To make 500 ml of hypertonic saline with 856 meq/l of sodium isotonic, you'll need to add 2557.14 ml of sterile water for injection.
Here's how we can calculate the volume of sterile water required:
Define the initial and desired concentrations:
Initial volume of hypertonic saline: 500 ml
Initial sodium concentration: 856 meq/l
Desired isotonic sodium concentration: 140 meq/l (typical for body fluids)
Calculate the total amount of sodium in the initial solution:
Sodium amount = volume * concentration = 500 ml * 856 meq/l = 428,000 meq
Determine the volume of solution needed to achieve the desired sodium concentration after dilution:
Volume needed = total sodium amount / desired concentration = 428,000 meq / 140 meq/l = 3064.29 ml
Calculate the volume of sterile water required:
Volume of water = volume needed - initial volume = 3064.29 ml - 500 ml = 2564.29 ml
Therefore, you need to add approximately 2557.14 ml of sterile water for injection to the 500 ml of hypertonic saline to make it isotonic.