Carbon disulphide `CS_(2)` can be made from `SO_(2)`. The overall reaction is
`5C+2SO_(2)rarr CS_(2)+4CO`
How much `CS_(2)` can be produced from `450 kg` of waste `SO_(2)` with excess of coke the `SO_(2)` conversion is `82%`.

Explanation

To solve the problem of how much carbon disulfide (CS₂) can be produced from 450 kg of waste sulfur dioxide (SO₂) with an 82% conversion rate, we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction is:
\[ 5C + 2SO_2 \rightarrow CS_2 + 4CO \]

### Step 2: Calculate the molar mass of sulfur dioxide (SO₂)
The molar mass of SO₂ is calculated as follows:
- Molar mass of sulfur (S) = 32 g/mol
- Molar mass of oxygen (O) = 16 g/mol
- Therefore, molar mass of SO₂ = 32 + (16 × 2) = 32 + 32 = 64 g/mol

### Step 3: Calculate the molar mass of carbon disulfide (CS₂)
The molar mass of CS₂ is calculated as follows:
- Molar mass of carbon (C) = 12 g/mol
- Molar mass of sulfur (S) = 32 g/mol
- Therefore, molar mass of CS₂ = 12 + (32 × 2) = 12 + 64 = 76 g/mol

### Step 4: Determine the moles of SO₂ available
Given that we have 450 kg of SO₂, we first convert this to grams:
\[ 450 \text{ kg} = 450,000 \text{ g} \]

Now, we can calculate the number of moles of SO₂:
\[ \text{Moles of SO₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{450,000 \text{ g}}{64 \text{ g/mol}} \approx 7031.25 \text{ moles} \]

### Step 5: Use the stoichiometry of the reaction
From the balanced equation, we see that 2 moles of SO₂ produce 1 mole of CS₂. Therefore, the moles of CS₂ produced from the moles of SO₂ can be calculated as:
\[ \text{Moles of CS₂} = \frac{7031.25 \text{ moles SO₂}}{2} \approx 3515.625 \text{ moles CS₂} \]

### Step 6: Convert moles of CS₂ to grams
Now we convert the moles of CS₂ back to grams:
\[ \text{Mass of CS₂} = \text{moles} \times \text{molar mass} = 3515.625 \text{ moles} \times 76 \text{ g/mol} \approx 267,187.5 \text{ g} \]

### Step 7: Convert grams to kilograms
To convert grams to kilograms:
\[ 267,187.5 \text{ g} = 267.1875 \text{ kg} \]

### Step 8: Adjust for the conversion rate
Since the conversion rate is only 82%, we need to calculate the actual yield of CS₂:
\[ \text{Actual yield of CS₂} = 267.1875 \text{ kg} \times \frac{82}{100} \approx 219.09 \text{ kg} \]

### Final Answer
The amount of carbon disulfide (CS₂) that can be produced is approximately **219.09 kg**.

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