Problem 114 - Chemistry The Central Science

Question

The U.S. standard for arsenate in drinking water requires that public water supplies must contain no greater than 10 parts per billion \((\mathrm{ppb})\) arsenic. If this arsenic is present as arsenate, 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? Parts per billion is defined on a mass basis as $$\mathrm{ppb}=\frac{\text { g solute }}{\mathrm{g} \text { solution }} \times 10^{9}$$

Step-by-Step Solution

Answer

The mass of sodium arsenate present in a 1.00-L sample of drinking water that just meets the standard for arsenate concentration (10 ppb) is \(10^{-5}\;\text{g}\).

Step 1: Calculate the mass of the solution

First, we need to find the mass of the 1.00-L water sample. The density of water is approximately 1 g/mL or 1 g/cm³. Since 1 L = 1000 mL = 1000 cm³ , the mass of the water sample is: Mass of water = Volume x Density Mass of water = 1.00 L x 1 g/mL x 1000 mL/L Mass of water = 1000 g

Step 2: Set up the equation for ppb

Now, we will use the equation for ppb: ppb = \(\frac{\text{g solute}}{\text{g solution}} \times 10^9\) We know the allowed ppb for arsenate is 10, the mass of the solute (sodium arsenate) is unknown, and the mass of the solution is 1000g. Substitute the known values into the equation: 10 = \(\frac{\text{g solute}}{1000 \text{ g}} \times 10^9\)

Step 3: Solve for mass of sodium arsenate

Now, let's solve for the mass of sodium arsenate (g solute): g solute = \(\frac{10 \times 1000 \text{ g}}{10^9}\) g solute = \(\frac{10^4 \text{ g}}{10^9}\) g solute = \(10^{-5} \text{ g}\)

Step 4: Calculate mass of sodium arsenate (AsO\(_{4}^{3-}\)) in the 1.00-L sample

Since we have the mass of sodium arsenate (AsO\(_{4}^{3-}\)) in grams, we can now calculate the mass of sodium arsenate present in the 1.00-L sample: Mass of sodium arsenate = \(10^{-5}\;\text{g}\) Therefore, the mass of sodium arsenate present in a 1.00-L sample of drinking water that just meets the standard is \(10^{-5}\;\text{g}\).

Key Concepts

Sodium Arsenate

Sodium arsenate is a chemical compound that contains the arsenate ion ( AsO_4^{3-} ) , which is a form of arsenic. It’s a salt derived from arsenic acid and is commonly used in various industries, including agriculture and wood preservation.
This compound is significant when discussing water safety and public health, mainly because arsenic compounds, including sodium arsenate, are toxic.
When dissolved in water, sodium arsenate breaks down, releasing arsenate ions that can be harmful if present in high concentrations.
This is why strict standards are set for arsenic levels in drinking water to protect consumers from potential health risks.
For instance, long-term exposure to arsenic can lead to health problems such as cancer and heart disease. It's essential to understand sodium arsenate and its implications in contaminating resources because treating water contaminated with arsenic typically requires specialized filtration systems or chemical treatments.
Therefore, understanding the chemical makeup and how it interacts with environmental systems is crucial for maintaining water safety.

Arsenic Standards

Arsenic standards are critical in ensuring safe drinking water.
In the United States, the Environmental Protection Agency (EPA) has set a maximum allowable concentration of arsenic in public water at 10 parts per billion (ppb).
This limit aims to minimize arsenic exposure and prevent potential health issues associated with its consumption. Arsenic can enter the water supply through natural deposits in the earth or from industrial and agricultural pollution.
Therefore, monitoring concentrations of arsenic, including its compounds like sodium arsenate, helps maintain water safety and public health. When we talk about parts per billion, it provides a way of representing very dilute concentrations of substances.
A concentration of 10 ppb means that for every billion parts of the solution, there are 10 parts of arsenic.
This precision is crucial for substances as toxic as arsenic since even minimal exposure over time can have severe health consequences. Governments and health organizations enforce these standards to ensure that the water supply is safe, motivating continuous research and improvement in water treatment technologies to comply with these limits.

Mass Calculation

Mass calculation in the context of monitoring arsenic, such as sodium arsenate, involves determining the amount of the contaminant present in a solution.
It is a practical skill in both environmental science and public health to ensure compliance with safety standards.To calculate the mass of sodium arsenate in water, we use the formula for parts per billion (ppb):
\[\text{ppb} = \frac{\text{grams of solute}}{\text{grams of solution}} \times 10^9\]This helps us find how much of the solute, in this case, sodium arsenate, is present.Given the problem, we had a 1-liter sample of water, and its mass is about 1000 grams since the density of water is 1 g/mL.
By substituting the ppb standard of 10 and the water's mass into the formula, we solve for the mass of sodium arsenate. Here's the step-by-step calculation:

• Set up the equation allowing ppb at 10 and the solution mass at 1000 grams.
• Substitute into the formula: 10 = \(\frac{\text{g solute}}{1000}\) \times 10^9.
• Solve for mass of solute: g solute = \(\frac{10 \times 1000}{10^9} = 10^{-5}\) g.

After calculating, the mass of sodium arsenate that would just meet the 10 ppb standard is accurate and reliable, assisting in ensuring water safety.