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By admin, September 28, 2009 11:32 am

What is the density of a 50% (w/w) Glucose Solution?

I need to find out (or predict) the density of a 50% (w/w) glucose solution i.e. 500 g of dextrose anhydrous dissolved in 500 g of water.

Density is mass of solution divided by volume of solution.

To solve this problem I will make use of the densities of both pure water and pure glucose (1 g/ml and 1.54 g/ml respectively) and will add the individual volumes together. To test whether the volume approximation is a good estimate or not, I will calculate the density of the 40% solution first to compare it to your reported value.

We know that in a 40% (w/w) solution we have 40 grams of glucose in 100 grams of solution. This means that 60 grams of mass correspond to water. Therefore, the individual volumes will be:

V(H2O) = (60 g) x (1 mL/1 g) = 60 mL
V(glucose) = (40 g) x (1 mL/1.54 g) = 26 mL
Total Volume = V(H2O) + V(glucose) = 86 mL

Now we have everything we need to calculate the density (d):

d = mass solution/volume solution = 100g/86mL = 1.16 g/mL = 1.16 kg/L

This means that approximation works! Let’s try it now with the 50% (w/w) solution:
Mass(H2O) = 50 g
Mass(glucose) = 50 g
Mass(solution) = 100 g
V(H2O) = (50 g) x (1 mL/1 g) = 50 mL
V(glucose) = (50 g) x (1 mL/1.54 g) = 32.5 mL
Total Volume = V(H2O) + V(glucose) = 82.5 mL

d(solution) = mass(solution)/Total volume = 100 g/82.5 mL = 1.21 g/mL = 1.21 kg/L

Hope this made it clear.