Question

The safe drinking water standard for arsenic (which is usually found as arsenate, see $4.115)$ is 50 parts per billion (ppb) in most developing countries. (a) How many grams of sodium arsenate are in 55 gallons of water, if the concentration of arsenate is 50 ppb? (b) In 1993 , naturally occurring arsenic was discovered as a major contaminant in the drinking water across the country of Bangladesh. Approximately 12 million people in Bangladesh still drink water from wells that have higher concentrations of arsenic than the standard. Recently, a chemistry professor from George Mason University was awarded a $\mathrm{\$}1$ million Grainger Challenge Prize for Sustainability for his development of a simple, inexpensive system for filtering naturally occuring arsenic from drinking water. The system uses buckets of sand, cast iron, activated carbon, and wood chips for trapping arsenic-containing minerals. Assuming the efficiency of such a bucket system is $90\mathrm{\%}$ (meaning, $90\mathrm{\%}$ of the arsenic that comes in is retained in the bucket and $10\mathrm{\%}$ passes out of the bucket), how many times should water that is 500 ppb in arsenic be passed through to meet the 50 ppb standard?

Short answer

The mass of sodium arsenate in 55 gallons of water at a concentration of 50 ppb is approximately 0.01040985 g. To meet the 50 ppb standard for a water source with an initial arsenic concentration of 500 ppb, the water should be passed through the 90% efficient bucket filtration system 1 time.

Step-by-step solution

1. Convert given data and find volume of water

First, we need to convert the given data to SI units (or compatible units). We need to convert 55 gallons of water into liters (L) (as 1 ppm = 1 mg in 1 L). Also, note that 1 ppb is equal to 0.001 ppm. We are given that there are 50 ppb in 1 L of water, which is equivalent to 0.05 ppm, and we need to find the grams of sodium arsenate in 55 gallons of water. We begin by converting gallons to liters: $55\text{ gallons}=55\times 3.78541\text{ L}=208.197\text{ L}$

2. Calculate the mass of sodium arsenate

Now, we need to calculate the mass of sodium arsenate in 208.197 L of water at a concentration of 50 ppb. As 1 ppm is equal to 1 mg in 1 L, we can calculate the mass of sodium arsenate in the given volume of water: $\text{Mass of sodium arsenate}=(0.05\text{ ppm})\times (208.197\text{ L})\times (0.001\frac{\text{g}}{1\text{ L}})$ $\text{Mass of sodium arsenate}=0.01040985\text{ g}$ Now we have the mass of sodium arsenate in 55 gallons of water at a concentration of 50 ppb. For Part (b) now, we have a bucket filtration system with 90% efficiency.

3. Calculate the number of filtration cycles

We know that the concentration of arsenic in the water is 500 ppb, and we want to reduce it to 50 ppb, a reduction of 90% in concentration. We know the efficiency of the filtration system is 90% per cycle. Let's denote $n$ as the number of filtration cycles. We can set up the following equation: $500\times (1-0.9{)}^n=50$ $(0.1{)}^n=0.1$ $n=1$ Therefore, the water should be passed through the filtration system 1 time to meet the 50 ppb standard.

Key concepts

Drinking Water Standards

Drinking water standards are guidelines and regulations that ensure our water is safe for consumption. These standards set limits on the concentration of contaminants, such as arsenic, that are permissible in drinking water. In different parts of the world, these limits may vary. For instance, while many developing countries adhere to a standard of 50 parts per billion (ppb) for arsenic, other regions might have stricter or more lenient guidelines.

The purpose of these standards is to protect human health by reducing exposure to harmful substances. Regulatory bodies frequently review and update these standards to reflect new research and technological advancements. This ensures that public health remains a top priority, and that water quality is maintained at a safe level. By understanding and adhering to these standards, communities can ensure that their water supply is safe and clean for all users.

Arsenic Contamination

Arsenic contamination in drinking water is a pressing global issue due to its toxic effects on human health. This naturally occurring element can leach into groundwater from surrounding rocks and soils. Unfortunately, this has led to significant health risks in various countries, most notably Bangladesh, as mentioned in the exercise.

Arsenic exposure has been linked to numerous health issues, including skin lesions, cancers, and cardiovascular diseases. Since it is colorless, tasteless, and odorless, detecting arsenic in water is challenging without proper testing equipment.

• Long-term exposure: Can lead to chronic health conditions.
• Acute exposure: Causes immediate but often less severe symptoms.

To mitigate arsenic contamination, various filtering technologies have been developed. Individuals living in affected areas are encouraged to test their water regularly and use appropriate filtration methods to ensure their health and safety.

Filtration Efficiency

Filtration efficiency is the measure of how effectively a filtration system removes contaminants from water. In the case of arsenic, a filtration system with high efficiency means more arsenic is captured and less remains in the water.

The exercise describes a bucket filtration system that boasts 90% efficiency. This implies that only 10% of the arsenic present in the water would pass through the filter and remain untreated.

• Efficiency rates: Determine how much of a contaminant is removed per filtration cycle.
• Impact on health: Higher efficiency results in safer drinking water.

It's crucial to understand that different filtration methods vary in effectiveness based on the type of contaminant. A well-designed system focuses on maximizing contact between the filter media and arsenic particles to ensure optimal removal rates. Regular maintenance and replacement of filtration materials can further sustain high efficiency levels and safe drinking water.

Sodium Arsenate Calculations

Calculating the amount of sodium arsenate in a given volume of water involves converting measurements into consistent units and applying concentration formulas. As outlined in the exercise, when dealing with 55 gallons of water contaminated with arsenic at a level of 50 ppb, the correct approach involves several steps.

First, converting gallons to liters allows us to use the standard ppb to ppm conversion (1 ppb = 0.001 ppm), facilitating easier calculations. From here, you can compute the mass by applying the proportion of sodium arsenate in ppm across the total liters:
$$\text{Mass of sodium arsenate}=(0.05\text{ ppm})\times (208.197\text{ L})\times (0.001\frac{\text{g}}{1\text{ L}})$$

This formula shows that sodium arsenate in water is directly proportional to its concentration and the water volume being treated. Grasping this relationship is essential for solving real-world problems where contamination levels need to be precisely managed and minimized for safety.