Question

A sample of sea water contains $5 \times 10^{-3}$ g of dissolved oxygen in 1 kilogram of the sample. The concentration of O\textsubscript{2} in that sea water sample in ppm is}

• A. $5 \times 10^{-4}$
• B. $5 \times 10^{-3}$
• C. $5 \times 10^{-2}$
• D. $5 \times 10^{-1}$
• E. 5

Hint:

A very convenient shortcut: 1 ppm is equivalent to 1 mg of solute per 1 kg of solution ($1 \text{ mg/kg}$). Since $5 \times 10^{-3} \text{ g} = 5 \text{ mg}$, the answer is simply 5 ppm!

Answer 1

Answer: (E)

Concept: Parts per million (ppm) is a unit of concentration used for very dilute solutions.
• Definition: ppm = $\left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 10^6$.

Step 1: Set up the ratio. Mass of solute ($O_2$) = $5 \times 10^{-3}$ g. Mass of solution (sea water) = 1 kg = 1000 g.

Step 2: Calculate the ppm concentration. \[ \text{ppm} = \frac{5 \times 10^{-3} \text{ g}}{1000 \text{ g}} \times 10^6 \] \[ \text{ppm} = (5 \times 10^{-6}) \times 10^6 \] \[ \text{ppm} = 5 \]