Parts per Billion (ppb) Formula: Worked Examples

🧪 Quick Study Guide

• ⚖️ Parts per billion (ppb) is a way to express very low concentrations.
• ➗ The formula for ppb is: $\text{ppb} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9$
• 💧 The 'solute' is the substance being dissolved, and the 'solution' is the mixture it's dissolved in.
• 🧪 Make sure the units of mass for the solute and solution are the same (e.g., both in grams or both in kilograms).
• 🔢 $1 \text{ ppb}$ is equivalent to $1 \mu g$ of solute per $1 \text{ kg}$ of solution (assuming the density of the solution is approximately $1 \text{ g/mL}$).

🤔 Practice Quiz

1. Question 1: What does 'ppb' stand for?
   1. (A) Parts per base
   2. (B) Parts per billion
   3. (C) Parts per binary
   4. (D) Pascals per bar
2. Question 2: The formula for calculating ppb is:
   1. (A) $\frac{\text{mass of solute}}{\text{mass of solvent}} \times 10^6$
   2. (B) $\frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$
   3. (C) $\frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9$
   4. (D) $\frac{\text{mass of solvent}}{\text{mass of solution}} \times 10^9$
3. Question 3: If you have 5 grams of salt in 1000 kg of water, what is the concentration of salt in ppb?
   1. (A) 5,000 ppb
   2. (B) 500 ppb
   3. (C) 5 ppb
   4. (D) 5,000,000 ppb
4. Question 4: What is the equivalent of 1 ppb?
   1. (A) 1 mg of solute per 1 kg of solution
   2. (B) 1 μg of solute per 1 g of solution
   3. (C) 1 μg of solute per 1 kg of solution
   4. (D) 1 g of solute per 1 kg of solution
5. Question 5: In a solution, the mass of the solute is 2 mg, and the mass of the solution is 2 kg. What is the concentration in ppb?
   1. (A) 1 ppb
   2. (B) 100 ppb
   3. (C) 1,000 ppb
   4. (D) 10 ppb
6. Question 6: A water sample contains 0.004 g of lead in 2000 kg of water. Calculate the concentration of lead in ppb.
   1. (A) 2 ppb
   2. (B) 20 ppb
   3. (C) 2,000 ppb
   4. (D) 20,000 ppb
7. Question 7: If a solution has a concentration of 3,000 ppb, how many grams of solute are present in 500 kg of the solution?
   1. (A) 1.5 g
   2. (B) 0.15 g
   3. (C) 15 g
   4. (D) 0.015 g