The mercury content of a stream was believed to be above the minimum considered safe limit (1 part per billion, by mass). An analysis indicated that the concentration was 1.68 parts per billion. How many Hg atoms are present in 15 L of water, the density of which is 0.998 g/ml. (Hg = 200)

Options

A. `7.57 xx 10^(13)`
B. `7.57 xx 10^(19)`
C. `7.57 xx 10^(16)`
D. `5.37 xx 10^(16)`

Explanation

To solve the problem, we need to determine how many mercury (Hg) atoms are present in 15 liters of water, given that the concentration of mercury is 1.68 parts per billion (ppb) and the density of water is 0.998 g/mL. The atomic mass of mercury is given as 200 g/mol.

### Step-by-Step Solution:

**Step 1: Convert the volume of water from liters to grams.**
- We know that 1 liter = 1000 mL.
- Therefore, 15 liters = 15 × 1000 mL = 15000 mL.
- Using the density of water (0.998 g/mL), we can calculate the mass of 15 liters of water:

\[ \text{Mass of water} = \text{Volume} \times \text{Density} = 15000 \, \text{mL} \times 0.998 \, \text{g/mL} = 14970 \, \text{g} \]

**Step 2: Calculate the mass of mercury in the water.**
- The concentration of mercury is given as 1.68 parts per billion (ppb), which means there are 1.68 grams of mercury in 10^9 grams of water.
- To find the mass of mercury in 14970 grams of water, we set up a proportion:

\[ \text{Mass of Hg} = \left( \frac{1.68 \, \text{g}}{10^9 \, \text{g}} \right) \times 14970 \, \text{g} = \frac{1.68 \times 14970}{10^9} \, \text{g} \]

\[ \text{Mass of Hg} \approx 2.52 \times 10^{-5} \, \text{g} \]

**Step 3: Convert the mass of mercury to moles.**
- To find the number of moles of mercury, we use the molar mass of mercury (200 g/mol):

\[ \text{Moles of Hg} = \frac{\text{Mass of Hg}}{\text{Molar mass of Hg}} = \frac{2.52 \times 10^{-5} \, \text{g}}{200 \, \text{g/mol}} \approx 1.26 \times 10^{-7} \, \text{mol} \]

**Step 4: Calculate the number of mercury atoms.**
- To find the number of atoms, we use Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol):

\[ \text{Number of atoms} = \text{Moles of Hg} \times \text{Avogadro's number} = 1.26 \times 10^{-7} \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \]

\[ \text{Number of atoms} \approx 7.57 \times 10^{16} \, \text{atoms} \]

### Final Answer:
The number of mercury atoms present in 15 liters of water is approximately \(7.57 \times 10^{16}\) atoms.

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