Dilution of Ingested Glucose
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In the last section on Low Glycemic Index Foods and Blood Glucose Concentration we saw two examples where it is convenient to determine the concentration of a solution made by diluting a solution of known concentration.
First, we calculated the plasma glucose concentration that would result from ingesting 24.71 cm3 of a sample of 1.30 M Karo syrup if it were diluted to our blood volume of about 4.7 L (Example 2 below). Next, we noted the importance of creating standard solutions of exactly known glucose concentration, in order to calibrate a glucometer. Often several solutions of different concentrations are necessary, so a rapid method of preparing them is desired. Dilution of a single stock solution of known concentration provides a rapid method. Aliquots (carefully measured volumes) of the stock solution can then be diluted to any desired volume. See Example 2 Below.
In other cases it may be inconvenient to weigh accurately a small enough mass of sample to prepare a small volume of a dilute solution. Each of these situations requires that a solution be diluted to obtain the desired concentration.
Example 1: Concentration of Diluted Solution
A buret is used to measure 24.71 ml of 1.30 M glucose, which is ingested and diluted to 4.7 l in the circulatory system. What is the concentration of the diluted solution?
Solution
To calculate concentration, we first obtain the amount of glucose in the 24.71 ml (24.71 cm3) of solution:
nglucose=24.71 mL×10−3L1mL×1.30 mol1 L=0.0321 mol
Dividing by the new volume gives the concentration
cglucose=nglucoseV=0.0321 mol4.7 L=0.00684molL
Thus the new solution is 0.00684 M. This is not high enough to be classified as hyperglycemic (>0.007 M or 7 mM).
Alternatively,
nglucose=24.71 cm3×1.30 mmol1 cm3=32.1 mmol
Dividing by the new volume gives the concentration
cglucose=nglucoseV=32.1 mmol4700 cm3=0.00684mmolcm3
Example 2: Volume Needed
What volume of 0.1000 M glucose solution is necessary to make 500 mL of a 0.006000 M standard solution?
Solution
Using the volume and concentration of the desired solution, we can calculate the amount of glucose required. Then the concentration of the original solution (0.1000 M) can be used to convert that amount of glucose to the necessary volume. Schematically
Vnewcnew→nglucosecold→Vold
Vold=500.00 cm3×0.00600 mmol1 cm3×1 cm30.100 mmol=30.00 cm3
Thus we should dilute a 30-ml aliquot of the stock solution to 500.00 ml. This could be done by measuring 30.00 ml from a buret into a 500.00-ml volumetric flask and adding water up to the mark.
Note that the calculation above can be simplified, since the concentration and volume of a concentrated solution (Cconc and Vconc) were used to calculate the amount of solute, and this amount was entirely transferred to the dilute solution:
Cconc×Vconc=nconc=ndil=Cdil×Vdil
So
Cconc×Vconc=Cdil×Vdil
So for Example 2,
(0.006000 M) ×Vconc=(500.00 mL)× (0.1000 M)
Vconc=30.00 mL which will be diluted to 500.00 mL as before.
Note
The calculated volume will have the same dimensions as the input volume, and dimensional analysis tells us that in this case we do not need to convert to liters, since L cancels when we divide M (mol/L) by M (mol/L).
From ChemPRIME: 3.11: Diluting and Mixing Solutions
Contributors and Attributions
Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.
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