bullseye. The area of each annulus is u(R
R and r are the outer and inner radii.
+ r)(R - r ) where
Determine the average radius of each annulus. A linear arithmetic average is satisfactory although it is possible to calculate the radius that divides the annulus into two equal areas. Assumine that 200 trials are sienificant. calculate the pn,babiliti"f finding a dot in each ;;f.the sin areas. This can bedone by finding theBof the total trials that fall withineach area. Plot a eraoh .. . to show the deoendence of the densitv of dots on the average distance from the center for each area. Also. d o t a maoh to show the orobabilitv of a dot comoared to its d&tancLfrom the center ;sing the average radii of the annuli for this value. If a teacher wishes, he could use the target provided here to prepare an overhead transparency by using a photocopier. He might also use the two graphs provided for the same purpose. The data in the table were determined from the target illustrated, and the calculations made. radius Ring inner outer # (cml
Average R
(arithl (cml
Aver-
ageR (equal areal
No. of Dots
Annuli (cm'l
Ales of Denrify
% Probability
lenmeyer flasks containing samples of the different oxidation states of vanadium: blue vanadium(IV), green vanadium(III), and violet vanadium(I1). These s a m ~ l e scan be prepared in advance and aid in the ire-lab discussion as well as serving as a color guide for the students while they are performing the titration. The samples of the different oxidation states of vanadium will remain stable if stored in tightly stoppered flasks. Vanadium(I1) will remain stable if a 25-ml Erlenmeyer flask is almost completely filled and then tightly stoppered with a rubber stopper. The problem of aerial oxidation of vanadium(I1) should be discussed during the demonstration and pre-lab discussion. The students perform the oxidation of the vanadium by titrating it with 0.1 M potassium permanganate. Each student is given 10 ml of vanadium(I1) and the titration is begun promptly. As the students perform the titration, they can compare the color of their sample to those prepared earlier by the teacher. As an end product of the oxidation, the students obtain a yellow sample of vanadium(V). This experiment supplements the high school laboratory program, and a great deal of information can be related to the experiment. Writing a laboratory report on the experiment serves as a review of oxidation-reduction equations. The changes taking place may be summarized in the following equations V(I1) + V(II1) V(IV) V(V) Violet Green Blue Yellow 5V2++ MnOl- + 8Hf Mn2+ + 4Hz0 + 5V3+ 5V3++ MnOi- + 8H+ MnZC+ 4Hz0 + 5V4+ 5V4++ +no4- + 8Ht Mn2+ + 4Hz0 + 5VSt +
-
-
-
Vanadium for High School Students A. Ward Grant, Jr. Brockton High School Brockton, Massachusetts 02402 The titrimetric determination of the oxidation states of vanadium has been discussed as a suitable exoeriment for college students,' and with minor adaptations, the experiment is audirnhle for hieh school students. The tpacher can ~erform .. the reduction of an aqueous solution of vanadium&') as a demonstration, and the students can perform the oxidation of the vanadium(I1) back to its original state. Prior to the lab period, prepare the solution by dissolving 2 g of ammonium metavanadate in 50 ml of 1M sodium hydroxide solution. While stirring the resulting solution, add 80 ml of 3 M sulfuric acid, and then dilute to 250 ml with distilled water. This solution of vanadium(V) is now ready for the demonstration. Fill a separatory funnel approximately one-third full of 30 mesh zinc. Pour the solution of vanadium(V) into the separatory funnel and allow it to flow over the zinc. As the vanadium passes over the zinc i t is reduced to the vanadium(I1) oxidation state and the solution is collected in a flask. The students are reedily aware of the reaction, and the progress is vividly demonstrated as the color changes from yellow, to blue, t o green, and eventually to violet. The teacher may have Er-
500 1 JouMl of Chemical Education
Students often have difficulty visualizing the concept of different oxidation states. The different colors, resulting from the different oxidation states of vanadium, make this principle easier to comprehend. The teacher can also extend the postlab discussion to show that the different colors result in part from the loss of 3d electrons, thus relating the concept of oxidation and reduction to atomic structure. The CHEM film "Vanadium: A Transition Element" is an excellent summation of the post-lab discussion. Davis, J. M., J. CHEM. EDUC., 45,473 (1968).
Errata In the July 1976 High School Forum, the equation Hgzt
should read Hg?+
-
2 Hg2+
+ 2e
2 HgZ+
+ 2e-
In the final section of the June 1976 High School Forum it is suggested that NO, NO2 and or Hz may be products of a reaction between Mg and 6 M HNOs. Charles Rutenber, Elmira College, Elmira, New York points out that Mg is a strong reducing agent and that the reported results can be explained by HNOs being reduced to NH3. Neutralization of the solution with 6 M NaOH will result in the characteristic odor of NH3.
