of North Carolina at Chapel Hill Chemistry Department. C2016. General Chemistry 102L Lab Manual: Spring 2017. Plymouth (MI): Macmillan Learning Curriculum Solutions. pp. 1-10.

Purpose: The purpose of this experiment is to use Boyle’s Law and Gay-Lussac’s Law to work with gas-phase samples and study the relationships between pressure and volume and of pressure and and temperature. Introduction: The Ideal Gas Law defines the relationships between pressure, temperature, volume, and number of moles of a gas. PV = nRT

One mole of ideal gas occupies a volume of 22.414 L, and the gas constant (R) is 0.08206 Latm/Kmol. In 1662, Robert Boyle established a relationship between the pressure and volume of a confined gas. This is known as Boyle’s Law and is defined as P1V1=P2V2. In the 1800’s, Joseph Gay-Lussac described the relationship between pressure and temperature. Gas molecules are in constant motion and pressure occurs due to collisions with the walls of the container. When the temperature increases, the velocity and number of collisions increases. This is known as Gay-Lussac’s Law or Amonton’s law. This experiment will use air to test these laws. Air is not a pure substance, but in the lower atmosphere the action of thermal gradients and wind motions maintain a reasonably uniform concentration of the mixture. Dry air is composed of: 78.09% nitrogen (N2), 20.95% oxygen (O2), 0.93% argon (Ar), and 0.03% carbon dioxide (CO2). Dry air can therefore be treated as an ideal gas with an effective molar mass of 28.96 g/mol. This is calculated by taking the weighted average of the molar mass of each component. The density of dry air at 298 K is 0.001185 g/mL. Water vapor can complicate measurements, especially if the vapor pressure is high enough for condensation to occur. However, at room temperature, water vapor makes up only 3% of the composition of air and thus its effects are limited.

Experimental Process and Measurements Boil about 400 mL of water in a 600 mL beaker using a hot plate. Begin setting up hardware by starting the Science Workshop 500 interface. Connect to a computer and connect the pressure sensor to port A and the temperature sensor to port B. Open Capstone Software on the computer and select “Table and Graph”. Connect the Workstation 500. When properly connected, a small green sun will appear. Select analog port A and select “Pressure Sensor, Absolute”. Select analog port B and select “Temperature Sensor”. Click on “Common Rate” and select “Temperature Sensor”. Select a sample rate of 10s. Calibrate the temperature sensor by selecting two standard calibration. Place the bulb of the alcohol thermometer near the bottom of the temperature sensor. Record the

temperature value from the thermometer in the Calibration Point 1 Standard Value box and click Set Current Value to Standard Value. Place the thermometer and sensor in the boiling water and wait for the temperature reading to stabilize on the thermometer. Record the temperature in the Calibration Point 2 Standard Value. Click the CALIBRATION button. The temperature reading on the thermometer is 100 fold greater than the voltage output from the temperature sensor. In this experiment, volume data will be entered manually. In the software, select continuous mode and select “keep mode”. The left hand column should be absolute pressure (kPa) and the right hand column should be “volume” in mL. To analyze the pressure and volume relationship, determine room temperature and record in the data table. Set the syringe plunger at 5 mL. Connect the syringe to the sensor. Record the initial pressure and enter the initial volume. Extend the syringe by 1 mL, hold the plunger in place for at least 15 seconds, then click “keep” and enter the volume in the table. Repeat until the syringe is extended to 15 mL. Run a second trial and save the results. To analyze the pressure and temperature relationship, insert the temperature sensor into the hole of the rubber stopper. Connect the pressure sensor to the rubber stopper and insert the stopper firmly into a 250-mL Erlenmeyer flask. Clamp the flask in the hot water bath so that at least ½ of the flask is submerged. Continue heating the water to warm the flask until the temperature of the gas in the flask is above 60 degrees C. Set the software to see a real-time temperature reading. When the temperature is greater than 333 K, turn down the heat on the water bath. Watch the fluctuations in pressure and click “keep” whenever there is a change of about 0.4-0.5 kPa. Continue collection until temperature drops to 320 K. Repeat to collect a second set of data. Using a graduated cylinder, determine the actual volume of the 250-mL Erlenmeyer flask and record in the data table. Data analysis for the pressure vs. volume calculations to include a scatter plot of Density of Air (g/L) vs. Temperature (K) and a trendline. Convert kPa to atm and convert mL to L. Calculate the inverse volume and determine the mathematical relationship between the pressure and volume. Generate a scatter plot of Pressure (atm) vs. Volume (L) and perform a linear regression. Generate a scatter plot of Pressure (atm) vs. Inverse Volume (1/L) and perform a linear regression. Using the ideal gas law and the generated graphs to determine the gas constant under these experimental conditions. Calculate the percent error.

