The maximum amounts of lead and copper allowed in drinking water are 0.015 mg/kg for lead and 1.3 mg/kg for copper. Express these values in parts per million, and tell the maximum amount of each (in grams) allowed in 100 g of water.

검증된 단계별 안내

Step 1: Understand the relationship between parts per million (ppm) and mg/kg. Since 1 ppm is equivalent to 1 mg of solute per 1 kg of solution, the given values for lead (0.015 mg/kg) and copper (1.3 mg/kg) are already expressed in ppm. Therefore, lead is 0.015 ppm, and copper is 1.3 ppm.

Step 2: To find the maximum amount of lead allowed in 100 g of water, first convert the mass of water from grams to kilograms. Since 1 kg = 1000 g, 100 g of water is equivalent to 0.1 kg.

Step 3: Use the concentration of lead in ppm (0.015 ppm) to calculate the mass of lead in 0.1 kg of water. Multiply the concentration (in mg/kg) by the mass of water (in kg): \( \text{Mass of lead} = 0.015 \text{ mg/kg} \times 0.1 \text{ kg} \).

Step 4: Similarly, calculate the maximum amount of copper allowed in 100 g of water. Use the concentration of copper in ppm (1.3 ppm) and multiply it by the mass of water (in kg): \( \text{Mass of copper} = 1.3 \text{ mg/kg} \times 0.1 \text{ kg} \).

Step 5: Convert the calculated masses of lead and copper from milligrams to grams. Since 1 mg = 0.001 g, divide the results from Steps 3 and 4 by 1000 to express the masses in grams.

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주요 개념

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Parts Per Million (PPM)

Parts per million (PPM) is a unit of measurement used to describe the concentration of a substance in a solution. It indicates how many parts of a substance are present in one million parts of the total solution. For example, 1 PPM means 1 milligram of a substance in 1 liter of water, which is equivalent to 1 mg/kg in terms of concentration.

Conversion from mg/kg to PPM

The conversion from milligrams per kilogram (mg/kg) to parts per million (PPM) is straightforward, as 1 mg/kg is equal to 1 PPM. This equivalence arises because 1 kilogram of water is approximately equal to 1 liter, making the two units interchangeable in the context of water solutions.

Calculating Maximum Allowable Amounts

To find the maximum allowable amounts of lead and copper in grams for a specific volume of water, you can use the concentration values in PPM. For 100 g of water, you multiply the concentration (in PPM) by the mass of the water (in grams) and then convert from milligrams to grams, as there are 1000 mg in a gram.