Help with a Homework problem, I'm stuck... didn't know where else to turn

[Mr Doc Turr]

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A patient was brought into the hospital showing signs of serious dehydration. A student attempted to give her water, however she vomited it back up, so he gave her 1L of sterile distilled water IV.

Assume her RBC are impermeable to solutes and the conc of solute particles inside the cells is 300 mOsm/L.

Questions:

2. The vol of the patient’s plasma was 3 L before the administration of the IV. Assume there was complete mixing of the administered water with her plasma, but no mixing with her interstitial fluid. Calculate her plasma osmolarity after the infusion mixed with her plasma but before any water entered her RBC’s.

3. Assume that the RBC volume was 2 L before the IV was given. Calculate her plasma volume & osmolarity after the infused water came to equilibrium. How much would her RBC volume change?


The resident administers a sucrose solution via IV.

4. What conc sucrose solution should have been given to the patient when she was first admitted?

5. 1 L of what conc sucrose solution should be administered NOW in order to treat the patient?

 

[Piano Doc]

2. 1L of sterile distilled water IV is added to the plasma but no mixing with her interstitial fluid and before any water entered her RBC’s. Therefore simple calculation, (3+1)L*X mOsm/L =3*300mOsm/L
X=225, so her plasma osmolarity after the infusion mixed with her plasma would be 225mOsm/L

3. This too, is simple math. Blood volume is RBC volume+Plasma volume. It says "came to equilibrium" so the RBC volume&Plasma volume would have the same osmolarity. Equilibrium osmolarity=300*2/(2+X)=225*4/(4-X). Therefore X=0.4 and the RBC volume change would be 0.4L.

4. Her blood osmolarity was 300mOm/L so she should have been given a 300mOm/L sucrose solution

5. Her total Blood volume is 6L now and the osmolarity is 250mOsm/L. Therefore we should alter this osmolarity back to 300mOsm/L which is the normal number. The equation would be (6*250+1*X)/(6+1)=300. X=600, so 1L of 600mOsm/L of sucrose solution should be administered.

 

[Mr Doc Turr]

2. 1L of sterile distilled water IV is added to the plasma but no mixing with her interstitial fluid and before any water entered her RBC’s. Therefore simple calculation, (3+1)L*X mOsm/L =3*300mOsm/L
X=225, so her plasma osmolarity after the infusion mixed with her plasma would be 225mOsm/L

3. This too, is simple math. Blood volume is RBC volume+Plasma volume. It says "came to equilibrium" so the RBC volume&Plasma volume would have the same osmolarity. Equilibrium osmolarity=300*2/(2+X)=225*4/(4-X). Therefore X=0.4 and the RBC volume change would be 0.4L.

4. Her blood osmolarity was 300mOm/L so she should have been given a 300mOm/L sucrose solution

5. Her total Blood volume is 6L now and the osmolarity is 250mOsm/L. Therefore we should alter this osmolarity back to 300mOsm/L which is the normal number. The equation would be (6*250+1*X)/(6+1)=300. X=600, so 1L of 600mOsm/L of sucrose solution should be administered.

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