ABSTRACT The values for the universal gas constant R, and the volume of one mole of gas were determined. The experiment values of R and the volume of one mole of gas were then compared to the accepted values. The experimental values of R obtained were 0. 09067 (L∙ atm / mol ∙ K), 0. 09514 (L∙ atm / mol ∙ K), and 0. 09040 (L∙ atm / mol ∙ K).

The molar volumes of hydrogen gas obtained were 0. 1306 (L/mol), 0. 1365 (L/mol), and 0. 1390 (L/mol). The percent error of R was 12. 20%, and the percent error of the molar volume was 99.

40%. INTRODUCTION The purpose of this experiment was to determine the value of the universal gas constant R (L∙ atm / mol ∙ K), and the molar volume of hydrogen gas. In this experiment, a known mass of magnesium reacted with an excess amount of hydrochloric acid to produce hydrogen gas. The reaction that took place in the experiment was as follows: Mg (s) + 2 HCl (aq) MgCl 2 (aq) + H 2 (g) The balanced net ionic equation was as follows: Mg (s) + 2 H+ (aq) Mg 2+ (aq) + H 2 (g) The value of R was calculated using the Ideal Gas Law (PV = nRT), and the van der Waal's equation (P + an 2/V 2) (V-nb) = nRT. The value of R should be closer to the R value obtained from van der Waal's equation than the Ideal Gas Law because carbon dioxide was not under ideal conditions. The molar volume of hydrogen gas was determined at a known temperature and pressure.

The hydrogen gas was collected in a graduated cylinder by the downward displacement of water. The volume of gas collected was then converted to the volume of pure hydrogen using the Ideal Gas Law. The experiment was important because it demonstrates the behavior of gases when it is not under ideal conditions, such as high pressures and low temperatures. Understanding the behavior of gases is important in understanding the different gas laws, such as Boyle's Law, Charles's Law, the Ideal Gas Law, and Dalton's Law of Partial Pressures. EXPERIMENTAL The materials used in this experiment included dry ice, copper wire, magnesium ribbon (0. 07 grams, ) and 6.

0 M dilute hydrochloric acid (HCl. ) The equipment used were a ring stand, and ring clamp, paper clips, 100 mL graduated cylinder, paper towels, 125 mL Erlenmeyer flask, thermometer, crucible tongs, 800 mL beaker, stopper to fit Erlenmeyer flask, and a wash bottle. The procedures for the experiment were as follows: 1. ) The mass of a clean, dry, and stoppered Erlenmeyer flask was determined using an analytical balance to the highest precision. A small (2 cm x 2 cm x 1 cm) piece of solid carbon dioxide was placed inside the stoppered Erlenmeyer flask. Using a paper clip, a thermometer was suspended from a ring clamp that was attached to a ring stand.

The thermometer was inserted into the center of the un stoppered flask. When the entire carbon dioxide solid had sublimed, the temperature of the gas was recorded and the thermometer removed. The flask was then stoppered and the mass was determined. This was done twice more.

Using the same flask, tap water was filled to the brim and stoppered. The outside of the flask was dried, and the volume of the water was measured and recorded using a graduated cylinder. The barometric pressure and room temperature was also recorded. 2. ) The mass of a piece of Mg ribbon between 5 cm and 9 cm was determined.

The first trial was a pilot run. The mass and length was adjusted as necessary for additional trials. The Mg ribbon was rolled into a coil and wrapped with copper wire. An 800 mL beak was filled with 600 mL of distilled water. The Mg ribbon was dropped into the water.

25 mL of 6. 0 M HCl was measured in a 100 mL graduated cylinder. The cylinder was carefully filled to the brim with distilled water from a wash bottle. A piece of paper towel was cut so that it just covered the rim of the graduated cylinder. With the piece of paper towel on top of the cylinder, it was quickly inverted into the 800 mL beaker and lowered to the bottom. The paper towel was allowed to float free.

