Problem 95 - Chemistry The Central Science In Si Units

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

(a) 1000 ppm; (b) 0.00555 mol/kg; (c) density of blood is needed to find molarity.

Step 1: Understand % by mass

The concentration given is in terms of percentage by mass. Specifically, it means there is 0.10 grams of glucose per 100 grams of blood.

Step 2: Convert % by mass to ppm for part (a)

Parts per million (ppm) is calculated based on mass: 1. Since there are 0.10 grams of glucose per 100 grams of blood. 2. The calculation for ppm is: \[ \text{ppm} = \left( \frac{\text{mass of glucose}}{\text{mass of blood}} \right) \times 10^6 \] Substituting the values we get: \[ \text{ppm} = \left( \frac{0.10}{100} \right) \times 10^6 = 1000 \, \text{ppm} \]

Step 3: Understanding molality for part (b)

Molality is moles of solute per kilogram of solvent. Given the percent by mass, we start with 0.10 grams of glucose. We need to find its molality.

Step 4: Calculate moles of glucose

Find the molar mass of glucose (C₆H₁₂O₆): \(6 \times 12.01 + 12 \times 1.01 + 6 \times 16.00 = 180.18 \, \text{g/mol}\)Then, calculate moles of glucose: \( \text{moles of glucose} = \frac{0.10 \, \text{g}}{180.18 \, \text{g/mol}} \approx 0.000555 \, \text{mol} \)

Step 5: Calculate molality

Since blood is close to 100 g and glucose is very dilute, the mass of the solvent (water in blood) is approximately 100 grams or 0.1 kilograms.The molality (m) is:\[ m = \frac{\text{moles of glucose}}{\text{kg of solvent}} = \frac{0.000555 \, \text{mol}}{0.1 \, \text{kg}} = 0.00555 \, \text{mol/kg} \]

Step 6: Determine information needed for molarity for part (c)

To calculate the molarity, you need the density of the blood. Molarity is defined as moles of solute per liter of solution, so knowing the fluid's density would allow you to convert the mass to volume.

Key Concepts

ppm calculation

Parts per million, or ppm, is a measure of concentration. It is used when dealing with low concentrations of a substance in a solution. Imagine you want to determine how many parts of glucose are present in a million parts of blood. To do this, you use the formula:

• \( \text{ppm} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 10^6 \)

Looking at an example where glucose makes up 0.10% of blood by mass means you have 0.10 grams of glucose in every 100 grams of blood. Converting this percentage to parts per million:

• \( \text{ppm} = \left( \frac{0.10}{100} \right) \times 10^6 = 1000 \)

This calculation shows there are 1000 ppm of glucose in the blood. This method is handy because it simplifies understanding small concentrations without needing complex units.
**Key Points:** The conversion from percentage to ppm is straightforward. Remember to multiply by \(10^6\) since ppm means "parts per million," and stick to the simple ratio of solute to solution mass.

molality

Molality is a way of expressing concentration, defined as the moles of solute per kilogram of solvent. Here's why it's useful: molality does not change with temperature, because it is based on the mass of the solvent, not the volume of the total solution. Now, let's see how it is calculated.

• Start with the molar mass of your solute. For glucose, C₆H₁₂O₆, it's \(6 \times 12.01 + 12 \times 1.01 + 6 \times 16.00 = 180.18 \) g/mol.
• For 0.10 grams of glucose, the moles will be: \( \text{moles of glucose} = \frac{0.10}{180.18} \approx 0.000555 \) mol.

Next, determine the mass of the solvent. Since blood is roughly 100 grams and glucose is very dilute, assume water is the primary solvent at about 0.1 kg. The formula for molality is:

• \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \)

For our example:

• \( m = \frac{0.000555}{0.1} = 0.00555 \) mol/kg

This result expresses the molality of glucose in blood.

Remember, molality remains unaffected by temperature changes, making it ideal for various scientific applications.
**Application Tip:** Always use kilograms, and note the precision of molality when you require strict comparisons in chemical processes.

molarity determination

Molarity is the concentration of a solute in a solution expressed as moles of solute per liter of solution. It's one of the more commonly used concentration measures in chemistry and necessary when reactions take place in solution. Calculating molarity (M) requires additional information beyond what is given by percentage mass or ppm. Here's why:

• To determine molarity, you need both the number of moles of the solute and the total volume of the solution in liters.
• This involves converting the mass of the solution to its volume using density.

**Further Information Needed:**
For the glucose and blood scenario, you'd need to know the density of the blood to find its volume from its mass. Once you know the density, solving for the volume lets you use:

• \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \)

Understanding molarity is crucial for solutions where concentrations change with volume, such as when temperatures vary. While both molality and molarity measure concentration, molarity is volume-dependent, thus needing adjustments as fluid volumes change due to external conditions.
**Practical Insight:** Always ensure accurate density data for precise molarity calculations, especially in biologically relevant environments like blood or cellular fluids.