Silver_Is_Money
Larry Sayre, Developer of 'Mash Made Easy'
In another current thread there is a concern that Mash pH prediction should be measurably different with changes in mash thickness (mash water volume). This is in direct response to that question.
For the case of Mashing in 15L of Distilled water vs. Mashing in 30L of Distilled Water:
1) mEq's of Acid required to move 15 Liters of water from pH 7 to pH 5.40
10^-5.40 = 0.000003981 moles of H+ per Liter
0.000003981 x 1000 = 0.003981 mmoles H+ per liter
Charge for H+ = 1
Therefore 0.003981 mmoles/L = 0.003981 mEq/L
0.003981 mEq/L x 15L = 0.05972 mEq
It takes 0.05972 mEq's of Acid to move 15 Liters of Distilled Water from pH 7 to pH 5.40
88% Lactic Acid at pH 5.40 has an Acid Strength of 11.451 mEq/mL
Therefore:
0.05972 mEq ÷ 11.451 mEq/mL = 0.00522 mL of 88% Lactic Acid to move 15L of Distilled Water to pH 5.40
2) For brevity let's cut right to the chase and logically admit that it takes 0.05972 x 2 = 0.11944 mEq's of Acid to move 30L of distilled water to pH 5.40 pH
That is 0.00522 x 2 = 0.01044 mL of 88% Lactic Acid required to move 30L of Distilled Water to pH 5.40
3) Since MME is ignoring water volume in the Mash it is predicting an 88% Lactic Acid addition to be 0.00522 mL lower than is actually required for the case of Mashing in 15L of distilled water, and 0.01044 mL lower than is actually required for the case of Mashing in 30L of distilled water.
If we presume a 5 Kg. grist with a DI Mash pH of 5.70, and a Buffering Capacity (BC) of 35 mEq/Kg.pH, how far off will MME's Mash pH prediction be for the case of ignoring the acid required to acidify the water itself, both for the case of Mashing in 15L and 30L?
Let's calculate how many mEq's are required to move the grist alone (I.E., ignoring the mash water volume) from pH 5.70 to pH 5.40
(5.70 - 5.40) = mEq's/(35 x 5)
0.30 = mEq's/175
mEq's = 0.30 x 175
mEq's = 52.5
52.5 mEq's ÷ 11.451 mEq's/mL = 4.58475 mL of 88% Lactic Acid required to be added
(This is how MME would calculate it)
But for Mashing in 15L MME is 0.00522 mL short of 88% Lactic Acid, and 4.58475 + 0.00522 mL of 88% Lactic Acid is actually required. That equals 4.58997 mL as the correct 88% Lactic Acid addition.
And for Mashing in 30L MME is 0.01044 mL short of 88% Lactic Acid, and 4.58475 + 0.01044 mL of 88% Lactic Acid is actually required. That equals 4.59519 mL as the correct 88% Lactic Acid addition.
So we have MME telling us to add 4.58475 mL of 88% Lactic Acid vs. 4.58997 mL and 4.59519 mL respectively.
Ask yourself how accurately you can add 88% Lactic Acid as to mL decimal places.
Then ask what the maximum magnitude of MME's pH prediction error is:
The maximum error would be for the case of Mashing in 30 Liters, for which MME computes a deficit of 0.11944 mEq's as to its prediction output, as seen in #2 above.
Maximum_pH_error_MME = 0.11944/(35 x 5) = 0.0006825 pH points for the specific case of a 5Kg. grist with a pHDI of 5.70 and a BC of 35 mEq/Kg.pH
So by ignoring 30 Liters of water completely an output error of 0.0006825 pH is created. That would not likely even show up when rounding pH prediction to 2 decimal places.
Clearly in a buffered grist mash system the distilled water impact upon pH can be fully ignored, as can water volume doubling or halving as for Mash plus Sparge vs. No-Sparge.
For the case of Mashing in 15L of Distilled water vs. Mashing in 30L of Distilled Water:
1) mEq's of Acid required to move 15 Liters of water from pH 7 to pH 5.40
10^-5.40 = 0.000003981 moles of H+ per Liter
0.000003981 x 1000 = 0.003981 mmoles H+ per liter
Charge for H+ = 1
Therefore 0.003981 mmoles/L = 0.003981 mEq/L
0.003981 mEq/L x 15L = 0.05972 mEq
It takes 0.05972 mEq's of Acid to move 15 Liters of Distilled Water from pH 7 to pH 5.40
88% Lactic Acid at pH 5.40 has an Acid Strength of 11.451 mEq/mL
Therefore:
0.05972 mEq ÷ 11.451 mEq/mL = 0.00522 mL of 88% Lactic Acid to move 15L of Distilled Water to pH 5.40
2) For brevity let's cut right to the chase and logically admit that it takes 0.05972 x 2 = 0.11944 mEq's of Acid to move 30L of distilled water to pH 5.40 pH
That is 0.00522 x 2 = 0.01044 mL of 88% Lactic Acid required to move 30L of Distilled Water to pH 5.40
3) Since MME is ignoring water volume in the Mash it is predicting an 88% Lactic Acid addition to be 0.00522 mL lower than is actually required for the case of Mashing in 15L of distilled water, and 0.01044 mL lower than is actually required for the case of Mashing in 30L of distilled water.
If we presume a 5 Kg. grist with a DI Mash pH of 5.70, and a Buffering Capacity (BC) of 35 mEq/Kg.pH, how far off will MME's Mash pH prediction be for the case of ignoring the acid required to acidify the water itself, both for the case of Mashing in 15L and 30L?
Let's calculate how many mEq's are required to move the grist alone (I.E., ignoring the mash water volume) from pH 5.70 to pH 5.40
(5.70 - 5.40) = mEq's/(35 x 5)
0.30 = mEq's/175
mEq's = 0.30 x 175
mEq's = 52.5
52.5 mEq's ÷ 11.451 mEq's/mL = 4.58475 mL of 88% Lactic Acid required to be added
(This is how MME would calculate it)
But for Mashing in 15L MME is 0.00522 mL short of 88% Lactic Acid, and 4.58475 + 0.00522 mL of 88% Lactic Acid is actually required. That equals 4.58997 mL as the correct 88% Lactic Acid addition.
And for Mashing in 30L MME is 0.01044 mL short of 88% Lactic Acid, and 4.58475 + 0.01044 mL of 88% Lactic Acid is actually required. That equals 4.59519 mL as the correct 88% Lactic Acid addition.
So we have MME telling us to add 4.58475 mL of 88% Lactic Acid vs. 4.58997 mL and 4.59519 mL respectively.
Ask yourself how accurately you can add 88% Lactic Acid as to mL decimal places.
Then ask what the maximum magnitude of MME's pH prediction error is:
The maximum error would be for the case of Mashing in 30 Liters, for which MME computes a deficit of 0.11944 mEq's as to its prediction output, as seen in #2 above.
Maximum_pH_error_MME = 0.11944/(35 x 5) = 0.0006825 pH points for the specific case of a 5Kg. grist with a pHDI of 5.70 and a BC of 35 mEq/Kg.pH
So by ignoring 30 Liters of water completely an output error of 0.0006825 pH is created. That would not likely even show up when rounding pH prediction to 2 decimal places.
Clearly in a buffered grist mash system the distilled water impact upon pH can be fully ignored, as can water volume doubling or halving as for Mash plus Sparge vs. No-Sparge.
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