The inverted graduated cylinder should be placed over the coiled Mg ribbon. Observations should be made when the HCl reaches the Mg coil. When the reaction is completed, the graduated cylinder should be lowered or raised so that the liquid level in the beaker matches the liquid level in the cylinder. The volume of the cylinder will be recorded. The temperature of the water in the beaker and the atmospheric pressure was also recorded.

Two more trials were done, and the mass and length of the Mg ribbon was adjusted so that between 70 mL and 90 mL of gas was obtained from the reaction. RESULTS AND DISCUSSION Table 1: Mass and Temperature of CO 2 Trial Number Mass of CO 2 Temperature of Sublimed CO 2 (^0 C) 1 0. 0814 21. 0 2 0. 0707 21.

0 3 0. 0821 21. 0 Table 2: Volume of Flask Trial 1 140 mL Trial 2 140 mL Barometric Pressure: 750. 6 mmHg Room Temperature: 23. 8 ^0 C Sample Calculations (Trial 1): 0. 001174 g (density of air) x 125 mL Erlenmeyer flask = 0.

14675 g O 2 mL mass of flask O 2 mass of O 2 mass of flask 121. 6434 - 0. 14675 g = 121. 4966. 5 g mass of CO 2 & flask mass of flask mass of CO 2 121. 7248 g - 121.

49665 g = 0. 22815 g 0. 22815 g x 1 mole = 0. 0051840 moles CO 2 44. 01 g CO 2 PV = nRT (750.

6 mmHg x 1 atm/760 mmHg) (140 mL x 1 L/1000 mL) = (0. 0051840 mol) R (294. 15 K) 0. 09067 = R Table 3: Calculating R with Ideal Gas Law Trial number Mass of flask & O 2 (g) Mass of O 2 (g) Mass of flask (g) Mass of CO 2 (g) Moles of CO 2 (g) R (L∙ atm / mol ∙ K) 1 121. 6434 0. 14675 121.

49665 0. 22815 0. 005184 0. 09067 2 121.

6534 0. 14675 121. 50665 0. 21745 0. 004941 0. 09514 3 121.

6419 0. 14675 121. 49515 0. 22885 0. 005200 0. 09040 Average R value: (0.

09067 + 0. 09514 + 0. 09040) / (3) = 0. 09204 L∙ atm / mol ∙ K Precision Analysis: |Average R value - Experimental value| x 100 Average R value Table 4: Precision Analysis Trial number Precision Analysis 1 1. 49% 2 3. 37% 3 1.

78% Percent Error of R: |0. 08206 - 0. 09204| x 100 = 12. 20% (Accuracy) 0.

08206 van der Waal's equation: (P + an 2/V 2) (V-nb) = nRT P = 750. 6 mmHg x (1 atm/760. 0 mmHg) = 0. 98763 atm a and b was obtained from Chemistry 6 th Edition (1) V = 140 mL x (1 L/1000 mL) = 0.

140 L n = moles T = 21. 0^0 C + 273. 15^0 C 294. 15 K Calculating R using van der Waal's equation: (0.

98763 atm) + [ (3. 59[atm∙ L 2/mol 2]) (0. 005184 mol) 2 [0. 140 L - (0. 005184 mol) (0. 0427 L/mol) ] = (0.

00518405 mol) (R) (294. 15 K) 0. 08596 = R Table 5: R obtained using van der Waal's equation Trial number R obtained with van der Waal's equation 1 0. 09098 2 0.

09542 3 0. 09071 Average R value: (0. 09098 + 0. 09542 + 0. 09071) / (3) = 0.

09237 L∙ atm / mol ∙ K Precision Analysis: |Average R value (van der Waal) - Experimental value| x 100 Average R value Table 6: Precision Analysis for van der Waal's R value Trial Number Precision Analysis 1 1. 50 2 3. 30 3 1. 80 Percent Error: |0. 09237 - 0. 08206| x 100 = 12.

57% (Accuracy) 0. 08206 Table 7: Measurements for Part Two of Experiment Trial 1 Trial 2 Trial 3 Mass of ribbon (g) 0. 071 0. 074 0.

