Problem 115 - Chemistry: The Central Science

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, \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\), what mass of sodium arsenate would be present in a 1.00-L sample of drinking water that just meets the standard?

Step-by-Step Solution

Answer

In a 1.00-L sample of drinking water that just meets the 10 ppb arsenic standard, \(2.79 \times 10^{-6} \ g\) of sodium arsenate would be present.

Step 1: Convert the arsenic concentration from µg/L to moles/L

Using the molar mass of arsenic (As), we can convert the given concentration (10 µg/L) to moles/L. The molar mass of arsenic is 74.92 g/mol. Moles of arsenic per liter of water = \(\frac{10 \times 10^{-6} \ g}{74.92 \ g/mol} = 1.34 \times 10^{-7} \ mol/L\)

Step 2: Calculate the moles of sodium arsenate

Since sodium arsenate has the chemical formula Na3AsO4, the ratio of moles of arsenic (As) to moles of sodium arsenate (Na3AsO4) is 1:1. Therefore, the moles of sodium arsenate present in 1 L of water are equal to the moles of arsenic calculated in Step 1. Moles of sodium arsenate per liter of water = 1.34 × 10⁻⁷ mol/L

Step 3: Calculate the mass of sodium arsenate

Now, we need to calculate the mass of sodium arsenate present in the 1.00 L sample. To do this, we will use the molar mass of sodium arsenate. Molar mass of sodium arsenate (Na3AsO4) = (3 × 22.99) g/mol (sodium) + 74.92 g/mol (arsenic) + (4 × 16.00) g/mol (oxygen) = 207.87 g/mol. Mass of sodium arsenate present in 1.00 L sample = (1.34 × 10⁻⁷ mol/L) × (207.87 g/mol) × (1.00 L) Mass of sodium arsenate = 2.79 × 10⁻⁶ g In a 1.00-L sample of drinking water that just meets the standard, 2.79 × 10⁻⁶ g of sodium arsenate would be present.

Key Concepts

Safe Drinking Water Act

The Safe Drinking Water Act (SDWA) is an essential piece of legislation that helps safeguard the quality of drinking water in the United States. Enacted by Congress in 1974, the main goal of the SDWA is to protect the public from contaminants in water that could pose a risk to human health. This law allows the U.S. Environmental Protection Agency (EPA) to set national standards for drinking water protective measures, such as maximum contaminant levels for various pollutants.
One notable regulation under the SDWA is the limit on arsenic levels in public water supplies. By January 2006, water systems were required to limit arsenic concentrations to no more than 10 parts per billion (ppb). This regulation was introduced due to arsenic's potential to cause significant health problems, including cancer.
By enforcing these standards, the SDWA ensures communities continue to have access to safe and clean drinking water. The act plays a crucial role in maintaining the health and safety of millions of Americans by preventing exposure to hazardous contaminants.

Sodium arsenate concentration

Sodium arsenate is a chemical compound with the formula Na₃AsO₄, where arsenate ions are chemically bonded with sodium ions. The concentration of arsenic in water is a significant concern because of its toxicity, and regulations, like those in the Safe Drinking Water Act, aim to limit exposure.
When arsenic is present in water as arsenate, its concentration is measured in parts per billion (ppb). For the exercise in the original problem, the concentration of arsenate is specified at 10 ppb, the highest permissible level under current regulations. This measurement signifies that per every billion parts of water, 10 parts are arsenate.
To convert this to a more practical measure for chemical calculations (such as moles per liter), we utilize the weight of arsenic and the concentration of arsenate specified by regulations. This conversion is critical in further determining the mass of sodium arsenate permissible in a given volume of water.

Molar mass calculation

Understanding molar mass is fundamental to solving chemical equations and problems involving chemical compounds in solution. The molar mass of a substance is the mass of one mole of its molecules or atoms, typically expressed in grams per mole (g/mol).
For sodium arsenate ( Na₃AsO₄ ), the molar mass is calculated by summing the atomic masses of all atoms in the formula:

• Sodium (Na): 3 atoms × 22.99 g/mol = 68.97 g/mol
• Arsenic (As): 74.92 g/mol
• Oxygen (O): 4 atoms × 16.00 g/mol = 64.00 g/mol

Adding these together gives a total molar mass of 207.87 g/mol for sodium arsenate. This figure is crucial in converting between moles and grams in chemical quantification, enabling precise determination of mass in real-life chemical calculations.

Chemical calculation in solutions

Chemical calculations in solutions involve converting between different units of measurement to understand how a solute is distributed within a solvent, like water. For the exercise, it's essential to calculate how much sodium arsenate is permissible in a 1-liter sample of water, given a specific concentration of arsenic.
The process begins by converting arsenic mass concentration (in micrograms per liter) to a molar concentration (moles per liter) using arsenic's molar mass. This involves dividing the mass of arsenic by its molar mass to find moles.

• The concentration of arsenic is 10 µg/L, which is converted by calculating \(\frac{10 imes 10^{-6} \, \text{g}}{74.92 \, \text{g/mol}} \approx 1.34 \times 10^{-7} \, \text{mol/L}\).

Next, since sodium arsenate has a 1:1 molar ratio with arsenic in the compound, the moles of sodium arsenate will match those of arsenic. Finally, using the molar mass of sodium arsenate (207.87 g/mol), the mass of sodium arsenate in the solution can be found by multiplying the molarity by the molar mass.

• This leads to a mass calculation of \(1.34 \times 10^{-7} \, \text{mol/L} \times 207.87 \, \text{g/mol} = 2.79 \times 10^{-6} \, \text{g}\).

Such precise calculations are vital in ensuring chemical safety standards are adhered to in public water supplies, confirming compliance with regulations like those set forth in the Safe Drinking Water Act.