Question

The newest U.S. standard for arsenate in drinking water, mandated by the Safe Drinking Water Act, required that by January 2006, public water supplies must contain no greater than 10 parts per billion (ppb) arsenic. If this arsenic is present as arsenate, \(\mathrm{AsO}_{4}{ }^{3-}\), what mass of sodium arsenate would be present in a 1.00-L sample of drinking water that just meets the standard?

Short answer

The mass of sodium arsenate present in a 1.00 L sample of drinking water that just meets the standard is calculated as follows: \[m_{Na_{3}AsO_{4}} = \left(1000\;g \times \frac{10}{1,000,000,000} \right) \times \frac{1}{74.92\;g/mol} \times 207.98\;g/mol\] Upon calculating the final value, we obtain the mass of sodium arsenate in the water sample.

Step-by-step solution

Understanding the given information

To start, we can rewrite 10 parts per billion (ppb) as: \[10 \; ppb = \frac{10}{1,000,000,000}\; \% \] That means that if we have 10 parts per billion (ppb) of arsenic present in a sample, it is 10 parts of arsenic for every 1,000,000,000 parts of the solution. Furthermore, we know that the arsenic is present as arsenate \(\mathrm{AsO}_{4}{ }^{3-}\). Now, let's find the mass of sodium arsenate in 1.00 L (1000 g) of water that meets the standard.

Find the mass of arsenic present

First, we need to find the mass of arsenic (As) present in 1.00 L of water. We can use the percentage we found earlier: \[ \frac{m_{As}}{1000\;g} = \frac{10}{1,000,000,000}\] where \(m_{As}\) is the mass (in grams) of arsenic. Solve for \(m_{As}\): \[m_{As} = 1000\;g \times \frac{10}{1,000,000,000}\]

Convert the mass of arsenic to moles

Next, we use the molar mass of arsenic to convert the mass of arsenic to moles. The molar mass of arsenic (\(M_{As}\)) is approximately 74.92 g/mol. \[n_{As} = \frac{m_{As}}{M_{As}}\]

Find the moles of sodium arsenate

Now, we need to find the moles of sodium arsenate (\(n_{Na_{3}AsO_{4}}\)). Since there is a 1:1 ratio between moles of arsenate (\(AsO_{4^{3-}}\)) and moles of sodium arsenate (\(Na_{3}AsO_{4}\)), the moles of sodium arsenate will be equal to the moles of arsenate (which is equal to the moles of arsenic, \(n_{As}\)). \[n_{Na_{3}AsO_{4}} = n_{As}\]

Convert the moles of sodium arsenate to mass

To find the mass of sodium arsenate, we can use the molar mass of sodium arsenate (\(M_{Na_{3}AsO_{4}}\)) which is approximately 207.98 g/mol. \[m_{Na_{3}AsO_{4}} = n_{Na_{3}AsO_{4}} \times M_{Na_{3}AsO_{4}}\]

Calculate the mass of sodium arsenate present in drinking water

Now we can plug in the values we found in steps 2, 3, and 5 to calculate the mass of sodium arsenate in the 1.00 L sample of drinking water. Remember to keep track of units as well. \[m_{Na_{3}AsO_{4}} = \left(1000\;g \times \frac{10}{1,000,000,000} \right) \times \frac{1}{74.92\;g/mol} \times 207.98\;g/mol\] Once we calculate the final value, we get the mass of sodium arsenate present in a 1.00 L sample of drinking water that just meets the standard.

Key concepts

Safe Drinking Water Act

The Safe Drinking Water Act (SDWA) is a pivotal piece of legislation in the United States that protects public drinking water supplies from harmful contaminants. Enacted in 1974, it authorizes the Environmental Protection Agency (EPA) to set national health-based standards for drinking water to protect against both natural and man-made contaminants that may be found in drinking water.

For instance, arsenic, a naturally occurring element that can be toxic and carcinogenic, is one of the contaminants regulated by the SDWA. The Act requires that public water systems comply with established maximum contaminant levels (MCLs) to ensure safe consumption. In January 2006, the updated standard mandated by the SDWA for arsenic in drinking water was set at a maximum of 10 parts per billion (ppb), which is a stringent threshold aimed at protecting public health.

Parts Per Billion (ppb)

Understanding 'parts per billion' (ppb) is crucial when dealing with measurements that require high precision, such as contaminant levels in drinking water. One part per billion signifies that there is one unit of a substance for every one billion units of total volume. This unit of measure allows for expressing very small concentrations of substances, such as trace chemicals or contaminants in water.

To put it into perspective, one part per billion is equivalent to one drop of water in a swimming pool about the size of a standard Olympic pool. When applied to the SDWA regulations, the maximum permitted arsenic concentration in drinking water is 10 ppb, which means there can only be 10 parts of arsenic for every billion parts of water.

Sodium Arsenate

Sodium arsenate is a chemical compound that contains arsenic, and it is one form in which arsenic can occur in drinking water. When sodium arsenate dissolves in water, it can form arsenate ions, which are represented chemically as \(\mathrm{AsO}_{4}{ }^{3-}\). Sodium arsenate is used in some industrial processes and can contaminate water due to natural mineral deposits or industrial runoff.

It's important to note that due to the toxicity of arsenate, regulations such as those set forth by the SDWA are essential to control its concentration in drinking water. The step-by-step calculation we're discussing revolves around determining how much sodium arsenate is permissible under these strict guidelines.

Molar Mass

Molar mass is a fundamental concept in chemistry, defined as the mass in grams of one mole of a substance. A mole is a unit that represents \(6.022 \times 10^{23}\) entities (atoms, molecules, ions, etc.) of that substance. The molar mass is a bridge between the atomic scale and the macroscopic scale.

For instance, the molar mass of arsenic (As) is roughly 74.92 g/mol, which means that one mole of arsenic atoms weighs 74.92 grams. Knowing the molar mass allows chemists and environmental scientists to convert between mass and moles of a substance, an essential step in stoichiometry.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships that exist between the reactants and the products of a chemical reaction. It is founded on the laws of conservation of mass and the concept of the mole, allowing for the precise calculation of reactant and product quantities.

In the context of our problem, stoichiometry is used to convert the allowed mass of arsenic into the corresponding mass of sodium arsenate in water, given their respective molar masses. This calculation helps ensure that the concentration of sodium arsenate does not exceed the safe limit of 10 ppb as required by the SDWA. By following detailed stoichiometric calculations step by step, we can determine the exact amount of sodium arsenate allowable in a liter of water, reflecting the precision and the importance of stoichiometry in environmental chemistry.