The Determination of R: The Gas-Law Constant
Izabella D’Onofrio
Conducted on: January 24, 2015

Abstract An experiment was performed to determine “R”, the gas-law constant, using both the ideal gas law equation and the van der Waals equation. An ideal gas is considered a hypothetical gas whose pressure, volume, and temperature behavior correlates to the ideal gas equation, PV=nRT (Brown, et al. 2012). Using an apparatus involving a test tube and large beaker with rubber stoppers and tubing and equalized atmospheric pressure, the test tube contained approximately 0.02 g of MnO2 and 0.2972 g of KClO3 to yield 0.1322 g of oxygen and 80.0 mL of O2 gas. Because both equations and error analysis needed to be utilized to provide a lesser uncertainty of R, the determination was around 0.06434 L*atm/mol*K.
Introduction
In using the apparatus to determine the proper value of “R”, the test tube connected will be weighed and the barometric pressure observed after the procedure will determine the mass and volume of oxygen produced. These values help to solve the equation to determine “R”. Because determining “R” with the ideal gas law alone would not be precise enough, the van der Waals equation is used to lower possible uncertainty within the experiment. Using algebraic principles and plugging values into both equations determined by the procedure, a better understanding of how closely real gases obey the ideal gas law.
Procedure
1. Measure and record the initial mass of the test tube, and add around 0.02 g of MnO2 and 0.3 g of KClO3 (weight and record to the nearest 0.0001 g).
2. Assemble the apparatus as demonstrated by the instructor, but do not attach the test tube.
3. Fill glass tube A and rubber tubing with water by unscrewing the pinch clamp and apply pressure through tube B. Close clamp when filled.
4. Mix solids in the test tube and attach tube B. Be careful not to let the KClO3 and MnO2 to come in contact with the rubber stopper or an explosion may occur.
5. Fill the beaker halfway and insert glass tube A, open pinch clamp, and lift the beaker so that the levels of water in the beaker and bottle are equal. This equalizes the atmospheric pressure.
6. Open the pinch clamp and allow a little amount of water to flow out. Only some should flow and then stop for an airtight system.
7. Heat the lower part of the test tube with the pinch clamp open, and a steady stream of gas will be produced. The evidence will show when water starts to flow into the beaker. When the flow of gas slows down, increase the heat until oxygen no longer evolves.
8. Allow to cool to room temperature.
9. Equalize the atmospheric pressure again as before and close the clamp.
10. Transfer the water into the 250 mL graduated cylinder and record the volume of displaced water.
11. Remove and weigh the test tube with the final contents. The final mass minus the initial mass is the mass of oxygen produced.
12. Record barometric pressure. Take note of the vapor pressure table given at various temperatures.
Results
Adding heat to the mixture of solids in the test tube, finding the amount of oxygen produced aided in the determination of “R”. In conclusion of the procedure, the experiment yielded approximately 0.1322 g of oxygen. The volume of displaced water, 80.0 mL, is equivalent to 80.0 mL of oxygen gas. The vapor pressure of water at 21ºC as seen in Table 1 is 18.6 mmHg. The relevant vapor pressure in the experiment is equal to 0.02447 atm which lead to establishing the water vapor pressure of 0.9768 atm (a). A value of about 0.06434 L atm/mol·K (b) using the ideal gas law equation was determined for “R”; however, the uncertainty of accuracy in that value still remained. In utilizing the van der Waals equation the value of 0.06447 L atm/mol K was found (c). To truly determine the uncertainty in “R”, error analysis was performed for an average of 0.06434 L atm/mol K (d).
Mass of test tube 42.99 g
Mass of test tube + KClO3 + MnO2 43.3072