Calling Chemistry and Math Pros

[csmith]

I'm in need of assistance with reverse math. To follow is my equation used to figure liquid dosing. My PO4 level is a bit low (about 2 ppm) so for my next batch I'm upping it a bit. I'm in need of assistance with the reverse math of this.


Equation:
[(atomic mass of compound / mass of desired nutrient) * desired ppm] / (x) mL dosed for each 1 L of water column * 1000 (to convert the liter bottle to mL) / 1000 (to convert mg to grams)

K-H2-P-O4
K - 39.0983
H - 1.00794 *2
P - 30.973762
O - 15.9994 *4
0.5 mL dosed for every L of water column
Desired ppm of PO4 is 4

So...

{[39.0983 + (1.00794 * 2) + 30.973762 + (15.994 * 4)] / [30.973762 + (15.9994 * 4)] * 4} / 0.5 (removed the *1000 / 1000 for obvious reasons)=
{[39.0983 + 2.01588 + 30.973762 + 63.976] / [30.973762 + 63.976] * 4} / 0.5 =
[(136.063942 / 94.949762) * 4] / 0.5 =
11.46407861454145

So roughly 11.46 grams of KH2PO4 gives me 4 ppms of PO4 per 0.5 mL dosed in each L of water column from a 1000 mL stock. I've got that part. What I need to know is how to figure what 11.46 grams of KH2PO4 gives me as it concerns K. The following equation is as far as I can get. Desired ppm replaced with an (x) as it's now the variable. I've also changed the mass of desired nutrient to that of K.

{[39.0983 + (1.00794 * 2) + 30.973762 + (15.994 * 4)] / [39.0983] * (x)} / 0.5 = 11.46407861454145

Can anyone help me out here? I'm lost.

[Darkblade48]

Do you not simply solve for x?

For each 0.5 mL of your KH2PO4 stock solution that you add to 1 L of water, you will be increasing your potassium levels by 1.64 ppm.

By the way, why do you bother with how much potassium you are adding to your water column? Are you just ensuring that it is not lacking?

[csmith]

Do you not simply solve for x?

For each 0.5 mL of your KH2PO4 stock solution that you add to 1 L of water, you will be increasing your potassium levels by 1.64 ppm.

By the way, why do you bother with how much potassium you are adding to your water column? Are you just ensuring that it is not lacking?

You do solve for (x) I presume, I'm just not sure how to do it. Two answers I came up with were completely different and didn't make any sense to me. I want to figure how much K is in my KH2PO4 so I know how much K2SO4 to add as well.

[Tom Barr]

Note range C?
See how wide it is? Vs say A or B ranges?

This is a huge target, anywhere from 5-10ppm to 100ppm or more for K+.

While it might be interesting for some reason, the question will not help much in terms of management, most assume that the K+ from K2HPO4 is neglieble.
Quite a few folks simply use GH booster, which is about 50% K2SO4.

You get enough K from KNO3 anyway.
Lots of math and pain for not much gain.

Regards,
Tom Barr

[csmith]

While it might be interesting for some reason, the question will not help much in terms of management, most assume that the K+ from K2HPO4 is neglieble.
Quite a few folks simply use GH booster, which is about 50% K2SO4.

You get enough K from KNO3 anyway.
Lots of math and pain for not much gain.

Regards,
Tom Barr

I didn't know those things. So it would appear if your NO3 and PO4 are spot on then by default you're almost guaranteed of good K.

[Darkblade48]

You do solve for (x) I presume, I'm just not sure how to do it. Two answers I came up with were completely different and didn't make any sense to me. I want to figure how much K is in my KH2PO4 so I know how much K2SO4 to add as well.

Are you following your order of calculations correctly?

{[39.0983 + (1.00794 * 2) + 30.973762 + (15.994 * 4)] / [39.0983] * (x)} / 0.5 = 11.46407861454145

Multiply both sides by 0.5

{[39.0983 + (1.00794 * 2) + 30.973762 + (15.994 * 4)] / [39.0983] * (x)} = 5.73 (I'm cutting down the number of digits)

Simplify the L.H.

139x/39 = 5.73

Solve for x

x = 1.64

I didn't know those things. So it would appear if your NO3 and PO4 are spot on then by default you're almost guaranteed of good K.

Pretty much. Some people want to be extra sure there is no potassium deficiency, so they dose K2SO4 to compensate.

[Tom Barr]

I didn't know those things. So it would appear if your NO3 and PO4 are spot on then by default you're almost guaranteed of good K.

Yep

Regards,
Tom Barr