The units of parts per million (ppm) and parts per billion (ppb) are commonly used by environmental chemists. In general, 1 ppm means 1 part of solute for every 106 parts of solution. (Both solute and solution are measured using the same units.) Mathematically, by mass, ppm can be expressed as shown below.

ppm = µg solute/ g solution = mg solute/ kg solution

In the case of very dilute aqueous solutions, a concentration of 1.0 ppm is equal to 1.0 µg of solute per 1.0 mL of solution, which equals 1.0 g of solution. Parts per billion is defined in a similar fashion. Calculate the molarity of each of the following aqueous solutions.

(a) 4.9 ppb Hg in H2O

__M

(b) 1.8 ppb CHCl3 in H2O

__M

(c) 33.0 ppm As in H2O

__M

(d) 0.28 ppm DDT (C14H9Cl5) in H2O

__M

I have another unit I use. 1 ppm = 1 mg solute/1 L solution and

1 ppb = 1 ug solute/1 L solution.
a, So 4.9 ppb Hg = 4.9 ug Hg/L
Convert ug Hg to grams Hg.
Convert g Hg to mols Hg and since mols/L is the definition of M that is it.

The others are done the same way. Post your work if you get stuck.

Knock, knock!

Who's there?

Molarity.

Molarity who?

Molarity, the answer to your question! Let's calculate it together.

(a) 4.9 ppb Hg in H2O:

To convert ppb to Molarity, we need to know the molar mass of Hg. Assuming it's 200.59 g/mol, we can calculate:

4.9 ppb Hg = 4.9 µg Hg / 1 mL H2O

Now, we need to convert µg to grams and mL to liters to get the Molarity:

4.9 µg Hg = 4.9 x 10^-9 g Hg
1 mL = 1 x 10^-6 L

Molarity = (4.9 x 10^-9 g Hg) / (1 x 10^-6 L H2O) / (200.59 g/mol Hg)

Molarity = 2.45 x 10^-14 mol/L

(b) 1.8 ppb CHCl3 in H2O:

Similarly, let's convert ppb to Molarity:

1.8 ppb CHCl3 = 1.8 µg CHCl3 / 1 mL H2O

Converting units:

1.8 µg CHCl3 = 1.8 x 10^-9 g CHCl3
1 mL = 1 x 10^-6 L

Molarity = (1.8 x 10^-9 g CHCl3) / (1 x 10^-6 L H2O) / (119.38 g/mol CHCl3)

Molarity = 1.5 x 10^-14 mol/L

(c) 33.0 ppm As in H2O:

Converting ppm to Molarity:

33.0 ppm As = 33.0 mg As / 1 L H2O

Molarity = (33.0 mg As) / (1 L H2O) / (74.92 g/mol As)

Molarity = 4.40 x 10^-4 mol/L

(d) 0.28 ppm DDT (C14H9Cl5) in H2O:

Converting ppm to Molarity:

0.28 ppm DDT = 0.28 mg DDT / 1 L H2O

Molarity = (0.28 mg DDT) / (1 L H2O) / (354.49 g/mol DDT)

Molarity = 7.9 x 10^-7 mol/L

I hope that helps! Let me know if you need any more assistance with your chemistry calculations.

To calculate the molarity of each of the given aqueous solutions, we need to convert the given ppm or ppb values to moles of solute. Then, we can use the volume of the solution to calculate the molarity. Let's solve each case step-by-step.

(a) 4.9 ppb Hg in H2O:
To convert ppb to moles, we need to know the molar mass of Hg. Hg has a molar mass of 200.59 g/mol.

1 ppb means 1 part of solute for every 10^9 parts of solution.
Therefore, 4.9 ppb means 4.9 parts of solute for every 10^9 parts of solution.

Let's assume we have 1.0 L of solution (1000 mL), which is equal to 1000 g (since 1 mL of water has a mass of approximately 1 g).

The mass of Hg in 1.0 L of solution = (4.9/10^9) * 1000 g = 4.9 * 10^-6 g

To convert the mass of Hg to moles, we divide by the molar mass:
Moles of Hg = (4.9 * 10^-6 g) / (200.59 g/mol) = 2.44 * 10^-8 mol

Now, we can calculate the molarity:
Molarity = Moles of solute / Volume of solution in liters
Molarity = (2.44 * 10^-8 mol) / 1.0 L = 2.44 * 10^-8 M

So, the molarity of 4.9 ppb Hg in H2O is approximately 2.44 * 10^-8 M.

(b) 1.8 ppb CHCl3 in H2O:
Using the same process as before:

ppb means parts per billion, so 1.8 ppb means 1.8 parts of solute for every 10^9 parts of solution.

Let's assume we have 1.0 L of solution (1000 mL), which is equal to 1000 g.

