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