[Pajamasam]

In studies, dose is often expressed in mg/day. It is calculated as follows: Dose=Concentration*Intake Rate. The units of concentration and intake rate vary. Concentration can be in units of w/w, w/v, v/v (e.g. %, ppm). Intake rate can be in units of weight or volume (e.g. 1 L/day or 1 g/day) but dose is often mg/day. I am confused about when to correct for density and when not, and I wondered whether there were any general rules about this or some tables that relate the units of concentration to intake units in terms of density correction.

Here are two examples: In this example I've used the density of the entire solution.
Calculate the mg/day dose of 100 mL of a 10 ppm w/w solution of ciprofloxacin in pure glycerin.
10 ppm w/w= 10 mg/kg. The density of the entire solution is 1.26 g/mL at 20oC. Thus, 1 kg of the solution would have a volume of 793.65 mLs and 100 mL of this solution will contain 1.26 mg of ciprofloxacin and the dose would be 1.26 mg/day.

In this example, I've used the density of the solute:
Calculate the mg/day dose of 100 mL 40%v/v solution of pure ethanol in pure water.
40%v/v ethanol=40 mL ethanol made up to 100 mL of water. Ethanol density=0.789 g/mL at 20oC. Thus, 100 mL of this solution will contain 31.572 g (40 mL *0.789 g/mL=31.572 g) of ethanol. At an intake of 100 mL per day, the daily dose would be 31.572 g/day.

Not sure what would happen if you have a concentration in w/v and an intake in units of weight. Anyway please let me know if there are any errors (above) or general rules about this.

[Arkcon]

I am confused about when to correct for density and when not, and I wondered whether there were any general rules about this or some tables that relate the units of concentration to intake units in terms of density correction.

You've done lots of work, and it will certainly come in handy as we solve your problems, but I wanted to help you with this one part for starters. 

*Ahem*

The density of pure water is 1.  (Not really, but we use that for most purposes.)  Anything multiplied or divided by 1, remains the same number.  So we never use the density of pure water in such a calculation.

Glycerin and ethanol don't have a density of 1.  Their density is far from 1.  If you don't use the density, the solution will be too strong or too weak.

You have to think about this, when you make a solution -- if you make it weight per weight or volume per volume, it doesn't matter.  But if you expect to measure weight or volume and get the other value, you have to compensate if the density isn't 1.

[Borek]

To add to what Arkcon wrote: while water has a density of (nearly exactly) 1 g/mL, water solutions have typically different density. As long as they are diluted we can ignore the difference, as the error we are making in our calculations is negligible. When solution become more concentrated thing are getting more difficult, as their density becomes more and more different from 1 g/mL and has to be taken into account.

Note, that the same holds for other solvents.

[Pajamasam]

Agreed; When I see solutions in water or normal saline I do a little happy dance inside my head because I know I don't have to worry about the density of the solvent (as it approaches 1 g/mL) ! As Borek pointed out, the more concentrated even aqueous solutions become the density should be accounted for. For example, with normal saline the density is the same as water, but as the saline becomes more hypertonic (like brine), density has to be accounted for. Some of the solvents I see have densities quite different from 1: e.g. incredibly dense (carboxymethylcellulose for example) or light (ethanol).

[Borek]

To be VERY precise:

pure water @ 20°C - 0.99823 g/mL
normal saline @ 20°C - 1.0046 g/mL

so there is about 0.6% difference in densities.

[Pajamasam]

Yes, might be a good idea to check density for any solvent (including dilute aqueous) just to see if it is worth correcting for.