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 (a) 1000 ppm and (b) \(5.56 \times 10^{-3}\) mol/kg. (c) To determine the molarity, we need further information, such as the density of the solution and the volume occupied by solute particles, to calculate the volume of the solution.

Step 1: (a) Calculating concentration in ppm

To express the concentration in ppm, we need to know the composition's percentage. Since glucose makes up about 0.10% of human blood, we can calculate the concentration in ppm as follows: ppm = mass percentage × 10^6 ppm = 0.10% × 10^6 ppm = 0.0010 × 10^6 ppm = 1000 ppm So, the concentration of glucose in blood is 1000 ppm.

Step 2: (b) Calculating concentration in molality

Molality (m) is the moles of solute per kilogram of solvent. Given that glucose makes up 0.10% of human blood by mass, we can calculate the molality as follows: 1. Assume a 100 g sample of human blood (any amount could be chosen, but 100 g simplifies the calculation). 2. 0.10% of 100 g is the mass of glucose in the sample: 0.10 g. 3. Convert grams of glucose to moles by using the molar mass of glucose (C6H12O6) which is 180.18 g/mol. Moles of glucose = (0.10 g) / (180.18 g/mol) = \(5.55 \times 10^{-4}\) moles. The mass of solvent (Blood - glucose) = (100 g - 0.10 g) = 99.9 g = 0.0999 kg. Molality (m) = moles of solute / mass of solvent in kg = \(5.55 \times 10^{-4}\) moles / 0.0999 kg = \(5.56 \times 10^{-3}\) mol/kg So, the molality of glucose in human blood is \(5.56 \times 10^{-3}\) mol/kg.

Step 3: (c) Determining molarity

To determine the molarity (M) of a solution, we need to know the moles of solute present in one liter of the solution. Since molarity is dependent on the volume of the solution, the calculation of molarity requires the knowledge of two additional pieces of information: 1. The density of the solution: Knowing the density will allow us to convert the mass of the solvent to volume and, in turn, find the volume of the solution. 2. The volume occupied by solute particles in the solution: With the knowledge of the volume occupied by the solute, we can subtract it from the total volume to obtain the volume of the solution that we can use to calculate molarity.

Key Concepts

Parts per Million (ppm)

When dealing with very diluted solutions, we often use the concentration unit called 'parts per million' (ppm). This helps to express small amounts of a substance in a more convenient and understandable way. To put it simply, if you have 1 ppm of a substance, it means in a 'million parts' of the total solution, one part is the substance you're considering.

To convert a percentage to ppm, you multiply by 10,000, which is the same as multiplying by \(10^6\). This is because one percent is equal to one part per hundred, and one million is ten thousand hundreds. For example, if a solute makes up 0.10% of a solution, you would calculate its concentration in ppm by multiplying 0.10% (or 0.001 when converted to a decimal) by 10,000, which gives you 1,000 ppm.

Molality

Molality is a measurement of the concentration of a solution that expresses the moles of a solute per kilogram of solvent. Unlike molarity, molality is not affected by changes in temperature since it is based on mass rather than volume.

Calculating molality involves dividing the number of moles of your solute by the mass (in kilograms) of the solvent. For the given glucose example, if you have a 100 g sample of human blood, you need to first determine the mass of glucose in this sample which would be 0.10 g. Then, upon converting this to moles using the molar mass of glucose, and further dividing by the mass of the solvent in kilograms, we find the molality of the solution.

Molarity

Molarity, sometimes noted as \(M\), is a measure of concentration that describes the number of moles of a solute in one liter of solution. To calculate molarity, you need to know the total moles of solute and the volume of the solution in liters.

It is important to remember that unlike molality, molarity does change with temperature as it involves volume, which can expand or contract with temperature fluctuations. Information you need to calculate molarity includes the density of the solution which allows you to find the volume of the solution from a given mass, and sometimes the volume occupied by the solute particles if the solution is concentrated.

Solute-Solvent Interactions

The interactions between the solute and the solvent in a solution are essential to understand because they affect solubility, reaction rates, and other solution properties. In a solution, solute particles are surrounded by solvent molecules, which can lead to various forms of interactions based on the nature of the solute and solvent molecules.

Electrostatic interactions, hydrogen bonding, and van der Waals forces are examples of such interactions. These affect how the solute dissolves and how stable the resulting solution is. When we calculate concentrations using molality or molarity, we often assume that these interactions don't significantly alter the volume or mass of the components, but in reality, the nature of solute-solvent interactions can make a significant difference, especially in concentrated or biochemically relevant solutions like human blood glucose levels.