Problem 95 - Chemistry: The Central Science in SI Units, Global Edition

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 approximately 1000 ppm. The molality of glucose in human blood is approximately 0.00556 \(mol/kg\). To determine the molarity of the glucose solution, we would need to know the volume of blood in which the given moles of solute (glucose) are dissolved.

Step 1: (a) Converting mass percent to ppm

To convert the mass percent concentration to parts per million (ppm), we need to multiply the mass percent by 10,000 (since there are 1,000,000 parts in a million and 100 parts in a percent): ppm = mass percent × 10,000 ppm = 0.10% × 10,000 ppm = 1000 Therefore, the concentration of glucose in human blood is approximately 1000 ppm.

Step 2: (b) Calculating the molality

To calculate molality, we need to find the moles of glucose and mass of solvent (water) in 1L solution. Since the given problem states that glucose makes up 0.10% by mass of human blood, we will consider 1L of blood with a density of \(1 g/mL\), meaning total mass of blood is \(1000g\). First, let's find the mass of glucose in 1000g blood, mass of glucose = mass percent × total mass mass of glucose = (0.10 / 100) × 1000 = 1g Next, we will find the mass of the solvent (water): mass of water = total mass - mass of glucose mass of water = 1000 - 1 = 999g Now let's find the moles of glucose. Given the molecular formula of glucose, C6H12O6, its molar mass is \(6 × 12.01(g/mol) + 12 × 1.01(g/mol) + 6 × 16.00(g/mol) = 180.16(g/mol)\). moles of glucose = mass / molar mass moles of glucose = 1 / 180.16 = 0.00555 mol Finally, let's find the molality, molality = moles of solute / mass of solvent (in kg) molality = 0.00555mol / 0.999kg = 0.00556 \(mol/kg\) Therefore, the molality of glucose in human blood is approximately 0.00556 \(mol/kg\).

Step 3: (c) Further information needed to determine molarity

To determine the molarity of the glucose solution, we would need to know the volume of blood (solvent) in which the given moles of solute (glucose) are dissolved. Since molarity is the moles of solute per liter of solution, knowing the volume of the solution would allow us to calculate the molarity.

Key Concepts

Mass Percent

Mass percent is a way to express the concentration of an element or compound in a mixture. It is calculated by taking the mass of a particular component, dividing it by the total mass of the mixture, and then multiplying by 100 to get a percentage.
For example, if glucose makes up 0.10% by mass of human blood, this means that in 100 grams of blood, 0.10 grams are glucose.
This simple method allows you to easily understand the proportion of a component in a solution. To convert between mass percent and other units of concentration like ppm or molality, you'll apply specific conversion factors, as explained further in this article.

ppm (Parts Per Million)

Parts per million (ppm) is a unit of concentration that denotes the number of parts of a solute per one million parts of the solution. It's often used to describe very dilute solutions.
To convert from mass percent to ppm, multiply the mass percent by 10,000. This step accounts for the factor in converting from percent (which is out of 100) to parts per million (which is out of 1,000,000).
In our example, glucose is present in blood at 0.10%. Thus, to find the ppm:

• ppm = 0.10 × 10,000
• ppm = 1,000

So, the concentration of glucose in human blood is 1,000 ppm. This visualization helps in understanding the level of solute present in large quantities, typical in health and environmental sciences.

Molality

Molality is another way to express the concentration of a solution. It is defined as the number of moles of solute per kilogram of solvent. It is particularly useful because it doesn’t change with temperature, unlike molarity.
The formula for molality is:

• Molality = moles of solute / mass of solvent (in kg)

In our glucose example, to find moles of glucose, compute it using its molar mass, which is 180.16 g/mol. In 1,000 grams of blood, the glucose mass is 1 gram, leading to 0.00555 moles of glucose.
After this, calculate the mass of the solvent (water in this case), which is 999 grams or 0.999 kg.
This results in:

• Molality = 0.00555 mol / 0.999 kg = 0.00556 mol/kg

This constant measure helps analyze reactions and properties of solutions at varying conditions.

Molarity

Molarity measures the concentration of a solution in terms of moles of solute per liter of solution. It’s dependent on the volume, which can change with temperature, affecting precision in some applications.
To calculate molarity, you need the precise volume of the solution. Using our glucose example, if we wish to determine its molarity, we will need the exact volume of blood that the glucose is dissolved in. Without this volume information, estimating molarity isn't feasible.
Molarity is helpful in laboratory settings, where solutions need to react predictably and consistently at a specific concentration. Despite its temperature sensitivity, molarity is widely used due to the straightforward relation with volume metrics in experiments.