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 need to understand the relationship between mass and volume in the context of a solution.
1 mg/L and 1 ppm equivalence:
- mg/L: This represents the mass of a substance (in milligrams) dissolved in a volume of solution (in liters). Therefore, 1 mg/L means there is 1 milligram of a substance in every liter of solution.
- ppm (parts per million): This is a way to express the concentration of a substance in a solution. It means that for every 1 million parts of solution, there is 1 part of the substance. The units of ppm can be mass/volume or volume/volume, but in the case of solutions where the solvent is primarily water, the mass of the solvent is approximately the same as the mass of water (1 liter of water is close to 1 kilogram).
Converting mg/L to ppm:
- 1 milligram (mg) is equal to 0.001 grams (g) because: 1 mg=0.001 g1 \, \text{mg} = 0.001 \, \text{g}1mg=0.001g
- 1 liter (L) of water is approximately 1 kilogram (kg), which is equivalent to 1,000 grams (g).
- So, 1 mg of solute in 1 liter of water can be expressed as: 1 mg1 L=0.001 g1 L\frac{1 \, \text{mg}}{1 \, \text{L}} = \frac{0.001 \, \text{g}}{1 \, \text{L}}1L1mg=1L0.001g
- Since we know that 1 ppm is equivalent to 1 mg of solute in 1 liter of solution (in the case of water), we can conclude that 1 mg/L is equal to 1 ppm.
This is because in solutions where water is the solvent, 1 mg of solute in 1 liter of solution corresponds to 1 part per million (ppm).
Conclusion:
Thus, 1 mg/L is indeed equal to 1 ppm for most aqueous solutions, particularly when the solvent is water. This equivalence holds because the mass of 1 liter of water is nearly 1,000 grams, so the ratio of the mass of solute to the mass of solution in mg/L is the same as the ratio expressed in ppm
