Using the fact that fresh water has a density of 1000 kg/m3 , show that 5ppm Pb = 5 mg/L Pb .
I assume that is ppm w/v.
5 ppm = 5 g Pb/10^6 g H2O =
5 mg Pb/10^3 g H2O =
5 mg Pb/1000 g H2O =
5 mg Pb/1L H2O if density of H2O is 1.00 g/mL (or 1000 kg/m^)
To show that 5 parts per million (ppm) of lead (Pb) is equal to 5 milligrams per liter (mg/L) of lead, we can use the fact that fresh water has a density of 1000 kg/m3.
Step 1: Understand the meaning of parts per million (ppm):
Parts per million is a unit used to express the concentration of a substance in a solution. It represents one part of the substance per one million parts of the solution.
Step 2: Convert ppm to milligrams per liter (mg/L):
Since 1 ppm represents one part of a substance per one million parts of the solution, we can assume that 1 ppm of lead in water is equal to 1 milligram of lead in one liter of water.
Step 3: Use the density of water to relate mass and volume:
The density of water is given as 1000 kg/m3. We can use this information to convert the mass of lead from milligrams to kilograms and the volume from liters to cubic meters.
1 kg/m3 = 1 mg/L
1000 kg/m3 = 1000 mg/L
Step 4: Apply the conversion factors:
Using the information from Step 3, we can write the following conversion factors:
1 ppm Pb = 1 mg Pb / 1 L water
1000 kg/m3 = 1000 mg/L
Combining these conversion factors, we get:
1 ppm Pb = 1 mg Pb / 1 L water
= 1 mg Pb / 1000 mg/L water
= 1 / 1000 Pb / L water
So, 1 ppm Pb is equivalent to 1/1000 Pb/L, which simplifies to:
1 ppm Pb = 0.001 Pb/L
Since we want to show that 5 ppm Pb = 5 mg/L Pb, we can multiply both sides of the equation by 5:
5 ppm Pb = 5 x 0.001 Pb/L
= 0.005 Pb/L
Therefore, we have shown that 5 ppm Pb is equal to 5 mg/L Pb.
To show that 5 parts per million (ppm) of lead (Pb) is equivalent to 5 milligrams per liter (mg/L) of lead, we need to use the fact that fresh water has a density of 1000 kilograms per cubic meter (kg/m³).
First, let's understand what ppm means. "Parts per million" is a unit used to express the concentration of a substance in a solution. It represents the ratio of the number of parts of the substance to one million parts of the solution. In this case, we are interested in the concentration of lead in fresh water.
To convert ppm to mg/L, we need to understand that 1 mg/L is equivalent to 1 milligram per liter, which means that for every liter of water, there is 1 milligram of lead.
Now, since fresh water has a density of 1000 kg/m³, we can say that 1 cubic meter of fresh water weighs 1000 kilograms. We can also assume that 1 liter of fresh water weighs 1000 grams (since the density of water is very close to 1 g/mL).
So, if we have 5 ppm of lead in fresh water, it means that for every 1 million parts of water, there are 5 parts of lead. Since 1 liter of fresh water weighs 1000 grams (or 1 kilogram), we can convert the ppm to mg/L as follows:
5 ppm of lead = 5 parts of lead per 1 million parts of water
= 5 grams of lead per 1 million grams of water
≈ 5 milligrams of lead per 1 million milligrams of water
= 5 mg of lead per 1 million mg of water
= 5 mg/L of lead
Therefore, we have shown that 5 ppm of lead is equivalent to 5 mg/L of lead based on fresh water's density of 1000 kg/m³.