Problem 92 - Chemistry The Molecular Science

Question

Some dietitians recommend drinking six 8-oz glasses of water each day. If your drinking water contains the maximum contamination level for arsenic, 0.010 ppm, how much arsenic would you consume in a week following this recommendation?

Step-by-Step Solution

Answer

You would consume approximately 0.0994 mg of arsenic in a week.

Step 1: Calculate Daily Water Intake

First, let's calculate the total amount of water intake per day. Since the recommendation is to drink six 8-oz glasses of water, the total daily intake is:\[ 6 \text{ glasses} \times 8 \text{ oz/glass} = 48 \text{ oz} \] Thus, you drink 48 ounces of water per day.

Step 2: Convert Ounces to Liters

Next, we need to convert the daily water intake from ounces to liters. We know that 1 US ounce is approximately 0.0295735 liters. Therefore, the daily water intake in liters is:\[ 48 \text{ oz} \times 0.0295735 \text{ L/oz} \approx 1.42 \text{ L} \] So, you consume approximately 1.42 liters of water per day.

Step 3: Calculate Weekly Water Consumption

Now, calculate the total amount of water consumed in a week by multiplying the daily water intake by 7 days:\[ 1.42 \text{ L/day} \times 7 \text{ days} = 9.94 \text{ L} \] You drink approximately 9.94 liters of water in a week.

Step 4: Convert PPM to Grams per Liter

The water contains arsenic at a concentration of 0.010 ppm, which means 0.010 grams of arsenic per 1,000,000 grams of water. Since the density of water is 1 g/mL, 1 liter of water weighs 1,000 grams. Therefore, 0.010 ppm is equivalent to 0.010 mg/L.

Step 5: Calculate Weekly Arsenic Intake

Now, find the total arsenic consumption in a week using the weekly water consumption and the arsenic concentration:\[ 9.94 \text{ L/week} \times 0.010 \text{ mg/L} = 0.0994 \text{ mg/week} \] Thus, you would consume approximately 0.0994 milligrams of arsenic in a week.

Key Concepts

Daily Water Intake

Understanding daily water intake is the first step in solving this problem. Dietitians often recommend drinking plenty of water, and a common guideline is to consume six 8-ounce glasses each day. This is to promote proper hydration and maintain bodily functions. To calculate your total daily water intake:

• Multiply the number of glasses (6) by the volume of each glass (8 oz).
• This gives you a total of 48 ounces of water per day.

With this amount, you are ensuring that your body gets the hydration it needs daily.

Unit Conversion

Unit conversion is needed when measurements are in different units than needed. In our problem, the water intake is initially given in ounces, but we need liters for further calculations. To convert ounces to liters, use the conversion factor:

• 1 ounce is approximately 0.0295735 liters.

For our calculation:

• 48 oz/day multiplied by 0.0295735 L/oz equals approximately 1.42 L/day.

This conversion is important as it allows you to relate the water intake with standard scientific measures used in concentration calculations.

PPM Calculation

PPM, or parts per million, is a measurement of concentration often used for pollutants. In this scenario, water contains 0.010 ppm arsenic. To convert this into practical terms:

• 0.010 ppm means 0.010 grams of arsenic per 1,000,000 grams of water.
• Since 1 liter of water weighs 1,000 grams, this is equivalent to 0.010 mg/L.

Understanding ppm readings is crucial for determining the amount of contaminant present in each liter of water.

Weekly Arsenic Consumption

To calculate weekly arsenic consumption, you need two pieces of information: the weekly water intake and arsenic concentration in ppm. First, calculate the total volume of water consumed in a week:

• 1.42 L/day multiplied by 7 days equals 9.94 liters per week.

Then, multiply the arsenic concentration by the weekly water volume:

• 9.94 L imes 0.010 mg/L = 0.0994 mg of arsenic per week.

This shows the total amount of arsenic ingested over seven days, based on the water contamination level and your water consumption habits.