# Calculate the pH Slope using 7.0 and 10.0 buffers

Hi, I'm trying to calculate the slope of a pH probe using 7.0 and 10.0 buffer solutions. I've been searching for hours but all examples use 7.0 and 4.0. I've calibrated my probe using the 7.0 and 4.0 buffers and calculated the slope, then I used 7.0 and 10.0, used the same math for the slope and it was quite different so I don't know if that's normal or I'm doing something wrong.

This is using 7.0 and 4.0 and confident its correct.

pH electrode generated –5 mV in pH 7.00 buffer and +165 mV in pH 4.00 buffer.
165 mV – (-5 mV) = 170 mV
170mv/3 = 56.66mV/pH unit
56.66/59.16 x 100 = 95.8% slope

Now this is an example with 7.0 and 10.0, is this correct?

pH electrode generated –5 mV in pH 7.00 buffer and -165 mV in pH 10.00 buffer.
-165 mV – (-5 mV) = -160 mV
-160mv/3 = -53.33mV/pH unit
53.33/59.16 x 100 = -90.15% slope

Obviously with a 2nd buffer over 7.0 the slope always comes out as a negative number, would I just invert it to a positive number?

Thanks

Borek
Mentor
Your approach to calculating the ΔV is inconsistent. If you go for Vat lower pH - Vat higher pH you should do it for both cases.

• DeepThinking
Thanks, something like this?

This is using 7.0 and 4.0

pH electrode generated –5 mV in pH 7.00 buffer and +165 mV in pH 4.00 buffer.
165 mV – (-5 mV) = 170 mV
170mv/3 = 56.66mV/pH unit
56.66/59.16 x 100 = 95.8% slope

This is using 7.0 and 10.0

pH electrode generated –5 mV in pH 7.00 buffer and -165 mV in pH 10.00 buffer.
-5 mV – (-165 mV) = 160 mV
160mv/3 = 53.33mV/pH unit
53.33/59.16 x 100 = 90.15% slope

Borek
Mentor
Yes.

symbolipoint
Homework Helper
Gold Member
Any one or two pH buffers will not be enough to allow for finding a slope for either pH. You need titration data for the region containing the pH change value of each buffer. This is not just one or two points in each pH region. You might take a slope using pH 7 and pH 10, but this is not the intent of doing a titration curve.

Thanks Borek!

Sorry symbolipoint I don't understand that. The formula seems to be common for some meters, I got it from a Hanna manual but it only shows the first example.

Can I ask about a formula for temperature compensation? Best I found is 0.003 pH/ºC/pH but I don't know how to apply that.

symbolipoint
Homework Helper
Gold Member
Sorry symbolipoint I don't understand that. The formula seems to be common for some meters, I got it from a Hanna manual but it only shows the first example.

Can I ask about a formula for temperature compensation? Best I found is 0.003 pH/ºC/pH but I don't know how to apply that.
I might by some chance miss what you meant. Your first post #1 seemed to be about slope in relation to what SHOULD be using or making a titration curve, but you asked for slopes(?) for pH 7 and pH 10 indicators. No mention about temperature there was given. One would be looking at titrant volume versus pH (or mv) measurement,and then use the points to find the slope at the inflection point, FOR EACH intended indicator solution.

symbolipoint
Homework Helper
Gold Member
I really do now think I misunderstood. Are you really looking for a slope? Calibration of the pH meter? If this, then you can use pH 7 AND pH 10 BUFFER SOLUTIONS. to ADJUST the pH meter. Someone else, for example, Borek, can explain this better.

Sorry for the confusion, I was only asking about the slope of the electrode using the mid and high calibration settings so I can check the condition of the electrode after calibration. What Borek said makes sense, I just wasn't sure.

Ultimately I'm trying to achieve the following.

1. Calculate slope of pH electrode using mid/low buffer, mid/high buffer or mid/low/high buffer. (I think this is figured out now)
2. Apply calibration using mid buffer (1 point), mid/low buffer (2 point), mid/high buffer (2 point) or
mid/low/high buffer (3 point).
3. Temperature compensation for calibrating and monitoring pH

For the 3 different types of calibration this is what I have, do the formulas look ok? Only 1 of the 3 would be used.

2 point calibration - 2nd point buffer is 4.0
mV = -5.00; // raw mV
buffer1 = 0.00; // buffer 7.00
buffer2 = 177.48; // buffer 4.00
cal_mV1 = -15.00; // pH reading during calibration using 7.0 buffer (point 1)
cal_mV2 = 160.0; // pH reading during calibration using 4.0 buffer (point 2)
referenceRange = buffer2 - buffer1;
mV = (((mV - cal_mV1) * referenceRange) / readingRange) + buffer1;
pH = fabs(7.0 - (mV / 59.16));

2 point calibration - 2nd point buffer is 10.0
mV = -5.00; // raw mV
buffer1 = 0.0 mV // buffer 7.00
buffer2 = -177.48; // buffer 10.00
cal_mV1 = -15.0 mV // pH reading during calibration using 7.0 buffer (point 1)
cal_mV2 = -192.2 mV // pH reading during calibration using 10.0 buffer (point 2)
referenceRange = buffer1 - buffer2;
mV = (((mV - cal_mV1) * referenceRange) / readingRange) + buffer1;
pH = fabs(7.0 - (mV / 59.16));

3 point calibration
mV = -5.00; // raw mV
buffer1 = 0.00; // buffer 7.00
buffer2 = 177.48; // buffer 4.00
buffer3 = -177.48; // buffer 10.00
cal_mV1 = -15.00; // pH reading during calibration using 7.0 buffer (point 1)
cal_mV2 = 160.0; // pH reading during calibration using 4.0 buffer (point 2)
cal_mV3 = -194.48; // pH reading during calibration using 10.0 buffer (point 3)
if (mV < 0) // if pH greater than 7.0
{
referenceRange = buffer1 - buffer3;
mV = (((mV - cal_mV1) * referenceRange) / readingRange) + buffer1;
}
else // if pH less than 7.0
{
referenceRange = buffer2 - buffer1;
mV = (((mV - cal_mV1) * referenceRange) / readingRange) + buffer1;
}
pH = fabs(7.0 - (mV / 59.16));

At this point I would have the calibrated pH value and would like to apply temperature compensation to it.

Thanks

IIRC, some clever pH meters happily self-calibrate their internal 'curve' for the whole range using but one buffer.

Even so, we checked ours daily at #4 & #10, to be sure, to be sure...

You must have a robust system in place for detecting and handling outages, such as a fouled electrode or stale buffer. I remember the scramble before we discovered that a certain pH-adjusted HPLC mobile phase would not play well with an electrode that wasn't 'squeaky clean'. As our routine daily checks had found that electrode was reading correctly, if a bit slower than usual, we were able to go back and double-check prior usage...

Also, we kept several sets of 'pH Strips' handy, as a sanity check...

• DeepThinking
Thanks Nik_2213, those are good tips to remember.