Finally, let's say this lemon tetra is in a 20 U.S. gallon tank. That's 75.7 L. 0.000 012 434 kg is equal to 12.434 mg (multiply by 10^6). 12.434 mg/75.7 L = 0.164 mg/L and since at dilute concentrations a mg/L is roughly a ppm, this means that one lemon tetra in a 20 U.S. gal tank makes about 0.16 ppm of ammonia per day.
Well done on the maths Bignose...one thing though, mg/L expresses the same thing as ppm no matter what the concentration
No, you are mistaken here, a mg/L and ppm are the same only for dilute concentrations in water.
Let me give you a farcical example. Take 1 liter of pure ethanol. Since it is pure, that would have a concentration of 1,000,000 ppm. But, it I guarantee it won't be 1,000,000 mg = 1 kg. It will weigh about 0.789 kg.
a ppm is a like over like measurement. That is, properly a ppm should be a volume over a volume (like microliters in one liter) or a mass over mass (like mg per kg) or any other like measurements. Quality control of manufacturing process are often reported in ppm. E.g. a manufacturing error rate of 100 ppm, would be 100 units with errors per 1 million units manufactured.
mg/L is not a like over a like. it is mass over volume. It works out to be the same as a ppm in dilute concentrations of water because you can convert mass to volume using the density of water and a microliter of water at 25 degrees C weighs one milligram.
The density of ammonia is actually 694.2 kg/m^3 Compare that with water which is 1000 kg/m^3. So, there is a small error in there, depending on whether you are talking about ppm v/v (v/v stands for volume/volume) or ppm m/m (mass/mass).
If there were no interactions between the water and ammonia: 1 ppm v/v ammonia in water is actually equal to 0.7 ppm m/m ammonia in water. 1 ppm m/m ammonia in water is actually 1.4 ppm v/v ammonia in water. But, of course, nature doesn't work like that. There will be interactions betweens the ammonia an water to find the final density. The mixture density will not just be the linear combination of the two densities weighted by the amounts of each pure component.
So, this is where the phrase "in dilute concentrations" becomes important. Because, 1 ppm of ammonia in water is almost wholly water, the density of the mixture is almost exactly the same as that of water, so the conversion between mg/L and ppm works. But again, as an extreme example, 1 ppm of water in ammonia, or 999,999 ppm of ammonia in water will not be 999,999 mg/L, it will be about 694,000 mg/L.
To be completely exact, there are temperature variations in there as well. The density of water is only 1000 kg/m^3 at 25 degrees C and 1 bar pressure. At other temperatures, and pressures, the value is slightly different. There will be temperature variations in the interactions between mixture components as well. But, all these variations are small, well within the measurement error of our home test kits.
In conclusion, however, the phrase "in dilute concentrations" is critically important because in non dilute situations a mg/L is NOT a ppm.