Problem 15 - Chemistry The Science in Context

Question

The concentrations of very dilute solutions are sometimes expressed as parts per million. Express the concentration of each of the following trace and ultratrace essential elements in parts per million: a. Fluorine, \(110 \mathrm{mg}\) in \(70 \mathrm{kg}\) b. Silicon, \(525 \mathrm{mg} / \mathrm{kg}\) c. Iodine, \(0.043 \mathrm{g}\) in \(100 \mathrm{kg}\)

Step-by-Step Solution

Answer

Question: Calculate the concentration of Fluorine, Silicon, and Iodine in parts per million (ppm). Answer: a. Fluorine: 1571.428 ppm b. Silicon: 525000 ppm c. Iodine: 430 ppm

Step 1: Converting units and calculating Fluorine concentration

To find the concentration of Fluorine in parts per million, we need to express the given mass quantities in the same units. Since we are given the mass of Fluorine as \(110 \mathrm{mg}\) and the mass of the solution as \(70 \mathrm{kg}\), it is convenient to convert the mass of the solution into grams. Conversion factor: \(1 \mathrm{kg} = 1000 \mathrm{g}\) Mass of solution: \(70 \mathrm{kg} \times \frac{1000 \mathrm{g}}{1 \mathrm{kg}} = 70000 \mathrm{g}\) Now, we can find the concentration in parts per million: \(\text{Fluorine (ppm)} = \frac{110 \mathrm{mg}}{70000 \mathrm{g}} \times 10^6\) \(\text{Fluorine (ppm)} = 1571.428\mathrm{ppm}\)

Step 2: Calculating Silicon concentration

Since the mass of Silicon is already given in milligrams per kilogram (\(\mathrm{mg / kg}\)), we can directly find the concentration in parts per million: \(\text{Silicon (ppm)} = 525 \frac{\mathrm{mg}}{\mathrm{kg}} \times \frac{10^6}{1000}\) \(\text{Silicon (ppm)} = 525000 \mathrm{ppm}\)

Step 3: Converting units and calculating Iodine concentration

To find the concentration of Iodine in parts per million, we need to express the mass quantities in the same units. Since we are given the mass of Iodine as \(0.043 \mathrm{g}\) and the mass of the solution as \(100 \mathrm{kg}\), it is convenient to convert the mass of Iodine into milligrams. Conversion factor: \(1\mathrm{g} = 1000\mathrm{mg}\) Mass of Iodine: \(0.043 \mathrm{g} \times \frac{1000 \mathrm{mg}}{1 \mathrm{g}} = 43 \mathrm{mg}\) Now, we can convert the mass of the solution into grams: Mass of solution: \(100 \mathrm{kg} \times \frac{1000 \mathrm{g}}{1 \mathrm{kg}} = 100000 \mathrm{g}\) Now, we can find the concentration in parts per million: \(\text{Iodine (ppm)} = \frac{43 \mathrm{mg}}{100000 \mathrm{g}} \times 10^6\) \(\text{Iodine (ppm)} = 430 \mathrm{ppm}\) Now we have found the concentrations of Fluorine, Silicon, and Iodine in parts per million: a. Fluorine: \(1571.428 \mathrm{ppm}\) b. Silicon: \(525000 \mathrm{ppm}\) c. Iodine: \(430 \mathrm{ppm}\)

Key Concepts

Concentration Calculations

When we talk about concentration calculations in chemistry, we're often looking to find out how much of a certain substance is present in a mixture or solution. Here, trace amounts of elements are measured, which means they are present in small quantities. To measure these concentrations accurately, a scale known as "parts per million" (ppm) is used. One part per million is equivalent to 1 milligram (mg) of a substance in 1 kilogram (kg) of solution. It uses a simple relationship where 1 ppm equals 1 mg per liter (l) of water when the solution density is similar to water. To calculate concentration in ppm:

• Convert all quantities to the same unit format, usually mg for solids.
• Use the formula: \[\text{Concentration (ppm)} = \left(\frac{\text{mass of solute in mg}}{\text{mass of solution in g}} \right) \times 10^6 \]

Breaking down the conversion helps ease these calculations. Understanding concentration in ppm bridges understanding from large, visible amounts to tiny, trace quantities in science.

Trace Elements

Trace elements are essential components found in very small amounts in both biological systems and the environment. Despite their low concentrations, these elements, like Fluorine, Silicon, and Iodine, play vital roles in maintaining biological processes.

• **Fluorine** helps in the maintenance of teeth structure and enamel, primarily found in tiny amounts in the human body.
• **Silicon** is significant for skeletal and connective tissue health. Even in small concentrations, it contributes to bone formation.
• **Iodine** is crucial for thyroid gland function and hormone production, influencing metabolism.

Knowing how to calculate their concentrations is vital for understanding their effects and roles. Trace elements are often overlooked due to their minute presence but remain critically important for optimal function in ecosystems and health.

Unit Conversion

Understanding unit conversion is a foundational skill essential in science, especially for working with concentrations in parts per million (ppm). Often conversions are necessary to standardize the units when calculating ppm.For example:

• To convert from kilograms to grams, use the relationship: \[1 \text{kg} = 1000 \text{g}\]
• Similarly, to convert from grams to milligrams: \[1 \text{g} = 1000 \text{mg}\]

These conversions are crucial because they align the units across the calculation, ensuring accurate ppm results. They simplify the process by using basic steps, making it easier to manage complex concentration problems efficiently.Having a strong grasp on how to convert units correctly enhances understanding of real-world problems in chemistry and various scientific studies.