Q.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):

Take a convenient $1\ \text{kg}$ ($1000\ \text{g}$) sample of the water solution.

1. Percent by mass. $15$ ppm means $15$ parts per million by mass, i.e. $15\ \text{g}$ of chloroform per $10^{6}\ \text{g}$ of solution.

   $\%\ \text{by mass} = \frac{15}{10^{6}} \times 100 = 1.5 \times 10^{-3}\ \%$

2. Molality. In $1000\ \text{g}$ of solution the mass of chloroform is

   $15\ \text{ppm} = \frac{0.015\ \text{g}}{1000\ \text{g of solution}}$

   so the sample holds $0.015\ \text{g}$ of $\mathrm{CHCl_3}$, and the mass of water is essentially $1000\ \text{g} = 1\ \text{kg}$. $M(\mathrm{CHCl_3}) = 12 + 1 + 3(35.5) = 119.5\ \text{g mol}^{-1}$ …

Step 1 — Read what "ppm by mass" means.

Parts per million by mass tells us the mass of solute present in every $10^{6}$ mass units of solution. So $15$ ppm means

Step 2 — (i) Convert to percent by mass.

Percent by mass is parts per hundred, so multiply the mass fraction by $100$:

Step 3 — Choose a convenient sample size for molality.

Molality needs moles of solute per kilogram of solvent. Take $1\ \text{kg} = 1000\ \text{g}$ of the solution. Scaling the ppm ratio down to this $1000\ \text{g}$ sample:

Since the chloroform is only a trace contaminant, the mass of water (the solvent) is essentially the whole sample:

Step 4 — Moles of chloroform.

The molar mass of $\mathrm{CHCl_3}$ is …

Method: Parts Per Million (ppm) to Mass Percentage and Molality Conversion

This problem uses two key concepts: ppm as a ratio and molality definition.

Step 1 — Understand what 15 ppm means

15 ppm (by mass) means:

15 grams of chloroform per $10^6$ grams of solution.

So we write:

Step 2 — Express as percent by mass

Percent by mass is:

Substitute:

Answer (i): $\boxed{1.5 \times 10^{-3} \%}$

Step 3 — Find molar mass of chloroform ($CHCl_3$)

Atomic masses:

• C = 12
• H = 1
• Cl = 35.5

Step 4 — Calculate molality

Molality ($m$) is:

Moles of chloroform:

Mass of solvent (water):

Since the solution mass is $10^6$ g and solute is 15 g: …

Here are the common mistakes students make when solving this Mass Percentage and Molality problem, along with clear strategies to avoid each.

Mistake 1: Confusing ppm with a direct percentage

The Error:

Students often think 15 ppm means 15% or they try to convert by simply moving the decimal (e.g., writing 0.15% or 1.5%).

Why it happens:

They don’t internalise that ppm = parts per million = $\frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$. Percent is per hundred, so the conversion factor is $10^4$ (since $10^6 / 10^2 = 10^4$).

How to avoid:

Always write the definition first:

Then convert to percent:

So for 15 ppm:

Key check: 15 ppm is a tiny amount — your answer should be a very small percentage (not 0.15% or 15%).

Mistake 2: Using the wrong molar mass for chloroform ($CHCl_3$)

The Error:

Students mis-count atoms — e.g., forgetting there are 3 chlorine atoms, or using atomic mass of carbon as 12.0 instead of 12.01 (though for this problem, 12 is acceptable if the exam allows rounding).

Why it happens:

Rushing through the formula without careful counting.

How to avoid:

Write the atomic masses clearly:

• C = 12.01 g/mol
• H = 1.008 g/mol
• Cl = 35.45 g/mol

Then sum:

Round to 119.4 g/mol for most exam purposes.

Mistake 3: Assuming 15 ppm means 15 g of solute in $10^6$ g of water (instead of solution)

The Error:

Students take the solvent mass as exactly $10^6$ g and ignore the solute mass when calculating molality.

Why it happens:

They confuse ppm by mass (solute/solution) with a ratio involving only the solvent.

How to avoid:

Remember:

• ppm by mass = $\frac{\text{mass solute}}{\text{mass solution}} \times 10^6$
• Molality = $\frac{\text{moles solute}}{\text{mass of solvent (in kg)}}$

For dilute solutions (like 15 ppm), the mass of solute is negligible compared to solvent, so you can approximate:

Mass of solution ≈ mass of solvent

But always state this approximation in your solution.

Mistake 4: Forgetting to convert solvent mass to kilograms for molality

The Error:

Using grams instead of kg in the denominator of molality.

Why it happens:

Molality is defined as moles per kg of solvent, but students plug in grams.

How to avoid:

Write the formula every time:

If you have mass in grams, divide by 1000.

Mistake 5: Incorrect unit handling in the molality calculation

The Error: …