Problem 95 - Chemistry: The Central Science

Question

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

Step-by-Step Solution

Answer

The concentration of glucose in human blood is 1,000 ppm. The molality of glucose in blood is 0.00555 mol/kg. To determine the molarity of the solution, we would need additional information about the volume of the blood (in liters).

Step 1: Recall the relationship between mass percent and ppm

We can easily convert mass percent to parts per million (ppm) using the following relationship: 1% = 10,000 ppm

Step 2: Convert 0.10% to ppm

Now that we know the relationship between percent and ppm, we can convert the given mass percentage (0.10%) to ppm: 0.10% * 10,000 ppm = 1,000 ppm So, the concentration of glucose in blood is 1,000 ppm. #b) Calculating molality#

Step 3: Find the molar mass of glucose

The molecular formula of glucose is C6H12O6. To find the molar mass, we add up the atomic masses of all the atoms in the formula: Molar mass of glucose = (6 × 12.01 g/mol) + (12 × 1.01 g/mol) + (6 × 16.00 g/mol) = 180.18 g/mol.

Step 4: Calculate molality

For simplicity, let's consider that we have 1 kg (1000 g) of blood. Thus, the mass of glucose in the blood would be: Mass of glucose = 0.001 × 1000 g = 1.00 g Now we can divide this mass by the molar mass to find the moles of glucose: Moles of glucose = 1.00 g / 180.18 g/mol ≈ 0.00555 mol Molality is defined as the moles of solute (glucose) per kilogram of solvent (blood). Therefore, considering that we have 1000 g (≈ 1 kg) of blood, we can find the molality: Molality = 0.00555 mol / 1 kg = 0.00555 mol/kg So, the molality of glucose in blood is 0.00555 mol/kg. #c) Additional information for molarity#

Step 5: Identify the additional information needed

To determine the molarity of glucose in blood, we need to know the volume of the solution, i.e., the volume of the blood in which the glucose is dissolved: Molarity = moles of solute / volume of solution (in L) In this case, we have calculated the moles of glucose, but we still need the volume of blood (in liters) to determine the molarity.