Gas Laws Assignment PDF

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Lab report on gas laws...

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Experiment 2

Name: Anika Anjum

Partner: Sophia Li

Student No: 20175044

Student No: 20150400

Lab Section: 019

Bench #: 38

Experiment 2: (1 week) (GAS) Gas Laws Purpose The aim is to gain knowledge about the gas laws by conducting direct tests to investigate the relations between the variables P, V, n, R, T.

Introduction1 There are four fundamental laws which determine how gases behave. Firstly, Boyles’ Law states that the pressure of a fixed mass of an ideal gas is inversely proportional to its volume at a fixed temperature. Secondly, Gay-Lussac’s Law states that the pressure of a fixed mass of an ideal gas is directly proportional to its temperature provided the volume is constant. Thirdly, Dalton’s Law states that the total pressure of a mixture of non-reacting gases is the sum of the partial pressures of the individual gases. Lastly, Avogadro’s Law states that at a constant temperature and pressure, the volume of a fixed mass of an ideal gas is directly proportional to the amount (moles) of the gas. Combining all these laws gives the ideal gas equation, PV=nRT where P is the pressure, V is volume, n is the number of moles, R is the gas constant and Tis temperature in Kelvin.

Procedure2 In part 1, the syringe air sample was set up by pushing the piston until the inner black ring reached the 10.0mL mark and then connected to the pressure sensor. To gather the pressure data for 5.0mL, the plunger is moved for the inner ring to be placed at the 5.0mL mark and held tightly till the pressure became stable to be saved using Logger Pro. This step was repeated to collect the pressure data for the other volumes, 7.5, 10.0, 12.5, 15.0, 17.5, and 20.0mL and written down on a datasheet. In part 2, the apparatus was set up at first following the instructions in the lab manual. Then, the flask is submerged into the boiling water bath using tongs and held till the temperature became stable and the valve is closed. The pressure and temperature data for boiling were collected using Logger Pro after becoming steady. After that, the flask is moved using tongs to be immersed in the hot water bath and data is taken. The same things were done to record the pressure and temperature data at room temperature and in ice. In part 3, a known mass of NaHCO3 was measured using the top loading balance and placed in a 125mL Erlenmeyer flask. 40mL of 1M acetic acid was taken in the syringe. The apparatus was set up then as written in the lab manual. The initial temperature and pressure were collected after they became steady. After that, the acid was injected into the flask with the plunger moved rapidly to its original place, ensuring no volume change. The flask is whirled for about 5 minutes and the final steady readings of pressure and temperature are recorded.

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Questions Part 1

1. Based on your data, what would you expect the pressure to be if the volume of the syringe was increased to 40.0 mL? Explain or show work to support your answer. If the volume of the syringe was increased to 40.0mL, the pressure would be expected to decrease more and become approximately half of the pressure, 0.563 atm when the volume was 20mL based on my data. The value of the pressure at 40.0mL would be around 0.312 atm. 2. Find the proportionality constant, k, from the data. If this relationship is direct P=kV, then k = P/V. If it is inverse P=k/V, then k = P×V. Based on your data, Calculate k for both equations and then indicate which formula gives the answer that is “constant” for all your P,V data pairs. Choose the correct one of these formulas and calculate the average k value for the seven ordered pairs in your data table (divide or multiply the P and V values). Calculate is the uncertainty, i.e. standard error, in this final mean value of k? (Use statistics; see the section on determining this in the introduction part of the lab manual) k=P/V

k=PXV

For V=5mL, k=(1.8832x101.325)/(5x10-3)

k=1.8832x101.325x5x10 -3

= 3.82x104 kPa/L

=0.954 kPaL

V=7.5mL, k=(1.3321x101.325)/(7.5x10-3)

k=1.332x101.325x7.5x10 -3

=1.80x104 kPa/L

=1.01 kPaL -3

k=1.0167x101.325x10x10 -3

V=10mL, k=(1.0167x101.325)/(10x10 ) =1.03x104 kPa/L

=1.03 kPaL -3

k=0.8435x101.325x12.5x10 -3

V=12.5, k=(0.8435x101.325)/(12.5x10 ) =0.684x104 kPa/L

=1.07 kPaL -3

k=0.7154x101.325x15x10 -3

V=15mL, k=(0.7154x101.325)/(15x10 ) =0.483x104 kPa/L

=1.09 kPaL -3

V=17.5mL, k=(0.6323x101.325)/(17.5x10 ) =0.366x104 kPa/L

k=0.6323x101.325x17.5x10 -3 =1.12 kPaL

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V=20mL, k=(0.5628x101.325)/(20x10 ) =0.285x104 kPa/L

k=0.5628x101.325x20x10 -3 =1.14 kPaL

P=k/V or k=PxV is the formula that is constant for all the P, V data pairs. Mean of k=(0.954+1.01+1.03+1.07+1.09+1.12+1.14)/7 =1.06 kPaL Standard Error=Standard Deviation/ =0.065359/ =0.02

