The Kinetics of Photographic Development A general chemistry experiment J. E. Byrd and M. J. Perona
California State College. Stanislaus Turlock, CA 95380 As teachers of chemistry, one of our goals is to make use of familiar, everyday phenomena to illustrate chemical principles. The experiment described here uses black and white photographic development to illustrate the determination of reaction rate, kinetic order of a reactant, and activation energy. In the presence of hydroquinone (HpQ), the development of the photographic emulsion involves the reactions
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Figure 1. Plot of development rate (reciprocaldevelopment time) versus hydroquinone concentration for the development of a black and white canfact print. Developer composition: 2.38 MNa2S03. 0.084 MNaBr. 0.312 MNaOH with varying amounts of hydroquinane. Temp.,24 1°C. where (Q) is quinone. The overall reaction is A[Ag] Constant Rate = --
For a given developer solution in which only the hydroquinone concentration is varied, and the pH is sufficiently high, the rate of development is given by Rate = k'[H2QIct
(3)
where a ranges from 0.75 to 1.0. The value of a depends upon the pH, Br- concentration, and the concentration range of the hydroquinone in the developer.' For this experiment, conditions (described in the Experimental Procedure) were chosen to make a equal to 1. The goal of the experiment is for the students to determine experimentally the value of a,(the order with respect to Hz$), and the activation energy of the overall development process, reaction (2). Method The students, working in pairs, first prepare several contact prints using a developer solution prepared by the stockroom personnel. The purpose of this part of the experiment is to give the students confidence that their exposure variables (light intensity, distance from light bulb to paper, and exposure time) are correct. I t also provides them with a "Reference Print" which represents a constant extent of reaction. The negative used to prepare the Reference Print is then used to make a series of four contact prints. Each print in the series is prepared using a developer with a different concentration of HpQ. The temperature of the developer and the exposure time are held constant throughout the series. The students use a stopwatch to measure the time needed to obtain a print with a darkness or density as close as possible to the "Reference Print." Thus, in each trial the extent of reaction, or the amount of silver produced, (A[Ag]), is a constant, and the rate of development is given by
(4)
At At where At is the time of development. That is, the rate is inversely proportional to the development time. Letting a in eqn. (3) equal 1, and combining eqns. (3) and (4) gives
Since the HzQ is in large excess over the silver halide, the concentration of HpQ is taken to he equal to its initial concentration. Thus, a plot of the reciprocal of the developmental time versus the initial H2Q concentration gives a straight line." A typical plot is shown in Figure 1.The reaction is clearly first order in HsQ. I t is interestine to note that the students obtain excellent agreement between their individual trials, typically within 10 sec ~- out of 2 min. This is no doubt a result of the autocatalytic nature oitht, develupment pruwss. The time inttrvnl during n,hirh the nrint chances from light - todark isshurt (ompnrea to the time of development. The activation energy is determined in a similar manner. The students carry out a set of experiments in which the developer solution is kept the same, but the temperature of the developer is varied. In this case l/At is directly proportional ~
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James. T. H. in "The Theory of the Photographic Process," (Editor: T. H. James). 3rd. Ed., The MacMillan Company. New York, 1966, p. 359. 2 Alternatively, as a referee has suggested,one could plot log (IIAt) versus log [H,Q], and obtain the order from the slope. Although this approach is more general, it introduces the added complication of a log-log plot. Volume 59 Number 4
April 1982
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Figure 2. Plots of the logla of the reciprocal of the development time versus recipr~caltemperature fa several setsof data. Thedeveloper wrluilon is identical to that in Figure 1 with 3.0 g of hydroqulnone fa200 mi of soluiion. Some of W plots have been displaced for clarity.
to the rate constant. Shown in Figure 2 a r e s o m e Arrhenius plots obtained b y several groups of s t u d e n t by plotting loglo(1lAt) versus the reciprocal of t h e absolute temperature. Analysis of the data from t w o typical l a b sections (16 pairs of students) yields an activation energy of 9.7 1.1kcal (average deviation), after the three obvious outliers were rejected. T h i s is in reasonable agreement w i t h t h e results obtained with
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Experimental Procedure At the beeinnine of the first 3-hr lab oeriod (two are normallv allotted for the experiment), the instructor briefly describes the mechanism of hlack and white development. We find this useful, because it provides a good example of redox chemistry (the reduction of Ag(1) t o Ag(O)), complex-ion chemistry and solubility (the fixation step), and acid-base chemistry (the stop hathL4 This is followed by a brief description of the actual experiment. At this time the students prepare their solutions and familiarize themselves with the orocedure. This isdonein thelieht. It is necessarv t o darken the room a t the time when all of the &dents are read; t o begin. Aluminum foil can he taped over the windows or heavy hlack plastic can be stapled onto a wooden frame which fits into the window well. Either works well, hut the plastic is much more durable and faster to install and remove. We supply the negatives that the students use. Normally, we photoeraoh the students a t work in the laboratorv about two weeks before t h i dhotoeraohv exneriment with a fast black and white film (e.e.. Xa i\d a'35-mm SLR camera using existine lieht. We can ~ d aT k ~ -, -~~ then attach the negative t o the correspond& p r i n t a i d have the students choose the negative they wish to work with. They appreciate this souvenir of the Chem Lab and all of the memories associated with it. Once the lights have heen turned off, the instructor can pass out the photographic paper. We use Kodabromide E-3 paper (8%X 11) which we cut in the dark to roughly 2 in. X 2 in. squares and store in a black envelone in a drawer in the lab. The safe liehts amole . orovide . baht for thestudentetu wurk,ro i t is unnecessary tu turnon the r u < m Ilgh~suntli the last prmt is in thr fixer or when the clean-uptlmr has arrived. ~~
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Experimental Apparatus The apparatus the students use for exposing the photographic paper is shown in Figure 3. I t consists of a simple ceramic light receptacle screwed onto a piece of l-in. thick wood. An aluminum rod is glued into a hole drilled in the side of the woad t o allow damping t o a ringstand. A 25-W bulb provides sufficient light, and a cylinder of aluminum foil is taoed onto the base of the reemtack to orevent We light frum interf~ringwth the workgting m a t the ~>therutatir,ns. have had as many w I U d these appnratu.*i
