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 sodium sulfate (Na₂SO₄) in parts per million (ppm) when 14.2 g is dissolved in 10² kg of water, we can follow these steps:

### Step 1: Convert the mass of Na₂SO₄ to kilograms
Since ppm is typically expressed in terms of kilograms, we first convert the mass of Na₂SO₄ from grams to kilograms.

\[ \text{Mass of Na}_2\text{SO}_4 = 14.2 \, \text{g} = \frac{14.2}{1000} \, \text{kg} = 0.0142 \, \text{kg} \]

### Step 2: Determine the total mass of the solution
The total mass of the solution is the mass of the solute (Na₂SO₄) plus the mass of the solvent (water). Since we have 10² kg of water, we can express this as:

\[ \text{Mass of water} = 10^2 \, \text{kg} = 100 \, \text{kg} \]

The total mass of the solution is:

\[ \text{Total mass} = \text{Mass of Na}_2\text{SO}_4 + \text{Mass of water} = 0.0142 \, \text{kg} + 100 \, \text{kg} = 100.0142 \, \text{kg} \]

### Step 3: Calculate the concentration in ppm
The formula for concentration in ppm is given by:

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

Substituting the values we have:

\[ \text{ppm} = \left( \frac{0.0142 \, \text{kg}}{100.0142 \, \text{kg}} \right) \times 10^6 \]

### Step 4: Perform the calculation
Calculating the fraction:

\[ \frac{0.0142}{100.0142} \approx 0.000142 \]

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

\[ \text{ppm} = 0.000142 \times 10^6 = 142 \, \text{ppm} \]

### Final Answer
Thus, the concentration of Na₂SO₄ in water is:

\[ \text{Concentration} = 142 \, \text{ppm} \]