075 Length of ribbon (cm) 7. 80 8. 20 8. 50 Volume of gas (mL) 75. 0 77.

0 84. 0 Temperature of water 22. 0 22. 0 20. 5 Barometric Pressure: 751. 2 mmHg Room Temperature: 24.

0^0 C Sample Calculations: (Trial 1) Partial Pressure of Pure Hydrogen P Total = PH 2 + PH 2 O 751. 2 mmHg = PH 2 + 19. 80 mmHg (Partial Pressure of water vapor was obtained from Chemistry 6 th Edition (1) P 1 V 1 = P 2 V 2 [ (731. 4 mmHg) (75. 0 mL) ] / (297. 15 K) = [ (760 mmHg) (V 2) ] / (273.

15 K) T 1 T 2 66. 3480 mL = V 2 Table 8: Partial Pressure of Pure Hydrogen and Volume of Hydrogen at STP Trial number Partial Pressure of Pure H 2 (mmHg) Volume of H 2 at STP (mL) 1 731. 40 66. 35 2 731. 40 68.

12 3 733. 14 74. 49 Moles of Hydrogen Gas 0. 0708 g Mg x 1 mole Mg x 1 mole H 2 = 0. 005825 moles H 24. 31 g 1 mole Mg Table 9: Moles of Hydrogen Trial number Moles of H 2 1 0.

002912 2 0. 003044 3 0. 003102 Molar Volume of Hydrogen 0. 006635 L / 0. 0029112 moles = 22. 791 L/mol Table 10: Molar Volume Trial number Molar Volume of H 2 (L/mol) 1 22.

791 2 22. 378 3 24. 014 Average molar volume: (22. 791 + 22. 378 + 24. 014) / (3) = 23.

061 L/mol Precision Analysis: |Average molar volume - experimental| x 100 Average molar volume Table 11: Precision Analysis Trial Number Precision Analysis 1 1. 17% 2 2. 96% 3 4. 13% Percent Error: |Average molar volume - Accepted value| x 100 = 2. 89% (Accuracy) Accepted Value The results obtained from the experiment included that the average R value obtained by the Ideal Gas Law was 0.

09207 L∙ atm / mol ∙ K, and the average R value obtained from van der Waal's equation was 0. 09237 L∙ atm / mol ∙ K. The R value obtained from van der Waal's equation was greater than the R value obtained from the Ideal Gas Law. This did not follow the hypothesis that the R value obtained from van der Waal's equation is closer the accepted value than the R value obtained from the Ideal Gas Law. Errors that affected the results included inaccurate analytical balances, barometric pressure and temperature readings.

Also, when the volume of the Erlenmeyer flask was determined, not all of the water droplets were transferred from the Erlenmeyer flask to the graduated cylinder for accurate measurements. The molar volumes obtained from the three trials were 22. 791 L/mol, 22. 378 L/mol, and 24. 014 L/mol, respectively, and the accepted value was 22.

414 L/mol. The results obtained were not too far from the accepted value; there was a 2. 87% error. Factors that affected the experiment included inaccurate analytical balances, inaccurate readings of volume of gas and temperature. The barometric pressure reading was inaccurate due to the fact that the gauge was hard to read. CONCLUSIONS The results obtained from the experiment concluded that the average R value was 0.

09207 L∙ atm / mol ∙ K and 0. 09237 L∙ atm / mol ∙ K for the Ideal Gas Law, and van der Waal's equation, respectively. There was a 12. 57% relative accuracy from van der Waal's equation, and a 12.

20% relative accuracy from the Ideal Gas Law. The average molar volume obtained was 23. 061 L/mol, with a 2. 89% relative accuracy. The experiment was important because it demonstrated the behavior of gases under ideal conditions and non-ideal conditions. The appropriate gas laws were used to determine the molar volume of hydrogen at STP conditions.

For future experiments, accurate measurements of mass, volume, barometric pressure, and temperature would improve the results, including a better method than having to invert the graduated cylinder into an 800 mL beaker. REFERENCES 1. Chang, Raymond, Chemistry, Sixth Edition, McGraw-Hill, San Francisco, California, 1998.