For the Pressure vs. Temperature calculations, convert pressure in kPa to atm. Determine the relationship between pressure and temperature and determine the gas constant for the data. Calculate the percent error. Generate a graph of Temperature (C) vs. Pressure and run a linear regression. The y-intercept value is the temperature at which pressure is zero. Experimental Report Information In this experiment, a hot plate will be used to boil water. Take all necessary precautions when working with hot materials. Wear hot-hands when touching hot materials and be careful not to melt cords or lab coats with the heat. The only substances used in this lab are water and air. ● H20 - Non-corrosive for skin. Non-irritant for skin. Non-sensitizer for skin. Non-permeator by skin. Non-irritating to the eyes. Non- hazardous in case of ingestion. Non-hazardous in case of inhalation. Non-irritant for lungs. Non-sensitizer for lungs. Non- corrosive to the eyes. Non-corrosive for lungs.

Turn off the hot plate, being careful with the hot surface. Empty the water down the drain and wipe off the temperature sensor with a Kimwipe. Put away all other materials.

Results Figure 1. Air Density vs. Temperature This figure shows the indirect correlation between air density and temperature. These values were found in table 11. 1 in the lab manual. Figure 2. Pressure (atm) vs. Volume (L) This figure shows the indirect relationship between pressure and volume in the two conducted trials. They form a negative linear relationship as seen in the regression line. Figure 3. Pressure (atm) vs. 1/Volume (1/L) This figure shows the direct relationship between pressure and the inverse of volume in the two conducted trials. They form a positive linear relationship as seen in the regression line.

Figure 4. Pressure (atm) vs. Temperature (K) This figure shows the direct relationship between pressure and temperature in the two conducted trials. They form a positive linear relationship as seen in the regression line. Figure 5. Pressure (atm) vs. 1/Temperature (K) This figure shows the indirect relationship between pressure and the inverse of temperature in the two conducted trials. They form a negative linear relationship as seen in the regression line. Figure 6. Temperature (

) vs. Pressure (atm)

This figure shows the direct relationship between temperature and pressure in the two conducted trials. They form a positive linear relationship as seen in the regression line. The y-intercept is where absolute zero occurs. Sample Calculations Density of air at measure temperature e quation of linear regression : y =− 0.0037x + 2.304 T rial 1 temperature : 291.35 K density = − 0.0037(291.35K) + 2.304 = 1.23 g/L T rial 2 temperature : 291.55 K density = − 0.0037(291.55K) + 2.304 = 1.23 g/L

Moles of air v olume of air found to be .2515 L 1.23 g/L * .2715 L = 0.334 g air molar mass of air : 28.96 g/mol 0.334 g air * 1mol/28.96g = .00115 moles air Conversion from kPa to atm 1 kP a = 0.00986923 atm

102 kP a * .00986923 atm = 1.01 atm Conversion from mL to L 1 L = 1000 mL 5 mL / 1000 L = 0.005 L Calculations of R from P vs. 1/V (from regression) T rial 1 E quation of regression line : y = 0.0027x + 0.3412 slope = change P /change (1/V ) = changeP * changeV = P V P V = nRT slope = nRT = 0.0027 R = .0027/(nT ) = .0027/(.00115 mol * 291.35K) R = 0.000806 Latm/molK

T rial 2 E quation of regression line : y = 0.0026x + 0.3848 slope = change P /change (1/V ) = changeP * changeV = P V P V = nRT slope = nRT = 0.0026 R = .0026/(nT ) = .0026/(.00115 mol * 291.55K) R = 0.000433 Latm/molK Percent Error in R mean experimental R = 0.000621 Latm/molK literature value of R = 0.08206 Latm/molK % error = (|theoretical − experimental|/theoretical ) * 100 % error = (|.08206 − .000621|/.08206) = 99.2% error Calculation of R from P vs. T (from regression) T rial 1 E quation of regression line : y = 0.0064x − 1.0145 slope = changeP /changeT = P /T P V = nRT R = P V /nRT R = (slope * V )/n 1mol/22.414L = xmol/.2715L = .012 mol R = (.0064 * .2715L )/.012 mol R = 0.1448 Latm/molK

T rial 2 E quation of regression line : y = 0.0075x − 1.3585 slope = changeP /changeT = P /T P V = nRT R = P V /nRT R = (slope * V )/n 1mol/22.414L = xmol/.2715L = .012 mol R = (.0075 * .2715L )/.012 mol R = 0.1694 Latm/molK

