Show that 1 mg/L is equal to 1 ppm of a solution, which is 1 g/mL.
The Correct Answer and Explanation is:
To show that 1 mg/L is equal to 1 ppm (part per million), we can work through the relationship between mass and volume in a solution.
Step 1: Understanding the relationship between mg and g.
First, note that 1 milligram (mg) is equal to 0.001 grams (g). Therefore:
1 mg=0.001 g1 \, \text{mg} = 0.001 \, \text{g}1mg=0.001g
Step 2: Defining ppm.
One part per million (ppm) represents one part of solute in one million parts of solution. Since ppm is a concentration term, it often describes mass of solute relative to mass of solution, or mass of solute relative to the volume of solution.
For water, which has a density close to 1 g/mL (or 1000 g/L), 1 ppm corresponds to 1 mg of solute per liter of solution. In this case, the concentration is 1 mg of solute in 1 liter of solution.
Step 3: Showing the equivalence.
Now, consider the concentration 1 mg/L:
- 1 mg/L means there is 1 milligram of solute in 1 liter of solution.
- 1 milligram is equal to 0.001 grams.
- Therefore, 1 mg/L is equivalent to 0.001 grams per liter (g/L).
Now, recall that 1 ppm means 1 mg of solute per liter of solution, which is also equal to 0.001 grams per liter (g/L).
Hence, 1 mg/L is indeed equal to 1 ppm, because both represent the same mass of solute (0.001 grams) in the same volume of solution (1 liter).
Conclusion:
Therefore, we have shown that 1 mg/L is equivalent to 1 ppm in a solution, particularly in water where the density is assumed to be 1 g/mL.
