ppm & ppb
Measuring Trace Concentrations | Basic Concepts of Chemistry
1. Why ppm and ppb?
Common concentration terms like Molarity ($M$) or Percentage ($\%$) are convenient for solutions with significant amounts of solute. However, when the solute is present in very minute quantities (trace amounts), such as pollutants in air or hardness in water, these units become cumbersome (e.g., 0.000005 M).
2. Parts per Million (ppm)
ppm represents the number of parts of the solute present in one million ($10^6$) parts of the solution.
Alternative Forms:
- By Volume (v/v): Use volume of solute and solution.
- For Dilute Aqueous Solutions: Since density of water $\approx 1 \text{ g/mL}$ ($1 \text{ kg} = 1 \text{ L}$): $$ 1 \text{ ppm} \approx 1 \text{ mg/L} \approx 1 \text{ mg/kg} $$
3. Parts per Billion (ppb)
ppb represents the number of parts of the solute present in one billion ($10^9$) parts of the solution. It is used for extremely trace contaminants.
Relation with ppm:
$$ 1 \text{ ppm} = 1000 \text{ ppb} $$4. Important Conversions
Relation with Mass Percent (% w/w)
Since $\% (w/w)$ is parts per 100:
$$ 1 \% = 10,000 \text{ ppm} $$ $$ x \% = x \times 10^4 \text{ ppm} $$Applications
- Water Hardness: Expressed in ppm of $CaCO_3$.
- Air Pollution: Pollutants like $SO_2$ expressed in $\mu g/m^3$ or ppm.
- Toxicology: Concentration of heavy metals (Lead, Mercury) in food/blood.
5. Worked Example
Question: A 500g sample of toothpaste contains 0.2g of Fluoride. Calculate the concentration in ppm.
Solution:
$$ \text{ppm} = \frac{\text{Mass Solute}}{\text{Mass Solution}} \times 10^6 $$ $$ \text{ppm} = \frac{0.2}{500} \times 10^6 $$ $$ \text{ppm} = \frac{200,000}{500} = 400 \text{ ppm} $$Practice Quiz
Test your ability to handle trace concentrations.
Really, content is more appreciable
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