500 ml of sample COD of water required 19.6 mg of `K_(2)Cr_(2)O_(7)` of water sample is

Options

A. 8 ppm
B. 6.4 ppm
C. 16.8 ppm
D. 4.9 ppm

Explanation

To calculate the Chemical Oxygen Demand (COD) of the water sample, we can follow these steps:

### Step 1: Understand the Given Information
- Volume of water sample = 500 ml
- Mass of K₂Cr₂O₇ used = 19.6 mg
- Molecular weight of K₂Cr₂O₇ = 294 g/mol

### Step 2: Convert the Mass of K₂Cr₂O₇ to Grams
Since the mass is given in milligrams, we need to convert it to grams:
\[ 19.6 \, \text{mg} = \frac{19.6}{1000} \, \text{g} = 0.0196 \, \text{g} \]

### Step 3: Calculate Moles of K₂Cr₂O₇
Using the molecular weight, we can find the number of moles of K₂Cr₂O₇:
\[ \text{Moles of K₂Cr₂O₇} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{0.0196 \, \text{g}}{294 \, \text{g/mol}} \]
Calculating this gives:
\[ \text{Moles of K₂Cr₂O₇} = 6.67 \times 10^{-5} \, \text{mol} \]

### Step 4: Determine Moles of Nascent Oxygen Produced
From the balanced reaction, we know that 1 mole of K₂Cr₂O₇ produces 3 moles of nascent oxygen. Therefore, the moles of nascent oxygen produced are:
\[ \text{Moles of nascent oxygen} = 3 \times \text{Moles of K₂Cr₂O₇} = 3 \times 6.67 \times 10^{-5} \, \text{mol} \]
Calculating this gives:
\[ \text{Moles of nascent oxygen} = 2.00 \times 10^{-4} \, \text{mol} \]

### Step 5: Convert Moles of Nascent Oxygen to Grams
The molar mass of oxygen (O) is approximately 16 g/mol. Therefore, the mass of nascent oxygen produced is:
\[ \text{Mass of nascent oxygen} = \text{Moles} \times \text{Molar mass} = 2.00 \times 10^{-4} \, \text{mol} \times 16 \, \text{g/mol} \]
Calculating this gives:
\[ \text{Mass of nascent oxygen} = 0.0032 \, \text{g} = 3.2 \, \text{mg} \]

### Step 6: Calculate COD for 1000 ml
Since the 3.2 mg of nascent oxygen corresponds to the 500 ml sample, we can find the COD for 1000 ml:
\[ \text{COD for 1000 ml} = \frac{3.2 \, \text{mg}}{500 \, \text{ml}} \times 1000 \, \text{ml} = 6.4 \, \text{mg} \]

### Conclusion
The Chemical Oxygen Demand (COD) of the water sample is **6.4 mg**.