14.2 g `Na_2SO_4` is present in `10^2` kg water. Its concentration in ppm is

Options

A. 10 ppm
B. 100 ppm
C. 142 ppm
D. 14.2 ppm

Answer

To find the concentration of \( \text{Na}_2\text{SO}_4 \) in parts per million (ppm), we can follow these steps:

### Step 1: Convert the mass of the solute to kilograms
The mass of \( \text{Na}_2\text{SO}_4 \) is given as 14.2 grams. To convert this to kilograms:
\[ \text{Mass in kg} = \frac{14.2 \, \text{g}}{1000} = 0.0142 \, \text{kg} \]

### Step 2: Identify the total mass of the solution
The total mass of the solution is the mass of water, which is given as \( 10^2 \) kg, or 100 kg.

### Step 3: Use the formula for concentration in ppm
The formula for concentration in ppm is:
\[ \text{ppm} = \left( \frac{\text{mass of solute in kg}}{\text{total mass of solution in kg}} \right) \times 10^6 \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
\[ \text{ppm} = \left( \frac{0.0142 \, \text{kg}}{100 \, \text{kg}} \right) \times 10^6 \]

### Step 5: Calculate the concentration in ppm
Calculating the above expression:
\[ \text{ppm} = \left( 0.000142 \right) \times 10^6 = 142 \, \text{ppm} \]

### Final Answer
The concentration of \( \text{Na}_2\text{SO}_4 \) in the solution is **142 ppm**.

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