At my pH & temp, what fraction of total ammonia (TAN) is toxic NH₃ across a 24-hr CO₂ swing?

Home/Store/Fish and Aquaria Related Articles/At my pH & temp, what fraction of total ammonia (TAN) is toxic NH₃ across a 24-hr CO₂ swing?

NH₃ fraction of TAN across a CO₂-driven 24-hour pH swing

Below is a rigorous, aquaculture-grade way to compute the toxic un-ionized ammonia fraction (NH₃) from TAN at your exact pH/temperature—including how the day/night CO₂ swing amplifies NH₃.

1) Core chemistry (freshwater)

Ammonia in water partitions as:

N H_{4}^{+} ⇌ N H_{3} + H^{+}

The mole fraction of NH₃ in total ammonia (TAN = NH₃ + NH₄⁺) is:

f_{N H_{3}} = \frac{1}{1 + 10^{(p K_{a} - p H)}}

For freshwater, the temperature dependence of $p K_{a}$ is well fit by:

p K_{a} \approx 0.09018 + \frac{2729.92}{T_{K}}

with $T_{K} = T_{(^{\circ} C)} + 273.15$ .

Result you use: Given your pH and °C, compute $f_{N H_{3}}$ . Then • If your test reads TAN as NH₃ units (mg/L as NH₃): $N H_{3} (m g / L) = T A N \times f_{N H_{3}}$ $N H_{3} (mg/L) = TAN \times f_{N H_{3}}$ • If your test reads TAN as N (mg/L as NH₃-N): $N H_{3} - N = {T A N}_{(a s N)} \times f_{N H_{3}}$ $N H_{3} - N = TAN_{(as N)} \times f_{N H_{3}}$ and $N H_{3} (m g / L) = N H_{3} - N \times \frac{17}{14}$ $N H_{3} (mg/L) = N H_{3} - N \times 14 17$ .

2) Salinity / ionic-strength correction (brackish & marine)

In saltier water, use a salinity-corrected $p K_{a}^{\*}$ :

p K_{a}^{\*} (T, S) \approx (0.09018 + \frac{2729.92}{T_{K}}) + 0.0415 \sqrt{S} - 0.000116 S

where $S$ is salinity in ppt. Then plug $p K_{a}^{\*}$ into the same fraction formula.

Direction of effect: higher salinity → slightly larger $p K_{a}$ → smaller NH₃ fraction at a given pH and °C (the effect is modest but real).

3) What the CO₂ swing does (the “multiplier”)

CO₂ affects pH (not TAN directly). With alkalinity roughly constant over the day, a pH rise at night (CO₂ off / degassing) increases NH₃ non-linearly.

If your pH is well below the ammonia $p K_{a}$ (~9.2–9.5 in typical tanks), a very accurate rule-of-thumb is:

\frac{f_{N H_{3}} (p H_{h i g h})}{f_{N H_{3}} (p H_{l o w})} \approx 10^{Δ p H}

So:

+0.1 pH ≈ 1.26× NH₃
+0.3 pH ≈ 2.0×
+0.5 pH ≈ 3.16×
+1.0 pH ≈ 10×

This is why even a “modest” night rise can turn a safe daytime NH₃ into a risky nighttime NH₃ without TAN changing at all.

Temperature effect: each +1 °C (at fixed pH) increases the NH₃ fraction by ~7% around typical conditions. If your tank runs warmer at night, include that.

4) Worked examples (26 °C, freshwater)

Using the exact equation above:

pH 7.0: $f_{N H_{3}} \approx 0.605 %$ of TAN
pH 7.5: $f_{N H_{3}} \approx 1.888 %$ of TAN
pH 8.0: $f_{N H_{3}} \approx 5.736 %$ of TAN
pH 8.5: $f_{N H_{3}} \approx 16.14 %$ of TAN

Across a realistic swing (CO₂ on by day, off at night):

Day pH 6.8 → Night pH 7.4 (ΔpH = 0.6): $f_{N H_{3}}$ $f_{N H_{3}}$ rises from 0.382% → 1.505% (≈ 3.94×).
If TAN is 0.50 mg/L as NH₃ units all day: Day NH₃ ≈ 0.0019 mg/L, Night NH₃ ≈ 0.0075 mg/L.

Salinity check (brackish/marine), 26 °C, pH 7.5:

S = 0 ppt: $f_{N H_{3}} \approx 1.888 %$
S = 10 ppt: $f_{N H_{3}} \approx 1.406 %$
S = 20 ppt: $f_{N H_{3}} \approx 1.246 %$
S = 35 ppt: $f_{N H_{3}} \approx 1.091 %$

5) How to compute your exact day/night NH₃ right now

Measure or log:
- Day pH (CO₂ on) and Night pH (CO₂ off)
- Day °C and Night °C
- TAN (ensure units: “as NH₃” vs “as N”)
- Salinity (ppt), if not freshwater.
Compute fractions using:

f_{N H_{3}, d a y} = \frac{1}{1 + 10^{(p K_{a} (T_{day}, S) - {p H}_{day})}}, f_{N H_{3}, n i g h t} = \frac{1}{1 + 10^{(p K_{a} (T_{night}, S) - {p H}_{night})}}

Multiply by TAN in matching units to get NH₃ (mg/L) for day and night.

I placed two interactive tables for you already:

“NH₃ % of TAN vs pH & Temperature (Freshwater)” — read off your % directly.

“NH₃ Multiplier Across a pH Swing (Assuming 26 °C)” — see how much the night pH amplifies NH₃ vs day.
There’s also a tiny helper you can run to print your exact % NH₃ at any pH/°C.

6) Practical notes (expert tips)

CO₂-to-pH mapping: With alkalinity roughly constant, doubling dissolved CO₂ lowers pH by ~0.30; a 10× change shifts pH by ~1.0. You can sanity-check your pH swing against your CO₂ schedule.
KH matters for swing amplitude: Higher alkalinity damps pH changes from CO₂, helping cap the NH₃ spike without changing TAN.
When pH ≳ 9, the “10^ΔpH” shortcut breaks down because you’re near $p K_{a}$ ; use the exact equation.
Logging: A cheap continuous pH logger plus one daily TAN test will let you compute a full 24-hr NH₃ profile (peak is typically late night to early morning, when pH is highest).