`A` chemical commonly called "dioxin" has been very much in the news in the past few years. (It is the by product of herbicide manufacture and is thought to be quite toxic.) Its formula is `C_(12)H_(4)Cl_(4)O_(2)`. If you have a sample of dirt `(28.3 g)` that contains `1.0xx10^(-4)%` dioxin, how many moles of dioxin are in the dirt sample?

Explanation

To find the number of moles of dioxin in the dirt sample, we can follow these steps:

### Step 1: Calculate the molecular weight of dioxin (C₁₂H₄Cl₄O₂)

1. **Carbon (C)**: There are 12 carbon atoms. The atomic mass of carbon is approximately 12 g/mol.
\[ \text{Mass from Carbon} = 12 \times 12 = 144 \text{ g/mol} \]

2. **Hydrogen (H)**: There are 4 hydrogen atoms. The atomic mass of hydrogen is approximately 1 g/mol.
\[ \text{Mass from Hydrogen} = 4 \times 1 = 4 \text{ g/mol} \]

3. **Chlorine (Cl)**: There are 4 chlorine atoms. The atomic mass of chlorine is approximately 35.5 g/mol.
\[ \text{Mass from Chlorine} = 4 \times 35.5 = 142 \text{ g/mol} \]

4. **Oxygen (O)**: There are 2 oxygen atoms. The atomic mass of oxygen is approximately 16 g/mol.
\[ \text{Mass from Oxygen} = 2 \times 16 = 32 \text{ g/mol} \]

5. **Total Molecular Weight**:
\[ \text{Molecular Weight of Dioxin} = 144 + 4 + 142 + 32 = 322 \text{ g/mol} \]

### Step 2: Calculate the mass of dioxin in the dirt sample

1. **Given**: The mass of the dirt sample is 28.3 g, and it contains \(1.0 \times 10^{-4}\%\) dioxin.
2. **Convert percentage to a fraction**:
\[ \text{Fraction of Dioxin} = \frac{1.0 \times 10^{-4}}{100} = 1.0 \times 10^{-6} \]

3. **Calculate the mass of dioxin in the sample**:
\[ \text{Mass of Dioxin} = 28.3 \text{ g} \times 1.0 \times 10^{-6} = 2.83 \times 10^{-5} \text{ g} \]

### Step 3: Calculate the number of moles of dioxin

1. **Use the formula for moles**:
\[ \text{Moles of Dioxin} = \frac{\text{Mass of Dioxin}}{\text{Molecular Weight of Dioxin}} \]
\[ \text{Moles of Dioxin} = \frac{2.83 \times 10^{-5} \text{ g}}{322 \text{ g/mol}} \]

2. **Calculate the moles**:
\[ \text{Moles of Dioxin} \approx 8.79 \times 10^{-8} \text{ mol} \]

### Final Answer
The number of moles of dioxin in the dirt sample is approximately:
\[ \text{Moles of Dioxin} \approx 8.79 \times 10^{-8} \text{ mol} \]