It was found that 20ml of water `(d = 1 (gm)/(ml))` sample contains
0.5 mg of free chlorine. What is concentration of chlorine in ppm.

Answer

To find the concentration of chlorine in parts per million (ppm), we can follow these steps:

### Step 1: Identify the mass of the solute (chlorine)
We are given that the sample contains 0.5 mg of free chlorine. To work with consistent units, we convert milligrams to grams:
\[ \text{Mass of chlorine} = 0.5 \, \text{mg} = 0.5 \times 10^{-3} \, \text{g} \]

### Step 2: Identify the mass of the solution (water)
We are given that the volume of water is 20 ml and the density of water is 1 g/ml. Therefore, the mass of the water can be calculated as:
\[ \text{Mass of water} = \text{Volume} \times \text{Density} = 20 \, \text{ml} \times 1 \, \text{g/ml} = 20 \, \text{g} \]

### Step 3: Calculate the concentration in ppm
The formula for parts per million (ppm) is given by:
\[ \text{ppm} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 10^6 \]
Substituting the values we have:
\[ \text{ppm} = \left( \frac{0.5 \times 10^{-3} \, \text{g}}{20 \, \text{g}} \right) \times 10^6 \]

### Step 4: Simplify the expression
Calculating the fraction:
\[ \text{ppm} = \left( \frac{0.5 \times 10^{-3}}{20} \right) \times 10^6 = \left( \frac{0.5}{20} \times 10^{3} \right) \]
\[ = \left( \frac{1}{40} \times 10^{3} \right) \]

### Step 5: Calculate the final value
Calculating \( \frac{1}{40} \):
\[ \frac{1}{40} = 0.025 \]
Now multiply by \( 10^{3} \):
\[ 0.025 \times 10^{3} = 25 \]

### Final Answer
Thus, the concentration of chlorine in ppm is:
\[ \text{Concentration of chlorine} = 25 \, \text{ppm} \]

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