Problem 148 - Chemistry The Science in Context

Question

Socks containing silver nanoparticles embedded in the fabric are currently marketed as an antidote to smelly socks. Silver is known to have antimicrobial properties, and silver ions are toxic to aquatic life. A study at Arizona State University found that much of the silver particles are lost upon laundering the socks in mild acid.a. Each sock in the study began with \(1360 \mu \mathrm{g}\) of silver. How many moles of silver are contained in each sock?b. As much as \(650 \mu \mathrm{g}\) of silver was lost after four washings. What percent of the silver was lost?

Step-by-Step Solution

Answer

Answer: Each sock contains 1.26 x 10^-5 moles of silver, and 47.79% of the silver is lost after four washings.

Step 1: Convert from micrograms to grams

To make the calculations easier, we will first convert the initial and the lost silver mass from micrograms (\(\mu \mathrm{g}\)) to grams (g). \(1 \mu \mathrm{g} = 1 \times 10^{-6} \mathrm{g}\) Initial silver mass in grams: \(1360 \mu \mathrm{g} \times 10^{-6} = 1.36 \times 10^{-3} \mathrm{g}\) Lost silver mass in grams: \(650 \mu \mathrm{g} \times 10^{-6} = 6.50 \times 10^{-4} \mathrm{g}\)

Step 2: Calculate the number of moles in each sock

We will now use the initial silver mass in grams and the molar mass of silver (\(107.87 \mathrm{g/mol}\)) to calculate the number of moles of silver contained in each sock using the formula \(n = \frac{m}{M}\). \(n = \frac{1.36 \times 10^{-3} \mathrm{g}}{107.87 \mathrm{g/mol}} = 1.26 \times 10^{-5} \mathrm{mol}\) Each sock contains \(1.26 \times 10^{-5}\ \mathrm{mol}\) of silver.

Step 3: Calculate the percentage of silver lost

We will now determine the percentage of silver lost after four washings using the formula: \(\% \text{ lost} = \frac{\text{Amount lost}}{\text{Initial amount}} \times 100\). Initial silver mass in grams = \(1.36 \times 10^{-3} \mathrm{g}\) Lost silver mass in grams = \(6.50 \times 10^{-4} \mathrm{g}\) Percentage lost: \(\% \mathrm{lost} = \frac{6.50 \times 10^{-4} \mathrm{g}}{1.36 \times 10^{-3} \mathrm{g}} \times 100 = 47.79\%\) As much as \(47.79\%\) of the silver was lost after four washings.

Key Concepts

Understanding Silver Nanoparticles

Silver nanoparticles are tiny particles of silver that measure between 1 and 100 nanometers. Due to their small size, they possess unique physical and chemical properties that larger silver particles don't. These nanoparticles are embedded in various products, like socks, to leverage their beneficial properties.
By embedding silver nanoparticles into materials like fabric, manufacturers aim to harness their exceptional abilities, especially their antimicrobial properties. This involves creating materials that can help inhibit the growth of bacteria, leading to products that can reduce odors and promote cleanliness.

• Size range: 1-100 nm
• Used in clothing, medical devices, and cosmetics
• Valued for antimicrobial properties

Manufacturing products with silver nanoparticles has both economic and environmental implications. While they are useful, the potential loss of these particles during processes like washing raises concerns about environmental impact and effectiveness.

Exploring Antimicrobial Properties

Silver has been known for its antimicrobial properties for centuries. Its ability to kill bacteria and other microorganisms makes it valuable in various applications, including healthcare and consumer products. Silver ions are particularly effective against a wide range of pathogens.
These ions disrupt crucial cellular processes in bacteria, affecting their ability to reproduce and thrive. This antimicrobial action is why silver is added to products like socks, to reduce unpleasant odors and prevent bacterial growth.

• Effective against bacteria, fungi, and viruses
• Used in wound dressings and coatings
• Concerns about resistance development

While beneficial, the use of silver in such a manner must be managed carefully to avoid adverse effects on beneficial bacteria and prevent environmental contamination.

Calculating the Molar Mass of Silver

Understanding the molar mass of silver is crucial in stoichiometry, which involves calculating the relationships between reactants and products in a chemical reaction. The molar mass is essentially the weight of one mole of a substance, measured in grams per mole (g/mol).
The molar mass of silver is 107.87 g/mol. This value is used to convert between mass and moles, enabling precise calculations in various chemical processes.

• Helps in converting mass to moles
• Essential for chemical equation balancing
• Used in determining composition and reaction yields

In practical applications, like the exercise given, knowing the molar mass allows for accurate determinations of how much silver is in a product and how much might be lost during use or washing.