√7

√N

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k=1.06(2)

Part 2

1. In order to perform this experiment, what two experimental factors were kept constant? The mass (amount) and volume of the gas were kept constant. 2. Write an equation to express the relationship between pressure and temperature (K). Use the symbols P, T, and k. P=kT 3. Find the proportionality constant k. Like above, if the relationship is direct, k = P/T. If it is inverse, k = PxT. Based on your answer to Question 2, choose one of these formulas and calculate k for the four ordered pairs in your data table (divide or multiply the P and T values). Show the answer in the fourth column of the Part 2 data table. How “constant” were your values? k=P/T When boiling, k=(1.4210x101.325)/373.15 =0.386 kPa/K

At room temperature, k=(1.0051x101.325)/293.35 =0.347 kPa/K

When hot, k=(1.0817x101.325)/312.75

When ice, k=(0.9594x101.325)/281.35

=0.350 kPa/K

=0.346 kPa/K

The average of value of k is 0.357 with a very small uncertainty of 0.005. A possible error would have been due to a leak in the system through which gases escape, causing pressure to decrease. Otherwise, the values were very constant and precise. 4. The data that you have collected can also be used to determine the value for absolute zero on the Celsius temperature scale. On the plot of Celsius temperature on the y-axis and pressure on the xaxis, find absolute zero. y=mx+b 100=(260.2x1.421)+b

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b=-269.5K(5)

5. Since “absolute zero” is the temperature at which the pressure theoretically becomes equal to zero, the temperature where the regression line (the extension of the temperature-pressure curve) intersects the y-axis (b in the y=mx+b equation) should be the Celsius temperature value for absolute zero. What is your experimental value for absolute zero? What is the uncertainty (do a visual estimate based on your plot)? Is your answer correct, i.e. does the real value lie within the limits of your experimental uncertainty? y=260x-269 Absolute zero= -269 Uncertainty=5.0 Yes, the answer is correct since the real value, -273.15ᵒC lies within the limits of the experimental uncertainty.

Part 3

1. Complete the data sheet and show all calculations in your notebook. PV=nRT n of gas=PV/RT =(1.0025x101.325x150x10-3)/(8.314x294.05) =6.23x10-3 mol Molar mass of NaHCO3=84.006 Mole no of CO2=Mass/Molar Mass

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=0.103/84.006 =1.23x10-3 mol 2. Use Dalton’s law to determine the partial pressure of the CO2 formed. Total pressure=Partial pressure of gas+ Partial pressure of CO2 Partial pressure of CO2=1.0823-1.0025=0.0798atm 3. Based on the known values: partial pressure (pressure change seen during the reaction), the volume of the flask, the number of moles of CO2 (found using mass of sample and molar mass of NaHCO3) and the final temperature in Kelvin (conversion: T in Celsius + 273.15) what is the value of the gas constant R? – Don’t forget units. Use PV=nRT and solve for R. Determine the uncertainty in R.

PV=nRT R=PV/nT =(0.0798x101.325x150x10-3)/(1.23x10-3x294.15) =3.3522 J K-1 mol-1 Uncertainty in R= 2.611

4. Compare this value to the accepted value. (8.3145 J K -1 mol-1). In this context, compare means that you should determine if the literature value for R agrees with your experimental value within your limits of uncertainty. No, the literature value of R does not agree with the experimental value as it is not within the uncertainty limit. This might be due to leaks which caused gases to escape causing the pressure to be lower than it actually should be.

DATA SHEET Part 1 Volume (mL)

Pressure (atm)

Constant, k P•V

(P / V)/104

5

1.88

0.954

3.82

7.5

1.33

1.01

1.80

10

1.01

1.03

1.03

12.5

0.844

1.07

0.684

15

0.715

1.09

0.483

17.5

0.632

1.12

0.366

20

0.563

1.14

0.285

Part 2 Water Bath

Pressure (atm)

Boiling

Hot Room temp

Ice

Temperature (°C)

Temperature (K)

Constant, k (P / T)

100

373.15

0.386

1.08

39.6

312.75

0.350

1.01

20.2

293.35

0.347

0.959

8.20

281.35

0.346

1.42

Part 3

Mass of NaHCO3 ____0.103__________g Volume of flask _____150_________mL Temperature (initial) ______20.9________˚C Temperature (final) ______21________˚C Pressure (initial) ______1.002________atm Pressure (final) ______1.082________atm Amount of gas initially in flask ________6.23x10-3______mol Amount of CO2 added ________1.23x10-3______mol

References 1.

pg#47, Lab Manuel, Introduction and Equation 19

2.

pg#49-55, Lab Manuel, Procedure

3.

Definitions of theories, Lecture Notes and Textbook...