RECONSTITUTION OF DEXTROSE SOLUTIONS INTO DESIRED STRENGTH.
Example 1:
Prepare 150ml of a 8.5% dextrose solution. You have D5W and D10W. How much of each solution is needed?
In the example above, there are three (3) different strengths/concentrations/percentages of dextrose solution:
5%, 8.5% and 10% dextrose solution.
The constituting strengths are 5% (solution A) and 10% (solution B).
The final strength is 8.5% (solution C).
METHOD 1.
The standard formula for calculating the strength and volume of constituted solution is:
(% of sol. A * Vol of sol. A) + (% of sol. B * vol of sol. B) = (% of sol. C * Vol of sol C)
% of Sol. A = 5%= 5÷100= 0.05
% of Sol B = 10%= 10÷100= 0.1
% of Sol C = 8.5%= 8.5÷100= 0.085
Vol of Sol A is unknown
Vol of Sol B is unknown
Vol of Sol C = 150ml
Vol A + Vol B = Vol C
A+B = 150
A= (150-B)
Insert the values into the formula.
(% of sol. A * Vol of sol. A) + (% of sol. B * vol of sol. B) = (% of sol. C * Vol of sol C)
(5%A) + (10%B) = (7.5%C) (5%)(150-B) + (10%B) = (8.5%150)
0.05(150-B) + (0.1B) = (0.085150) (0.05150 – 0.05*B) + 0.1B = 12.75
7.5 – 0.05B + 0.1B = 12.75
Collect like terms
0.1B – 0.05B = 12.75-7.5
0.05B = 5.25
B = 5.25 ÷ 0.05
B = 105ml
Remember that A = 150-B
A= 150-105
A= 45ml.
Therefore, 45ml of sol A (5% dextrose) will be added to 105ml of sol B (10% dextrose) to produce 150ml of sol C (8.5% dextrose).
ALTERNATIVE METHOD (METHOD 2).
Step 1: Find the difference between each constituting strength and the final strength.
Constituting strength= 5% and 10%
Final strength= 8.5%
Difference between 5% and 8.5%= 8.5%-5%= 3.5% (higher difference)
Difference between10% and 8.5%= 10%-8.5%= 1.5% (lower difference)
Step 2: Add the results of the difference in Step 1 above.
3.5+1.5= 5
Step 3: Divide each difference in step 1 by the sum of the difference in Step 2 and multiply by the volume of final solution.
(3.5÷5)150ml = 105ml (1.5÷5)150ml
= 45ml
Step 4: Assign the higher value to the constituting strength with lower difference (look at step 1); and the lower value to the constituting strength with higher difference (look at step 1)
There are two constituting strength: 5% and 10% dextrose.
So the higher value (105ml) is assigned to the constituting strength with lower difference (10% dextrose)
And the lower value (45ml) is assigned to the constituting strength with higher difference (5% dextrose)
In conclusion, 45ml of sol A (5% dextrose) will be added to 105ml of sol B (10% dextrose) to produce 150ml of sol C (8.5% dextrose).
Try this.
- Prepare 20 mL of dextrose 7.5% weight in volume (w/v) using dextrose 5% and dextrose 50%. How many milliliters of each will be needed?
This work is an excerpt from the book The Nurse, The Math, and The Medication, a handbook on drug dosage calculation written by Ogunlabi, David.
About The Author
A Certified Critical Care Nurse driven with strong passion to impact knowledge. Founder of the Global Impact Health Initiative (GiHi), a nongovernmental organization that seeks to impact knowledge through organizing trainings, seminars, tutorials and lectures for nurses and nursing students. The organization also holds a yearly national drug dosage calculation competition for nurses.
Author of THE NURSE, THE MATH AND THE MEDICATION, a Handbook on Drug Dosage Calculation, to get a copy of the book, send the author a direct message here. You can reach Ogunlabi David on Facebook, or on WhatsApp here and Instagram.
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