One tonne of air contains `2 xx 10^(-3)` g of carbon as smoke. Calculate the concentration of carbon in ppm in air.

Answer

To calculate the concentration of carbon in parts per million (ppm) in air, we can follow these steps:

### Step 1: Understand the given data
We are given:
- Mass of carbon (solute) = \(2 \times 10^{-3}\) grams
- Mass of air (solvent) = 1 tonne = 1000 kg = 1,000,000 grams (since 1 kg = 1000 grams)

### Step 2: Write the formula for ppm
The formula for parts per million (ppm) is given by:

\[ \text{ppm} = \left( \frac{\text{mass of solute}}{\text{mass of solvent}} \right) \times 10^6 \]

### Step 3: Substitute the values into the formula
Now, we substitute the values into the ppm formula:

\[ \text{ppm} = \left( \frac{2 \times 10^{-3} \text{ g}}{1,000,000 \text{ g}} \right) \times 10^6 \]

### Step 4: Simplify the expression
Calculating the fraction:

\[ \frac{2 \times 10^{-3}}{1,000,000} = \frac{2 \times 10^{-3}}{10^6} = 2 \times 10^{-3} \times 10^{-6} = 2 \times 10^{-9} \]

Now, multiply by \(10^6\):

\[ \text{ppm} = 2 \times 10^{-9} \times 10^6 = 2 \times 10^{-3} \]

### Step 5: Write the final answer
Thus, the concentration of carbon in air is:

\[ \text{ppm} = 2 \times 10^{-3} \text{ ppm} \]

### Summary
The concentration of carbon in air is \(2 \times 10^{-3}\) ppm.

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