This is a question I use in my IV fluid lecture. The lesson goes like this:
It starts by me asking the students what's the highest glucose they have ever seen. I go around the room and find the highest. Sometimes they'll have a cool story of a DKA or HONK. Then I tell them that they haven't seen anything until they've had an ESRD patient in DKA. Since dialysis can't make urine they escape the osmotic diuresis. The blood sugar doesn't have an escape route so the plasma levels sky rocket. Additionally the lack of profound volume loss allows these patients to delay treatment by avoiding the life threatening shock that typically hospitalizes the patient with DKA. I have seen blood sugars of 2,700 mg/dL.
After that lead in, I ask the students to guess what the concentration of glucose in D5W. Someone will say 50 mg/dL, but quickluy they will arrive at a consensus of 500 mg/dL. If someone says 5,000 it is quickly forgotten as unreasonable.
Then I pick on one student and walk through the trivial conversion of g/dL to mg/dL. I like to get a Canadian or foreigner since they are metric natives.
Once the students get that the concentration of glucose in D5W is 5,000 mg/dL the questions turns to why.
Why would anyone want a routine, off the shelf fluid, to have a such wildly non-physiologic glucose concentration?
At least one student knows the answer or I coach a dim group to the answer without much difficulty. The glucose is needed to make D5W iso-osmotic. If we Infused sterile water we would trigger hemolysis.
The last step in the lesson is showing the students that they already know how to calculate the osmolality of D5W
In the previous acid-base lesson the students learn to calculate an osmolar gap. In America one needs to convert the BUN and glucose from mg/dL to mOsm/L. This means dividing by the molecular weight and multiplying by 10. The equation looks like this:
So all we need to do to figure out the osmolality of the glucose is divide by 180 and multiply by 10. I have someone take 5000 and divide by 18 = 278 mOsm/Kg water, isosmotic to plasma. Its a great 5 minute diversion that teaches the students something important. It shows that these rules all fit together. I try to impress on them that fluids and electrolytes are internally consistent like math.
So it was rather embarassing to find out I have been wrong. The actual osmolality of D5W is 252 not 278. Here was my erroneous reply to @medCalc
The author, Michelle Lin chimed in with her reference. Nice work
The first thought was that the discrepancy was due to osmolarity versus osmolality.
Science teacher extradonair Gary Abud weighed in:
Michelle Lin then came up with the correct molecular weight. It's just glucose at 180 plus a water at 18 = 198
Then Bryan Hayes a pharmacist gives his stamp of approval.
The whole thing tumbled out from question to blog post in about 6 hours.
The biggest problem is my cool story problem and interactive lesson is off by about 10%.