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Q1.9 (i):
A sample of drinking water was found to be severely contaminated with chloroform (\(CHCl_{3}\)) supposed to be a carcinogen. The level of contamination was 15 ppm (by mass): (i) express this in percent by mass

Solution :

Step 1: Understanding the Definition of Parts Per Million (ppm)

The concentration of a solute in parts per million (ppm) is defined as the number of parts of the solute present in one million parts of the total solution by mass. Mathematically, this is expressed as:

$\text{ppm} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 10^6$ [Per the definition of mass-based concentration units in dilute solutions]

Step 2: Identifying the Given Variables

  • $\text{Concentration of } CHCl_{3} = 15 \text{ ppm}$
  • $\text{Target Unit: Percent by mass } (\% w/w)$

Step 3: Deriving the Conversion Factor

Percent by mass is defined as the mass of the solute per $100$ grams of solution:

$\text{Percent by mass} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100$

By comparing the two definitions, we can derive the relationship:

$\text{Percent by mass} = \frac{\text{ppm}}{10^6} \times 100$

Simplifying the exponent expression: [By the laws of indices $\frac{a^m}{a^n} = a^{m-n}$]

$\text{Percent by mass} = \frac{\text{ppm}}{10^4}$

Step 4: Performing the Calculation

Substitute the given value of $15 \text{ ppm}$ into the derived equation:

$\text{Percent by mass} = \frac{15}{10^4}$

$\text{Percent by mass} = 15 \times 10^{-4} \%$

$\text{Percent by mass} = 0.0015 \%$

Visual Representation of Concentration

15 parts 999,985 parts Mass of CHCl₃ Mass of Solvent (Water) Total Solution = 1,000,000 parts

Final Solution: The concentration of chloroform in the drinking water expressed as percent by mass is $1.5 \times 10^{-3} \%$ or $0.0015 \%$ (w/w).


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