To calculate the number of chlorine atoms in 0.2 g of DDT (C\(_{14}\)H\(_9\)Cl\(_5\)), follow these steps:
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Determine the molar mass of DDT:
- The molar masses of the constituent elements are approximately:
- Carbon (C) = 12.01 g/mol
- Hydrogen (H) = 1.008 g/mol
- Chlorine (Cl) = 35.45 g/mol
The molar mass of DDT can be calculated as follows: \[ \text{Molar mass of DDT} = (14 \times 12.01) + (9 \times 1.008) + (5 \times 35.45) \] \[ = 168.14 + 9.072 + 177.25 = 354.46 , \text{g/mol} \]
- The molar masses of the constituent elements are approximately:
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Calculate the number of moles of DDT in 0.2 g: \[ \text{Moles of DDT} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.2 , \text{g}}{354.46 , \text{g/mol}} \approx 0.000564 , \text{mol} \]
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Determine the number of chlorine atoms per molecule of DDT: Each molecule of DDT contains 5 chlorine atoms.
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Calculate the number of DDT molecules in 0.000564 moles: Using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol): \[ \text{Number of DDT molecules} = 0.000564 , \text{mol} \times 6.022 \times 10^{23} , \text{molecules/mol} \approx 3.40 \times 10^{20} , \text{molecules} \]
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Calculate the total number of chlorine atoms: Since each molecule of DDT contains 5 chlorine atoms: \[ \text{Total chlorine atoms} = 3.40 \times 10^{20} , \text{molecules} \times 5 , \text{Cl/molecule} \approx 1.70 \times 10^{21} , \text{Cl atoms} \]
Thus, the number of chlorine atoms in 0.2 g of DDT is approximately \(1.70 \times 10^{21}\).