Again, this is something that is done much better by Kerry Brandis.
I present here my own fist-and-crayon attempts to reason visually through the question of what happens when you infuse a patient with a bag of some fluid or other, or when you given them a concentrated intravenous electrolyte solution.
Below are the initial assumptions which hold for the above-linked discussions of what happens to infused water and electrolytes.
User experience may vary according to compartment proportions of actual humans. We are not a uniform series of shiny liquid-filled cylinders.
The fluid compartments for this experiment will have volumes rounded for simplicity of calculation:
The experimental body belongs to a 70kg person, who is 60% water by weight (which makes 42 litres of water)
This whole "intravascular volume" business is confusing. My approach has been to ignore it unless I am arguing about the change in volume (as sensed by baroreceptors).
Baroreceptors respond to the changes in this 5 litre "total intravascular volume". Of this volume, 3500ml is pure water, in which osmotically active substances are dissolved, and the rest is blood cells.
Only the intravascular water (the 3500ml) contains the electrolytes you infuse into the patients. Therefore, the resulting changes in osmolality are calculated with a volume of 3500ml in mind.
This transparent cylindrical patient has a serum osmolality of 280, which is near normal. This does not reflect the reality of a fasted anaesthetic patient, a vomiting dehydrated patient, a forgotten undernourished geriatric patient, et cetera. The waterlogged 20-litres-positive septic ICU patient is not represented by these diagrams and numbers. Additionally, one could go quite mad by complicating calculations with functional extracellular fluid, or whether to include or exclude transcellular fluid.
Yes, this means this may add a wider margin of error to my various attempts to work out changes in osmolality and ion concentration.
But not by more than the actual variation in patient fluid compartment volumes, their renal clearance rates, metabolic physiology, diuretic effects, pathological states, et cetera.
In short, I could be wrong about everything.