Question

A 2.6-L sample of water contains \(192 \mu \mathrm{g}\) of lead. Does this concentration of lead exceed the safety limit of 0.050 ppm of lead per liter of drinking water?

Short answer

Yes, the lead concentration exceeds the safety limit of 0.050 mg/L.

Step-by-step solution

Understanding the safety limit

The safety limit for lead concentration is given as 0.050 ppm, which means 0.050 parts per million. This translates directly to 0.050 milligrams of lead per liter of water, because 1 ppm is equal to 1 mg/L.

Convert micrograms to milligrams

First, we need to convert the given amount of lead from micrograms to milligrams. Since there are 1000 micrograms in 1 milligram, we can convert 192 micrograms as follows: \[192 \mu g = \frac{192}{1000} \text{ mg} = 0.192 \text{ mg}.\]

Calculate concentration in mg/L

Now, calculate the concentration of lead in milligrams per liter. Given 0.192 mg of lead in 2.6 L of water, the concentration is:\[\text{Concentration} = \frac{0.192 \text{ mg}}{2.6 \text{ L}} = 0.073846 \text{ mg/L}.\]

Compare with the safety limit

Now, compare the calculated concentration to the safety limit. We have calculated a concentration of 0.073846 mg/L, while the safety limit is 0.050 mg/L. Since 0.073846 mg/L > 0.050 mg/L, the lead concentration exceeds the safety limit.

Key concepts

Safety Limit

The safety limit refers to the maximum allowable concentration of a harmful substance, like lead, in drinking water that is still considered safe for human health. In the context of lead in water, safety limits are set by regulatory agencies to protect public health. For lead, a typical safety limit is 0.050 parts per million (ppm), equivalent to 0.050 milligrams of lead per liter. This means for each liter of water, only up to 0.050 mg of lead is permissible. Exceeding this limit may pose health risks, especially since lead is a toxic metal that can cause serious health issues.

ppm (Parts Per Million)

Parts per million (ppm) is a unit of measurement used to describe the concentration of a substance in a solution. It is a way to express very dilute concentrations. When we say that lead's safety limit is 0.050 ppm, it means there are 0.050 parts of lead in every one million parts of water. This is numerically equal to 0.050 milligrams of lead per liter of water because one million milligrams is equivalent to one liter. Understanding ppm helps assess whether contaminants like lead are at safe levels for consumption.

Microgram to Milligram Conversion

Micrograms and milligrams are units of mass, with micrograms being much smaller. To convert micrograms (\(\mu g\)) to milligrams (mg), one uses the conversion factor where 1000 \(\mu g\) equals 1 mg. For instance, converting 192 \(\mu g\) of lead to milligrams involves the calculation: \[192 \, \mu g = \frac{192}{1000} \, \text{mg} = 0.192 \, \text{mg}\] Converting units in calculations like these is crucial, particularly as safety regulations typically use milligrams per liter.

Chemical Calculations

Chemical calculations involve determining the concentration of substances in solutions. In our case, we calculated lead's concentration in water to see if it surpasses the safety limit. Here's a simplified breakdown:

• First, convert the mass of lead from micrograms to milligrams.
• Next, determine the concentration using the formula: \[\text{Concentration} = \frac{\text{mass of lead in mg}}{\text{volume of water in L}}\]
• If 0.192 mg of lead is in 2.6 L of water, the calculation is \[\text{Concentration} = \frac{0.192 \, \text{mg}}{2.6 \, \text{L}} = 0.073846 \, \text{mg/L}\]

Finally, compare this concentration with the safety limit. Because 0.073846 mg/L is greater than 0.050 mg/L, the water contains more lead than is regarded as safe according to the limit standards. This illustrates the importance of precise chemical calculations in ensuring water safety.