The mass of CHCl3 in 1.0 L of solution = (1.8/10^9) * 1000 g = 1.8 * 10^-6 g

To convert the mass of CHCl3 to moles, we divide by the molar mass of CHCl3:
Moles of CHCl3 = (1.8 * 10^-6 g) / (119.38 g/mol) = 1.51 * 10^-8 mol

Molarity = Moles of CHCl3 / Volume of solution in liters
Molarity = (1.51 * 10^-8 mol) / 1.0 L = 1.51 * 10^-8 M

So, the molarity of 1.8 ppb CHCl3 in H2O is approximately 1.51 * 10^-8 M.

(c) 33.0 ppm As in H2O:
Similarly:

ppm means parts per million, so 33.0 ppm means 33.0 parts of solute for every 10^6 parts of solution.

Let's assume we have 1.0 L of solution (1000 mL), which is equal to 1000 g.

The mass of As in 1.0 L of solution = (33.0/10^6) * 1000 g = 33.0 * 10^-3 g

To convert the mass of As to moles, we divide by the molar mass of As:
Moles of As = (33.0 * 10^-3 g) / (74.92 g/mol) = 4.40 * 10^-4 mol

Molarity = Moles of As / Volume of solution in liters
Molarity = (4.40 * 10^-4 mol) / 1.0 L = 4.40 * 10^-4 M

So, the molarity of 33.0 ppm As in H2O is approximately 4.40 * 10^-4 M.

(d) 0.28 ppm DDT (C14H9Cl5) in H2O:
Once again:

ppm means parts per million, so 0.28 ppm means 0.28 parts of solute for every 10^6 parts of solution.

Let's assume we have 1.0 L of solution (1000 mL), which is equal to 1000 g.

The mass of DDT in 1.0 L of solution = (0.28/10^6) * 1000 g = 0.28 * 10^-3 g

To convert the mass of DDT to moles, we divide by the molar mass of DDT:
Moles of DDT = (0.28 * 10^-3 g) / (354.49 g/mol) = 7.90 * 10^-7 mol

Molarity = Moles of DDT / Volume of solution in liters
Molarity = (7.90 * 10^-7 mol) / 1.0 L = 7.90 * 10^-7 M

So, the molarity of 0.28 ppm DDT (C14H9Cl5) in H2O is approximately 7.90 * 10^-7 M.

To calculate the molarity of the given aqueous solutions, we first need to convert the given concentrations from ppm/ppb to grams per liter (g/L). Once we have the concentration in g/L, we can use the molarity formula to calculate the molarity.

Molarity (M) is defined as moles of solute divided by liters of solution:

M = moles of solute / liters of solution

To convert the concentration from ppm or ppb to g/L, we can use the following conversions:

1 ppm = 1 mg/L = 1 x 10^-3 g/L
1 ppb = 1 µg/L = 1 x 10^-6 g/L

(a) 4.9 ppb Hg in H2O:

To convert ppb to g/L, we multiply the given concentration by the conversion factor:

4.9 ppb = 4.9 x 10^-6 g/L

Now we can calculate the molarity. However, we need the molar mass of Hg to convert grams to moles. The molar mass of Hg is 200.59 g/mol.

Molar mass of Hg = 200.59 g/mol

To convert g/L to moles/L, we divide the concentration in g/L by the molar mass of Hg:

Molarity (M) = (4.9 x 10^-6 g/L) / (200.59 g/mol) = 2.44 x 10^-8 mol/L

Therefore, the molarity of this aqueous solution is 2.44 x 10^-8 M.

(b) 1.8 ppb CHCl3 in H2O:

Using the same process as before:

1.8 ppb = 1.8 x 10^-6 g/L

To calculate the molarity, we need the molar mass of CHCl3, which is 119.37 g/mol.

Molar mass of CHCl3 = 119.37 g/mol

Molarity (M) = (1.8 x 10^-6 g/L) / (119.37 g/mol) = 1.51 x 10^-8 mol/L

The molarity of this aqueous solution is 1.51 x 10^-8 M.

(c) 33.0 ppm As in H2O:

To convert ppm to g/L, we use the conversion factor:

33.0 ppm = 33.0 x 10^-3 g/L

We need the molar mass of As, which is 74.92 g/mol.

Molar mass of As = 74.92 g/mol

Molarity (M) = (33.0 x 10^-3 g/L) / (74.92 g/mol) = 4.40 x 10^-4 mol/L

The molarity of this aqueous solution is 4.40 x 10^-4 M.

(d) 0.28 ppm DDT (C14H9Cl5) in H2O:

Using the same process as before:

0.28 ppm = 0.28 x 10^-3 g/L

We need the molar mass of DDT (C14H9Cl5), which is 354.55 g/mol.

Molar mass of DDT (C14H9Cl5) = 354.55 g/mol

Molarity (M) = (0.28 x 10^-3 g/L) / (354.55 g/mol) = 7.89 x 10^-7 mol/L

The molarity of this aqueous solution is 7.89 x 10^-7 M.