Question

Drinking water may contain a low concentration of lead ion, \(\mathrm{Pb}^{2+}\), due to corrosion of old lead pipes. The EPA has determined that the maximum safe level of lead ion in water is \(15 \mathrm{ppb}\). Suppose a sample of tap water was determined to have a lead ion concentration of \(0.0090 \mathrm{ppm}\). Assume the density of the solution is \(1.00 \mathrm{~g} / \mathrm{mL}\). (a) What is the concentration of lead ion in the tap water in units of \(\mathrm{ppb}\) ? Is it safe to drink? (b) What is the concentration of lead ion in units of \(\mathrm{mg} / \mathrm{mL}\) ? (c) What mass of lead ion is in \(100.0 \mathrm{~mL}\) of this drinking water? (d) How many moles of lead ion are in \(100.0 \mathrm{~mL}\) of the water?

Short answer

(a) The lead ion concentration in the tap water is 9.0 ppb. Yes, it is safe to drink. (b) The lead ion concentration is 0.000009 mg/mL. (c) There is a mass of 0.0009 mg of lead ions in 100.0 mL of the drinking water. (d) There are 4.35 x 10^-9 moles of lead ions in 100.0 mL of the water.

Step-by-step solution

Conversion from ppm to ppb

To find the concentration of lead in water from parts per million (ppm) to parts per billion (ppb), we should know that 1 ppm equals 1000 ppb. Therefore, to convert \(0.0090 \mathrm{ppm}\) to ppb, we simply multiply by 1000: \(0.0090 \mathrm{ppm} \times 1000 = 9.0 \mathrm{ppb}\)

Safety Check

The given value for maximum safe level of lead ion in water is \(15 \mathrm{ppb}\). Since the concentration we calculated is \(9.0 \mathrm{ppb}\) which is less than the EPA-determined safe level, the tap water is considered safe to drink. So, the answer is 'Yes, it is safe to drink.'

Conversion to mg/mL

To convert the lead concentration from ppm to milligrams per milliliter (mg/mL), we use the known relation 1 ppm = 1 mg/L. Since 1 L = 1000 mL, it follows that 1 ppm = \(0.001 \mathrm{mg/mL}\). Therefore, to convert \(0.0090 \mathrm{ppm}\) to \(\mathrm{mg/mL}\) we multiply by \(0.001 \mathrm{mg/mL}\): \(0.0090 \mathrm{ppm} \times 0.001 \mathrm{mg/mL} = 0.000009 \mathrm{mg/mL}\)

Calculation of Mass

With the concentration of lead in the water in \(\mathrm{mg/mL}\) and the volume of the water sample (100.0 mL), we can calculate the mass of lead in the sample by multiplying the volume by the concentration: \(0.000009 \mathrm{mg/mL} \times 100.0 \mathrm{mL} = 0.0009 \mathrm{mg}\)

Calculation of Moles

We know that the molar mass of lead is approximately 207.2 g/mol. To obtain the number of moles we need to convert the mass of lead from mg to g and then divide by the molar mass of lead. But first, let's convert mg to g: \(0.0009 \mathrm{mg} = 0.0000009 \mathrm{g}\). Then, calculate the number of moles: \(\frac{0.0000009 \mathrm{g}}{207.2 \mathrm{g/mol}} = 4.35 \times 10^{-9} \mathrm{mol}\)

Key concepts

ppm to ppb conversion

Understanding ppm (parts per million) and ppb (parts per billion) is crucial when dealing with the measurement of pollutant concentrations, such as lead in water. These units are a ratio of the amount of the substance to the total volume or mass of the mixture and are especially useful for very dilute concentrations.

The conversion between these units is straightforward since they are both based on a factor of a thousand. To convert from ppm to ppb, you multiply by 1,000. This works because 1 part per million means 1 unit of the substance is present for every 1 million units of the total mixture, and similarly, 1 part per billion corresponds to 1 unit of the substance per 1 billion units of the total mixture. So, for the example at hand, the tap water with a lead ion concentration of 0.0090 ppm translates to 9.0 ppb.

safe drinking water standards

Safe drinking water standards are established to protect public health by setting limits on the levels of contaminants in drinking water. The U.S. Environmental Protection Agency (EPA) regulates these standards under the Safe Drinking Water Act. For lead, a toxin that can cause serious health problems, the EPA's maximum contaminant level goal is 0 parts per billion (ppb), with an action level of 15 ppb.

This means that if lead concentrations exceed 15 ppb, water utilities must take action to reduce the level of lead. However, it is important to recognize that even levels below this threshold can still pose some health risks, so lower values are always preferable. When comparing tap water's lead ion concentration of 9.0 ppb to the EPA standard, we find that the water is within the acceptable range for safety.

calculating molarity

Molarity, symbolized by 'M', is a unit of concentration used in chemistry to describe the number of moles of a solute in one liter of solution. It allows chemists to relate the volume of a solution to the amount of a substance it contains. To calculate molarity, you divide the number of moles of the solute by the volume of the solution in liters.

In practice, if we have the mass of a substance, we must first convert it to moles by using the substance’s molar mass. For instance, in our scenario where we need to determine how many moles of lead ion are in 100.0 mL of the water, we would convert the mass of lead from milligrams to grams, use the molar mass of lead to find the number of moles and then relate it to the volume of the water in liters.

units of concentration

Units of concentration are various ways of expressing how much solute is contained in a given amount of solvent or solution. We have already discussed ppm and ppb, but there are many others, such as molarity (M), molality (m), and percent concentration (% w/w, % w/v, % v/v).

In the context of the exercise, when converting to mg/mL, we are essentially mapping ppm – a unit expressing the mass of solute in a mass of solution – to a unit that expresses mass of solute per volume of solution. This is directly useful when calculating the actual amount of substance in a given volume of liquid, which is often more intuitive for practical applications, such as in medicine or environmental sampling.