HAIR BIS-DINITROPHENYL CYSTINE INTERCHANGE 367 values (1269- 1650 Ix mole/g hair) (5). The equilibrium constant K for the interchange reaction in strong acidic medium (•9.6N) was determined to be 2.56. DETERMINATION OF THE REACTION RATE CONSTANTS The rate equation for the interchange reaction is d[C] - k•[A][B] - k2[C] 2 dt or (eq. 10) 1 d[C] k2 dt - K'(m[Cy] - 0.5[C]) - [C] • (eq. 11) The solution for eq. 11, i.e, the formation of mono-DNP-cystine (C) as a function of time (t) is E o, z ! o o E .5 o o 5 10 15 20 25 TIME (days) Figure 2. Formation of mono-DNP-cystine as a function of time for various concentrations of hair hy- drolysate from intact hair. The curves were calculated from eq. 12 with K' = 3.3 X 10 -3, k2 = 5.0 hr -•, and ICy] = 6.54 x 10 -4 mole/g hair. Key: (2) = 0.5 g ß -- 0.2 g ß -- 0.05 g of hair in 250 ml of 9.6 N HCI.

368 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS [C] = 0.5(0.5K' - Q)(e -k2Qt - 1) (eq. 12) 1 -- 0.SK' - Q . e_k2Qt 0.SK' + Q Eq. 12 may be rewritten as -k2Qt = ln([C] + 0'5(0'5K' - Q).0'5K' + QQ) [C] + 0.5(0 5K' + Q) 0.5K' - (eq. 13) Since K' and Q (or ICy]) are known, the right hand side of eq. 13 may be plotted as a function of time (t) from the kinetic data. The slope of this straight line is -k2Q. Therefore, the reaction rate constants k 2 and k• can be determined. The values for k• and k 2 for the hair keratin obtained using the least square linear regression are 12.80 and 5.00 hr-•, respectively. Figure 2 shows the formation of mono-DNP-cystine as a function of time for some hydrolysate concentrations. The curves in the figure were calculated from eq. 12. E .3 .2 o o lO 20 TIME (days) Figure 3. Formation of mono-DNP-cystine as a function of time using hydrolysates of hair which had undergone various degrees of bleaching in alkaline hydrogen peroxide solution. The curves were calculated from eq. 12 with K' = 3.33 X 10 -3 , k2 = 5.0 hr -•, and [Cy]s from Table I. Key: ß = untreated ß = 1X bleached • = 3X bleached ß = 5X bleached.