Determination of the Universal Gas Constant Thomas A. Lehmanl and Gwen Harms2 Bethel College, North Newton, KS 67117 Accepted values of the fundamental constants are assumed in countless experiments, and students typically are expected to take them for granted. This is usually the case when they are asked to perform a gas-law experiment. We have found a simple and convenient method for measuring the volume of gas evolved by a reaction occurring in a stoppered buret, and have incorporated it into an experiment that yields all the necessary data for a calculation of the universal gas constant, R = PVInT. The gas is produced by quantitative reaction inside a buret, and its volume is measured by noting the volume of solution forced through the open stopcock when the huret top is tightly closed. With the stopcock open, the pressure inside is assumed to he the same as that in [he laboratory and is measured harometrirally. The reaction is between nitrousacid and sulfamicacid and releases one mole of nitrogen gas for every mole of r e a ~ t a n t s . ~ Sulfamic acid is a solid; its relationship to sulfuric acid can be appreciated by writing its formula as (H0)SOdNHz). The corresponding formula for sulfuric acid is (HO)SO,(OH). Because sulfamic acid is a strong acid, its conjugate anion is the reactive species. In contrast, nitrous acid is not a very strong acid and enters into this reaction as a neutral molecule: HNO,
+ -OSO,(NH,)
-
N,
so that the amount of nitrogen gas depends entirely on the amount of the sulfamic acid used. This method of producing gas is our choice because i t introduces students to a reaction not otherwise seen during the first vear in our lahoratorv. Carbon dioxide could be produced"hy the familiar reaction of strong acid with the carbonate ion. hut the molar solubilitv of COI in water at room temper&re is about 50 times as great as that of Np, which is another reason to use the latter. An instructive comparison could be made if one group of students generated nitrogen as described above and another generated carbon dioxide as reaction gas. The competing factors are the lower solubility of nitrogen in water vs. the need for greater care in preparing the nitrous acid solution. Experimental
The equipment list follows: 1. One 50-mL huret and buret stand; plastic burets tend to retain
gas bubbles on the interior surface to a greater extent than do glass burets, which are preferred. Because of the nature of the experiment, glass burets with chipped tips may be used.
+ HSO, + H,O
The reaction is ouantitative. and one nitroeen atom comes from eachof the reactants: ~ l ; eamount of &ous acid that is used is always substantially greater than is really needed,
TO whom correspondence should be sent.
Present address: University of Arkansas. Fayetteville, AR 72701. Waser, J. Ouantltative Chemistry; Benjamin: New York, 1964; p 122.
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2. One 5-mL calibrated pipet and bulb, used tomeasure the volume of sulfamic acid solution. 3. One 25- or 50-mL graduated cylinder, used to transfer nitrous arid ..-solution.
4. A rubber stopper that fits the top of the buret. 5. A beaker to place under the buret. Its size is not important; 250
mL is convenient. 6. A small beaker, 50or 100mL,for transferringthe sulfamicacidto
the buret. Two reagent solutions are provided: 0.20 M sulfamic acid and approx. 0.25 M nitrous acid. The amount of nitrous acid that is available to produce gas is always substantially greater than the stoichiometric amount, so that the volume of product gas depends solely on the number of moles of sulfamic acid solution. Nitrous acid readily disproportionates to nitric acid and nitric oxide. It should he prepared four to eight hours before use and kent cool but not cold. I t is v r e ~ a r e dby dissolvine enough dry sodium nitrite, NaN02, in 6.25 M hydrochlor; acid to make a solution that is about 0.25 M nitrous acid and 0.25 M in excess nitrite ion. Nitric acid is not an acceptable substitute for HCI. Procedure A huret is set nn and filled to the 0.0 level with water. The wet stopper is placed firmly to close the top of the huret. The seal must he air-tight. The water level in the huret is accurately read, and the larger beaker is placed under it. The buret is then opened and will lose water briefly. Less than a milliliter of water will flow out if the stopper has sealed the huret tightly. When the flow has stopped, the water level is read again, after which the stopcock is closed and the stopper is removed. The ahove operations should he done repeatedly until the water loss is reproducible, as shown by the volume that flows out. T o carry out the reaction, the stopper is removed and the huret is drained to the 30-mL level. Then 20 mL of the nitrous acid solution is voured into the buret. followed by 4.0 mL of sulfamic acid soiution. This volume is measured using the ~ i ~and e tis transferred to the small heaker, from which it isboured into the buret. (The reason for thisextra transfer is that the solution can be poured rapidly from the beaker into the huret, and speed is essentiai &mixing reagents.) Gas begins to evolve as soon as the solutions mix, so the stoppeimust immediately be put into the huret and the stopcock must be opened. When solution is no longer draining from the buret, the atopcock should he closed and the buret removed from its stand. It is then held horizontally and tipped slightly hack and forth to release bubbles of gas
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Journal of Chemical Education
trapped in the solution. After this has been done long enough to remove many of the larger bubbles from solution the huret is returned to its stand ahove the heaker, and the stopcock is opened to release the pressure within. Removal of solutiontrapped gas in this manner should he done more than once. When it has been done for the last time. record the liauid level in the huret. The volume of releaskd gas is the final huret readine minus the initial readina minus the water loss determined Fn the previous paragraph': The ahove steps should he repeated, taking not less than 20 mL of nitrous acid solution with 3.0 mL of sulfamic acid solution, then 2.0 mL and 1.0 mL. The volume reading in the huret should always he close to 0.0 as the reaction starts. Determine the pressure in the laboratory and the temperature in the hulk solutions. The number of moles of gas produced hy the reaction must he calculated. and the atmos~hericnressure in the room. which is a good estimate of the pressure inside the huret when the sto~cockis oDen. should he corrected for water vapor. ~ x p r e s s i ntemperature ~ in kelvins, four values of R can he calculated, one for each volume of sulfamic acid. A graph should he constructed to determine whether the volume of pas has varied linearly with the moles of nitrogen released: Our results for R are typically low by 2-14%. Likely reasons for this are: (1)the Dressure inside the buret mav he slightly greater than the Aeasured barometric pressurldue to drag in the fluid flow as solution leaves the huret, (2) a small amount of gas escapes before the stopper is inserted, and (3)some of the eas bubbles remain t r a ~ v e din the liauid. with careful agitacon of the buret the th&d factor can he minimized. Dlscusslon The value of the experiment derives from several factors: (1) care must he exercised in carrying it out; it willgo badly if rushed; (2) the students determine a fundamental constant, thus removing it from the "mystery list" of things to he believed without experience; (3) data handling is within the abilities of beginning students, hut they must pay attention to units; (4) the graph of gas volume as a function of the number of moles of sulfamic acid is of interest in its own right. Acknowledgment We thank Paul Renich for clarifying the problems associated with the nitrous acid solution.
