Originally Posted by mabrungard
Unfortunately, its an issue with slope and offset. If the offset was adjusted with during the 7 calibration, it affects the calibration setting (offset) at 4. If you then went back and checked the calibration at 4, you may have found that the trimmer needed another tweak to properly set the slope. After that tweak, the instrument should be in calibration. But performing the calibration order in reverse and not revisiting the 4 calibration may mean that the instrument is not calibrated very well in the lower range as pH moves further from 7.
Calibrate at 7 first and then at 4.
This assumes an analogue style meter. If he went back to check the 4 setting then that's tantamount to doing the calibration properly as the offset adjustment is independent of slope but not conversely.
With a digital meter voltages and temperatures are measured and recorded and inserted into formulas which produce calibration constants. The constants are not calculated until both temperatures and voltages are recorded so it doesn't matter what order the measurements are taken in.
Here's a simplified explanation of how it works with an analog meter.
An ideal (perfect,brand new... electrode produces voltage
E = slope*(pH - 7)
with slope dependent on temperature
A real electrode produces a voltage
E = E0 + slope1*(pH - pHi) where slope1 is not the same as the ideal slope. It tends to become smaller in magnitude as the electrode ages. E0 is an offset voltage. pHi is the isoelectric pH of the meter. It should be close to 7. Let's suppose it is for simplicity.
The electrode is connected to an amplifier which has gain and offset settings. The latter controls a voltage which is added to the electrode voltage and the sum is then amplified (scaled) by the gain factor. The output of the meter is
E' = gain*(E0+ offset) + slope*gain*(pH - 7) (assuming pHi = 7)
Clearly we want to adjust the controls so that offset = -E0 and gain = 1/slope and it's clear that the way to do that is put the electrode in 7 buffer and adjust the offset control until the output of the amplifier is 0 (center scale on an analogue meter and that point is marked 7) and then put the electrode in pH 4 buffer and adjusts the gain until it is equal to 1/slope at which point the voltage is -3. This point on the meter face is marked 4. The meter is calibrated.
Now if one goes into 4 buffer first he'd adjust the gain until the voltage is -3 (meter reads 4) which would result in
gain = -3/(E0 - offset -3*slope)
which would give the correct gain (1/slope) only in the case where the offset happened to have been set at -E0 (from a previous calibration). If one now goes into the 7 buffer he can set the offset correctly to 0 the voltage (put the pin or A/D reading at 7) and this would required simply that the offset be equal (in magnitude) to E0. Thus going into 4 buffer first gives and erroneous slope setting but a correct offset. It should be clear from this that the error one encounters in doing this depends on how far away from pH 7 the sample falls. Close to 7 the readings will be quite accurate. Farther away, less so.