Mass balance on an intravenous injection (IV) bag
A nurse sets up an IV drip for a patient consisting of normal saline; assume that this is an
aqueous solution containing 150mM salt. The saline drip is supplemented with an antibiotic
solution; assume that this is an aqueous solution with 15 mg/mL antibiotic and 100 mM
salt. The treatment regimen for this particular patient calls for 4.0 mg of antibiotic to be
infused per hour. The saline solution drip is set at 0.75 mL/min. Assume that all solutions
have the density of water and that the MW of the salt is 58.5 g/mol.
(a) Draw and label a flowchart for this process.
(b) Perform a DoF analysis.
(c) Determine the drip rate (mL/min) of the antibiotic solution and the mass fraction of
salt and antibiotic in the stream that enters the patient.
(d) The drip rate of the saline solution is increased to 1.5 mL/min. What is the required
drip rate of the antibiotic solution to maintain the required 4.0 mg per hour dosage?
(e) The prescribed antibiotic dosage is doubled to 8.0 mg per hour. Using the 0.75
mL/min saline solution drip, solve for the required antibiotic solution drip rate.
(a) Flowchart for the process:
IV Bag
|
|———[Saline Solution (0.75 mL/min)]
|
|———[Antibiotic Solution (Unknown Drip Rate)]
(b) Degree of Freedom (DoF) analysis:
To perform a DoF analysis, we need to determine the number of unknowns and the number of independent equations.
Number of unknowns:
- Drip rate of the antibiotic solution (mL/min)
- Mass fraction of salt in the stream that enters the patient
- Mass fraction of antibiotic in the stream that enters the patient
Number of independent equations:
- Flow rate balance equation (sum of flow rates in equals sum of flow rates out)
- Mass balance equation for salt
- Mass balance equation for antibiotic
Therefore, the number of unknowns is 3 and the number of independent equations is also 3. Therefore, the DoF is 0.
(c) Determination of drip rate of the antibiotic solution and mass fractions:
To determine the drip rate of the antibiotic solution and the mass fractions, we need to set up and solve balance equations.
Flow rate balance equation:
0.75 mL/min (saline solution) = Drip rate of antibiotic solution
Mass balance equation for salt:
(0.75 mL/min * 150 mM) = (Drip rate of antibiotic solution * 100 mM)
Mass balance equation for antibiotic:
(Drip rate of antibiotic solution * 15 mg/mL) = 4.0 mg/hour
Solving these equations will give us the drip rate of the antibiotic solution and the mass fractions of salt and antibiotic in the stream that enters the patient.
(d) Calculation of required drip rate of antibiotic solution:
To calculate the required drip rate of the antibiotic solution when the drip rate of the saline solution is increased to 1.5 mL/min:
Flow rate balance equation:
1.5 mL/min (saline solution) = Drip rate of antibiotic solution
Solving this equation will give us the required drip rate of the antibiotic solution.
(e) Calculation of required antibiotic solution drip rate:
To calculate the required antibiotic solution drip rate when the prescribed antibiotic dosage is doubled to 8.0 mg per hour and the saline solution drip rate is 0.75 mL/min:
Flow rate balance equation:
0.75 mL/min (saline solution) = Drip rate of antibiotic solution
Mass balance equation for antibiotic:
(Drip rate of antibiotic solution * 15 mg/mL) = 8.0 mg/hour
Solving these equations will give us the required antibiotic solution drip rate.