Calibration of a glass electrode gave a reading of 139.3 mV with 0.05 m potassium dihydrogen citrate buffer standard (pH = 3.766) and a reading of -79.0 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 pH of an unknown that gives a reading of 21.7 mV with this electrode at 30°C?
To calculate the observed slope (mV/pH unit) of the calibration curve, we need to determine the change in millivolt (mV) reading for a change of 1 pH unit.
In this case, we have two calibration points:
1. With the 0.05 m potassium dihydrogen citrate buffer standard with pH = 3.766, the reading is 139.3 mV.
2. With the 0.08 m HEPES, 0.08 m NaHEPES, 0.08 m NaCl buffer standard with pH = 7.454, the reading is -79.0 mV.
Let's calculate the change in mV for a change of 1 pH unit.
1. Change in mV for the first point:
ΔmV = reading of second point - reading of first point
= -79.0 mV - 139.3 mV
= -218.3 mV
2. Change in pH for the first point:
ΔpH = pH of second point - pH of first point
= 7.454 - 3.766
= 3.688 pH units
Now, we can calculate the observed slope:
Observed slope = ΔmV / ΔpH
= (-218.3 mV) / (3.688 pH units)
(a) Therefore, the observed slope of the calibration curve is approximately -59.18 mV/pH unit.
To determine the pH of an unknown that gives a reading of 21.7 mV with this electrode at 30°C, we can use the observed slope.
(b) pH of the unknown:
pH = (mV - reading of second point) / observed slope
= (21.7 mV - (-79.0 mV)) / (-59.18 mV/pH unit)
Simplifying the equation:
pH = (21.7 mV + 79.0 mV) / (-59.18 mV/pH unit)
Now, you can calculate the pH value of the unknown using the given equation.
Please note that these calculations assume linearity and correctness of the calibration curve. Calibration curves should be checked for linearity and recalibrated periodically to maintain accuracy.