Question

Glucose makes up about \(0.10 \%\) by mass of human blood. Calculate the concentration in (a) ppm, (b) molality. What further information would you need to determine the molarity of the solution?

Short answer

The glucose concentration in human blood is 1000 ppm. The molality of the glucose solution in human blood is 0.00555 mol/kg. To determine the molarity of the solution, further information about the volume of blood in which the glucose is dissolved is needed.

Step-by-step solution

Convert the percentage concentration to parts per million (ppm)

First, let's convert the percentage concentration (0.10%) to parts per million (ppm). Recall that 1% is equal to \(10^4\) ppm. Therefore, we can convert the percentage concentration by multiplying by \(10^4\): \(0.10\% \times 10^4 ppm/\% = 1000 ppm\) So, the glucose concentration in human blood is 1000 ppm.

Determine the molality of the glucose solution in blood

Now, let's calculate the molality of the glucose solution in blood. Molality is defined as the moles of solute per kilogram of solvent. Since we know the glucose concentration in human blood is 1000 ppm, we can convert it to grams per kilogram: \(1000 ppm = 1000 \frac{g}{10^6 g} = 1 \frac{g}{10^3 g}\) Now, we will find the molar mass of glucose, which is C6H12O6: \(6 \times 12.01 g/mol_C + 12 \times 1.01 g/mol_H + 6 \times 16.00 g/mol_O = 180.18 g/mol\) We can now determine the molality of the glucose solution: \(Molality = \frac{1 g\text{ glucose}}{180.18 g/mol} \times \frac{1 mol}{10^3 g\text{ solvent}} = 0.00555 \,mol/kg\) So, the molality of the glucose solution in human blood is 0.00555 mol/kg.

Identify the additional information required to calculate the molarity of the solution

To determine the molarity of the glucose solution, we need to know the volume of blood in which the glucose is dissolved, as molarity is defined as the number of moles of solute per liter of solution. However, we are not given any information about the volume in this problem, so we cannot determine the molarity of the solution without additional information.