Question

Silver ions can be found in some of the city water piped into homes. The average concentration of silver ions in city water is \(0.028\) ppm. (a) How many milligrams of silver ions would you ingest daily if you drank eight glasses (eight oz/glass) of city water daily? (b) How many liters of city water are required to recover \(1.00 \mathrm{~g}\) of silver chemically?

Short answer

Answer: By drinking eight glasses of city water daily, you would ingest approximately 0.0530 milligrams of silver ions. Approximately 35,714.29 liters of city water are required to recover 1.00 gram of silver chemically.

Step-by-step solution

Convert concentration from ppm to mg/L

To convert the concentration of silver ions in city water from ppm to mg/L, simply keep the value the same. So, the concentration of silver ions in city water is 0.028 mg/L.

Calculate the volume of water consumed in liters

Each glass of water contains 8 oz. So, eight glasses contain 8 x 8 = 64 oz of water. To convert ounces to liters, we will use the conversion factor 1 L = 33.814 oz. Volume (in liters) = (64 oz) x (1 L / 33.814 oz) ≈ 1.8927 L

Calculate the amount of silver ions ingested daily

To calculate the amount of silver ions ingested daily, we will use the following formula: Amount of silver ions (in mg) = Concentration (in mg/L) x Volume of water (in L) Amount of silver ions (in mg) = (0.028 mg/L) x (1.8927 L) ≈ 0.0530 mg So, by drinking eight glasses of city water daily, you would ingest approximately 0.0530 milligrams of silver ions.

Calculate the amount of city water required to recover 1 gram of silver

Given that 0.028 mg of silver ions are present in 1 L of city water, we need to find how many liters of city water are required to have 1 gram (1000 mg) of silver ions. We will use the following formula: Volume of water (in L) = Amount of silver ions (in mg) / Concentration (in mg/L) Volume of water (in L) = (1000 mg) / (0.028 mg/L) ≈ 35714.29 L So, approximately 35,714.29 liters of city water are required to recover 1.00 gram of silver chemically.

Key concepts

ppm concentration

PPM, or parts per million, is a way of expressing very dilute concentrations of substances. It's often used to describe the concentration of contaminants or substances in water. If the concentration is 1 ppm, this means that there is one part of a substance in one million parts of the solution. It's a very common measure when dealing with water quality and describes how much of a particular ion, like silver ions, is present in a large volume of water.

For example, in the context of silver ions in city water, a concentration of 0.028 ppm indicates that there are 0.028 milligrams of silver ions in one liter of water. Understanding ppm helps when dealing with chemical calculations, especially when converting these units into more convenient forms for daily life or industrial measurements. By keeping the value the same when converting to mg/L, we simplify calculations related to ingestion or chemical recovery processes.

milligrams of silver ions

When we talk about milligrams of silver ions, we refer to the amount of silver in weight within a given volume of water. This metric is crucial in understanding the potential health implications and industrial uses of silver-laced water.

In our example, calculating the milligrams of silver ions ingested daily involves converting the volume of water consumed into liters and applying the concentration in mg/L. Let's break it down: if each glass of water is 8 oz, and you drink eight of them daily, that's 64 oz of water. Using the conversion factor (1 L = 33.814 oz), you convert this to approximately 1.89 liters. Then, by multiplying this volume by the ppm concentration (0.028 mg/L), you find how many milligrams of silver ions are ingested.

• Volume of water: 1.89 L
• Concentration: 0.028 mg/L
• Milligrams of silver ions: 0.0530 mg

This calculation shows that understanding how to manipulate the units and conversion factors is critical in determining the amount of substances like silver ions in water.

chemical recovery of silver

Recovering silver from solutions, like city water, involves a chemical process where silver ions are extracted and converted into solid silver. This process is an example of how chemical engineering principles can be applied to recover valuable materials from waste or diluted solutions.

In the case of the city's water with a silver concentration of 0.028 ppm, you need to know how much water is needed to recover 1 gram of silver. Since 1 gram is 1000 milligrams, you calculate the total volume of water required by dividing 1000 mg by the concentration of silver ions (0.028 mg/L). This gives us around 35,714.29 liters needed to collect 1 gram of silver.

Understanding this concept is critical when considering the economic feasibility and the environmental impacts of chemical recovery processes in large-scale operations.

conversion factors

Conversion factors are essential tools in chemistry and engineering, used to transform units and quantify measurements properly. By using conversion factors, we ensure that our calculations are accurate, whether for scientific experiments or practical applications like measuring contamination or recovering metals.

In our example, converting ounces to liters (1 L = 33.814 oz) was crucial for determining the volume of water consumed. Without applying conversion factors correctly, it would be impossible to calculate the daily intake of silver ions or estimate the total water needed for silver recovery.

Understanding and using conversion factors accurately allows you to transition smoothly between different scale units. This is fundamental in both academia and industry, where precision is vital.