Question

Calibration of a glass electrode gave a reading of 139.7 mV with saturated potassium hydrogen tartrate buffer standard (pH = 3.557) and a reading of -92.2 mV with 0.08 m HEPES, 0.08 m NaHEPES, 0.08 m NaCl buffer standard (pH = 7.454), both measured at 30°C.

(a) What is the observed slope (mV/pH unit) of the calibration curve?

(b) What is the theoretical slope at 30°C?

(c) What is β, the electromotive efficiency to three significant figures?? Open the hint panel below for the definition of electromotive efficiency.

(d) What is the pH of an unknown that gives a reading of 46.9 mV with this electrode at 30°C?

Answer 1

a.

Slope S = dE/dpH = (139.7-(-92.2))/(3.557-7.454) = - 231.9/3.897= - 59.51 mV/pH unit

b. The theoretical slope is

          -2.303RT/nF

    The known value at 298 K is - 0.05916 V (see Nernst equation)

     The value at 303 K is

        -0.05916 V x303K/298K = -0.06015 V = -60.15 mV/pH unit

c.

59.51 mV/pH / 60.15 mV/pH = 0.9893

d.

pH_x = pH + (Ex-E)/S      

                                          (pH and E, any known pair, look also at a., same equation)

                = 7.454 - (46.9 + 92.2)/ 59.51

                = 7.454 – 2.337 = 5.117