ENV-32

Total hardness as CaCO3

TH = 2.497 [Ca] + 4.118 [Mg] in mg/L as CaCO3.

Reading speed

Water chemistryAPHA 2340

Governing equation

\mathrm{TH}=2.497[\mathrm{Ca}]+4.118[\mathrm{Mg}]

$[Ca] \in \left[0, 200\right]$

where

[Ca]: Calcium (mg/L)
[Mg]: Magnesium (mg/L)
TH: Total hardness (mg/L as CaCO3)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathrm{TH}=2.497[\mathrm{Ca}]+4.118[\mathrm{Mg}]

$[Ca] \in \left[0, 200\right]$

$[Ca] = 0$ $TH = 49.42$

Along the curve

②

Domain of the variable — blue

[Ca]_{\min} = 0,\quad [Ca]_{\max} = 200

$[Ca] \in \left[0, 200\right]$

$[Ca] = 0$ $[Ca] = 0$

Along the curve

③

Response curve — green

\mathrm{TH}=2.497[\mathrm{Ca}]+4.118[\mathrm{Mg}]

$[Ca] \in \left[0, 200\right]$

$[Ca] = 0$ $TH = 49.42$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}TH}{\mathrm{d}[Ca]}

$[Ca] \in \left[0, 200\right]$

$[Ca] = 1.258$ $TH^{\prime} = 2.497$

Along the curve

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-32 — Total hardness as CaCO3) is the form associated with APHA 2340. Working symbols: $[Ca]$ , $[Mg]$ $\rightarrow$ $TH$ . Hardness is the equivalent CaCO3 of divalent cations. The factors convert mg/L Ca and Mg to mg/L CaCO3.

Purpose

Purpose: compute

TH

from

[Ca]

[Mg]

in Environmental via

\mathrm{TH}=2.497[\mathrm{Ca}]+4.118[\mathrm{Mg}]

TH = 2.497 [Ca] + 4.118 [Mg] in mg/L as CaCO3. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

[Ca] = 40.000\,\mathrm{mg/L}

[Mg] = 12.000\,\mathrm{mg/L}

, the governing relation

\mathrm{TH}=2.497[\mathrm{Ca}]+4.118[\mathrm{Mg}]

yields

TH = 149.3\,\mathrm{mg/L as CaCO3}

. A beaker, Ca and Mg bars, a hardness scale. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Calcium [Ca]40 mg/LMagnesium [Mg]12 mg/L

Outputs

Total hardness TH149.3 mg/L as CaCO3

Reading speed

Watch on YouTube

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Narration of this film

A beaker, Ca and Mg bars, a hardness scale.

Hardness is the equivalent CaCO3 of divalent cations. The factors convert mg/L Ca and Mg to mg/L CaCO3.

Reading speed

Watch on YouTube