Bobby N. lrby
Northeast Louisiana State College Monroe, Louisiana
Slide Rule Conversion of [H'] to pH
Solving the following simple manipulation may be of interest for students who already are sure of the mathematics of interconversion of hydrogen ion concentration to pH. To convert hydrogen ion concentration to pH directly, place the nonexponential factor of the hydrogen ion concentration on the C scale of a slide rule a t the D index and read the mantissa of thc log on the L scale a t the C index. The characteristic will be one less than the negative exponent (see Figure 1). For a [H+] of 2.25 X lo-= ill, the characteristic is 4, the mantissa is ,648, and the pH is 4.648. To convert pH to hydrogen ion concentration, reverse the procedure. Place the index of the
C scale on the L scale corresponding to the nlantissa and read the nonexponential factor of the hydrogen ion concentration on the C scale a t the D index, as shown in Figure 2. For a pH of 3.78 the exponential factor is lo-&,the nonexponential factor is 1.62, and the [H+] is 1.62 X M. This is essentially the same conversion obtained by using the CI scale as outlined by Butler.'
Figure 1. For o [H+] of 2.25 X lo-", tirro is 0.648,and the pH is 4.648.
Figure
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'BUTLER,JAMESN., "Solubility and pH Caleulstions" (paperback), Addison-Wesley, Inc., Reading, Massachusetts, 1964, p. 9.
2. For o pH of 3.780 the exponential fastoris 10-5 the nonexponenfial factor is 1.62, ond the [H +I is 1.62 X 1 0-aM.
