Question

A sample of drinking water has 15 ppm (by mass) of a carcinogen (molar mass 120 g mol\(^{-1}\)). The molality of carcinogen in water sample is:

• A. \(2.50 \times 10^{-4}\)
• B. \(2.50 \times 10^{-3}\)
• C. \(1.25 \times 10^{-4}\)
• D. \(1.25 \times 10^{-3}\)

Hint:

1 ppm = 1 mg per kg of solution. Always convert mg → g before calculating moles.

Answer 1

The Correct Option is C

Step 1: Density formula for a cubic lattice.
ρ = (Z × M)/(N_A × a³), where Z = 2 for bcc.

Step 2: Unit conversion of edge length.
a = 4 Å = 4 × 10⁻⁸ cm, so a³ = 64 × 10⁻²⁴ cm³.

Step 3: Plugging in the values.
10 = (2 × M)/(6.022×10²³ × 64×10⁻²⁴).

Step 4: Simplifying the denominator.
6.022×10²³ × 6.4×10⁻²³ ≈ 38.53.

Step 5: Determining M.
10 = (2M)/38.53 → M = (10×38.53)/2 ≈ 192 g mol⁻¹.

Step 6: Conclusion.
The molar mass of the element is approximately 192 g mol⁻¹.