Question

Excessive levels of nitrates found in drinking water can cause serious illness. When nitrates are converted to nitrites in the body, the nitrites can interfere with the oxygen-carrying capacity of the blood, causing blueness of the skin. The EPA has determined that the maximum safe level of nitrate ion in water is \(10 \mathrm{ppm}\). Suppose a sample of tap water was determined to have a nitrate ion concentration of \(95 \mathrm{ppb}\). Assume the density of the solution is \(1.00 \mathrm{~g} / \mathrm{mL}\). (a) What is the concentration of nitrate ion in units of ppm? Is it safe to drink? (b) What is the concentration of nitrate ion in units of \(\mathrm{mg} / \mathrm{mL}\) ? (c) What mass of nitrate ion is in \(100.0 \mathrm{~mL}\) of this drinking water? (d) How many moles of nitrate ion are in \(100.0 \mathrm{~mL}\) of the water?

Short answer

The nitrate ion concentration in the water sample is \(0.095 \, ppm\), which is safe to drink. The nitrate ion concentration in mg/mL is \(0.000095 \, mg/mL\). There are \(0.0095 \, mg\) of nitrate ion in \(100.0 \, mL\) of the water, which is equivalent to \(1.53 \times 10^{-7} \, mol\).

Step-by-step solution

Conversion from ppb to ppm

First, convert the given concentration from parts per billion (ppb) to parts per million (ppm) by dividing by 1000. Therefore, \(95 ppb = 0.095 ppm\).

Safety Evaluation

Since the allowed maximum level of nitrate ions in drinking water is \(10 ppm\) and the concentration in the sample water is \(0.095 ppm\), which is less than the maximum, it is safe to drink.

Conversion to mg/mL

Next, convert \(0.095 ppm\) to mg/mL. Given that \(1 ppm\) is equal to \(1 \, \mu g/mL\) or \(0.001\, mg/mL\), therefore, \(0.095 \, ppm = 0.095 \times 0.001 \, mg/mL = 0.000095 \, mg/mL\).

Mass Calculation

To calculate the mass of nitrate ion in \(100.0 \, mL\) of this drinking water, multiply the volume by the concentration from step 3: \(100.0 \, mL \times 0.000095 \, mg/mL = 0.0095 \,mg\).

Molar Calculation

Finally, calculate the number of moles of nitrate ion in \(100.0 \, mL\) of the water. Given that \(1 \, mol\) of nitrate ion (\(NO_3^-\)) has a molar mass of \(62.00 \, g = 62000 \, mg\), you can calculate \(0.0095 \, mg = \frac{0.0095}{62000} \, mol = 1.53 \times 10^{-7} \, mol\).

Key concepts

Water Safety Standards

Water safety is crucial for ensuring public health, and understanding the limits on various contaminants is part of this. The Environmental Protection Agency (EPA) sets guidelines for the permissible levels of various substances, including nitrate levels in drinking water. Nitrates at high levels can be harmful as they may convert to nitrites in the human body. This process affects the blood's ability to carry oxygen.

The EPA limits nitrate levels in drinking water to a maximum of 10 parts per million (ppm). Any concentration exceeding this level could pose health risks. If a water sample contains 0.095 ppm of nitrates—as found by converting from 95 parts per billion (ppb) to ppm—it is considered safe according to EPA standards since it falls well below the 10 ppm threshold.

Monitoring these levels helps assure consumers that their water is safe to drink, reinforcing the importance of strict water safety standards.

Unit Conversion in Chemistry

In chemistry, unit conversions are a frequent necessity to understand concentrations and various measurements effectively. Parts per billion (ppb) and parts per million (ppm) are common units for small levels of contaminants in solutions, with 1 ppm equal to 1,000 ppb. Conversion between these units often involves simple multiplication or division by 1,000.

For instance, to convert 95 ppb of nitrate ion concentration to ppm, you divide by 1,000, resulting in 0.095 ppm. This conversion demonstrates the practicality of unit conversion in making data meaningful and comparable against established standards. Another handy conversion is between ppm and mg/mL, where 1 ppm equals 0.001 mg/mL.

Grasping unit conversions in chemistry is crucial for accurate measurement and analysis in experiments and environmental assessments.

Molar Mass Calculations

Calculating molar mass is another fundamental step in chemistry, essential for converting between mass and moles. The molar mass of a compound, such as nitrate ion (\(NO_3^-\)), is a measure of the mass of one mole of its molecules or ions. For nitrate, the molar mass is calculated by summing the atomic masses of one nitrogen (N) and three oxygen (O) atoms, giving us approximately 62.00 g/mol.

When determining the mass of nitrate ions in a given volume of water, knowing its molar mass allows for converting mass to moles. In this exercise, with 0.0095 mg of nitrate ions in 100 mL of water, we convert this to moles using the molar mass: \[0.0095 \, \text{mg} = \frac{0.0095}{62,000} \, \text{mol} = 1.53 \times 10^{-7} \, \text{mol}\].

This process is vital for chemical reactions and analyses, where accurate measurements of substances are necessary.