Question

A water sample is found to contain the pollutant chlorobenzene with a concentration of 15 ppb (by mass). What volume of this water contains 5.00×102mg of chlorobenzene? (Assume a density of 1.00 g/mL.)

Answer 1

To find the volume of water containing 500 mg of chlorobenzene at a concentration of 15 ppb, calculate the mass of water needed using the ratio derived from the ppb concentration and then convert to volume using the density of water (1.00 g/mL). The final volume is 33,333.33 mL.

Step-by-step explanation:

The student has asked to calculate the volume of water that contains 5.00×102 mg of chlorobenzene given a concentration of 15 ppb (parts per billion) by mass and a density of 1.00 g/mL for water. To find this volume, we will first convert the concentration of chlorobenzene into a ratio that compares the mass of chlorobenzene to the mass of water. Since 15 ppb means there are 15 parts of chlorobenzene in one billion parts of water, we can express this concentration as:

15 mg chlorobenzene / 1×109 mg water

Now, using this ratio and the mass of chlorobenzene we have (500 mg), we can calculate the mass of water that will contain this amount of chlorobenzene:

Mass of water = (5.00×102 mg chlorobenzene) × (1×109 mg water / 15 mg chlorobenzene)

Mass of water = 3.33×107 mg of water

Sine the density of water is approximately 1.00 g/mL, the mass of water can be directly converted to volume in milliliters because the number of grams is equal to the number of milliliters:

Volume of water = Mass of water / Density of water

Volume of water = 3.33×107 mg / (1.00 g/mL)

Volume of water = 3.33×107 mL

Volume of water = 33,333.33 mL

Thus, 33,333.33 mL of the water are needed to contain 500 mg of chlorobenzene at a concentration of 15 ppb.

Answer 2

To find the volume of water that contains 5.00×102 mg of chlorobenzene, you need to convert the concentration of chlorobenzene to ppm or ppb. Then set up a proportion using the concentration and solve for the volume of water.

Step-by-step explanation:

To find the volume of water that contains 5.00×102 mg of chlorobenzene, we first need to convert the concentration of chlorobenzene to ppm (parts per million) or ppb (parts per billion). Since 1 ppm = 1 mg/L and 1 ppb = 1 µg/L, we can convert the concentration of 15 ppb to mg/L by multiplying by 1 µg/L. Therefore, the concentration of chlorobenzene is 15 µg/L.

Next, we can calculate the volume of water that contains 5.00×102 mg of chlorobenzene using the concentration of chlorobenzene in µg/L. We know that 1 L of water contains 15 µg of chlorobenzene, so we can set up a proportion: (5.00×102 mg / x) = (15 µg / 1 L).

Cross multiplying, we get (5.00×102 mg) * (1 L) = (15 µg) * (x). Solving for x, we find that the volume of water containing 5.00×102 mg of chlorobenzene is 3.33×104 L.