Discussion In this lab, we used the ideal gas law, Boyle’s Law, and Gay-Lussac’s Law in order to find R, the ideal gas constant, and compare it to the literature value of 0.08206 Latm/Kmol. The first part of the experiment compared pressure and volume at a constant temperature. We found an indirect correlation between pressure and volume, in accordance with Gay Lussac’s Law, as seen in Figure 2. We then created a scatter plot and compared pressure and the inverse of volume to find a direct correlation that could be used to find R (Figure 3). This scatter plot gave us an equation in which we could find a slope. The slope of a graph is change in y/change in x . Thus, for this graph it would be change in pressure/change in inverse volume . the lab manual to create a scatter plot of air density vs. temperature (figure 1) in order to find the density of air at the room temperatures we were working at. Using the density and the molar mass, we could find moles. We divided the slope by the moles and our found room temperature in order to find a mean experimental R value of 0.000621 Latm/mol (Table 1). Our trials had a percent difference of 53.7%. In the second part of this lab, we compared pressure and temperature, keeping a consistent volume. We found a direct correlation as seen in Figure 4. Figure 5 shows graph of pressure and the inverse of temperature, which shows an indirect relationship. Using the regression equations from Figure 4, we could retrieve a slope equal to change in pressure / change in temperature , or P/T. By manipulating the ideal gas equation, we find that R=PV/nT. Therefore, we multiplied the slope (P/T) by the volume and divided by the moles. We found moles using the knowledge that 1 mole of ideal gas occupies a volume of 22.414 L, and applied this to our volume of 0.2715 L. We found a mean experimental R value of 0.157 Latm/Kmol. Our trials had a percent difference of 85.5%. From our data, we concluded that our experiment was not very accurate for a variety of reasons. Using the P vs. 1/V method, we found a percent error of 99.2%, and using the P vs. T method, we found a percent error of 91.30%. Our calculated value for absolute zero had a percent error of 61.4% (Figure 6). These values and the percent differences between our trials lead us to believe some possible sources of error had occurred. One possible source of error

could be the air not acting entirely as an ideal gas. Other sources of error include: the stopper shifting when calculating temperature vs. pressure creating an incomplete seal, and incorrectly operating the syringe when calculating pressure vs. volume. These could contribute to inaccurate data and thus inaccurate results. When our values turned out to be larger than the accepted value, we expected the slope to be too steep. Conclusion By using Boyle’s Law, Gay-Lussac’s Law, and the ideal gas law, we found an indirect relationship between pressure and volume and a direct relationship between pressure and temperature. In the P vs. 1/V method we found a mean experimental value of 0.000621 Latm/mol, and in the P vs. T method we found a mean experimental value of 0.157 Latm/Kmol.

Post Lab Questions 1. We couldn’t use that 1 mole of gas occupies 22.414 L for all of our calculations because that only occurs at standard temperature (298K) and pressure (1 atm). Thus, at our calculated room temperature that was below standard temperature, we needed to use the regression equation of the graph of density of air vs. temperature. 2. According the the first postulate of the KMT (Amonton’s Law), when the temperature increases, the average speed and kinetic energy of the molecules increases. This causes the molecules to collide with the walls of the container more frequently and more intensely, thus increasing the pressure. The third postulate of the KMT (Boyle’s Law) states that if the volume decreases, the pressure increases. At a molecular level, if the volume decreases, there is less room for the molecules to move, and thus they collide with walls of the container more often, increasing the pressure. 3. Absolute zero refers to the theoretical temperature where pressure is equal to zero. This contributed to the development of the Kelvin scale because it occurs at 0 K (-273 ℃). 4. The R2 value is a statistical value that describes how close the data fits to the regression line. The closer an R2 value is to 1 or -1, the stronger the fit. We use regression lines to see how the data compares as a whole and to perform statistical analyzations. 5. In our experiment, the P vs. Temperature value found a closer value of R. We could improve this by making sure the stopper does not shift and break the seal when measuring pressure. Our absolute zero value was lower than the known value. This occurred because the y intercepts of our pressure vs. temperature graphs were too low. However, with our possible sources of error, this value does not surprise me too much.

Slope from linear regression

Calculated R

Mean Experimental R for this method

%Error

P vs. 1/V

(atm vs. L)

Latm/Kmol

Latm/Kmol

Trial 1

y = 0.0027x + 0.3412

0.000806

0.000621

Trial 2

y = 0.0026x + 0.3848

0.000433

P vs. T

(atm vs. K)

Latm/Kmol

Latm/Kmol

Trial 1

y = 0.0064x - 1.0145

0.1448

0.157

Trial 2

y = 0.0075x - 1.3585

0.1694

91.30 %

T vs. P

Intercept from linear regresion (atm vs. ℃)

Absolute Zero (K)

Mean Absolute Zero (℃)

%Error

Trial 1

0.89236

-124.2

-105.5

61.40 %

Trial 2

0.6686

-86.8

99%

Slope from linear regression

Calculated R

Mean Experimental R for this method

%Error

P vs. 1/V

(atm vs. L)

Latm/Kmol

Latm/Kmol

Trial 1

y = 0.0027x + 0.3412

0.000806

0.000621

Trial 2

y = 0.0026x + 0.3848

0.000433

P vs. T

(atm vs. K)

Latm/Kmol

Latm/Kmol

Trial 1

y = 0.0064x 1.0145

0.1448

0.157

91.30%

Trial 2

y = 0.0075x 1.3585

0.1694

T vs. P

Intercept from

Absolute Zero

Mean Absolute

%Error

99%

linear regresion (atm vs. )

(K)

Zero (

Trial 1

0.89236

-124.2

-105.5

Trial 2

0.6686

-86.8

)

61.40%...