Water-Quality Unit Conversions
Comparing a measured water-quality result against a prescribed safety limit is almost always a units problem in disguise — the raw measurement and the legal limit are often given in different units, and converting everything to the same basis is the entire task.
Converting Water-Quality Units to Compare Against Drinking-Water Limits is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Converting between g/m₃, mg/dm₃, mg/mL, ppm and ppb for dilute aqueous solutions
For dilute aqueous solutions (where the solution density is essentially that of water, about 1 kg/L), several common concentration units become numerically interchangeable once correctly converted: 1 mg/dm₃ = 1 mg/L = 1 ppm (parts per million, since 1 L of water weighs about 1 kg = 10⁶ mg, so 1 mg dissolved in it is 1 part per 10⁶). Converting other units to this common mg/dm₃ (= ppm) basis: 1 g/m₃ = 1 mg/dm₃ directly (since 1 m₃ = 1000 dm₃, so 1 g/1000 dm₃ = 1 mg/dm₃);
and ppb (parts per billion) is 1000 times smaller than ppm, so a ppb value divides by 1000 to convert to ppm. Converting every given concentration to the same mg/dm₃ (ppm) basis is the essential first step before any comparison against a prescribed limit can be made correctly.
Comparing each converted value against its prescribed limit one at a time
Once every concentration is on the same basis, compare each one individually against its own limit — do not average them or apply one pass/fail judgement to the whole sample at once. A concentration sitting exactly at a prescribed limit is not in excess of it, since excess means strictly greater than the limit; a concentration converted to ppm is a perfectly valid, checkable numerical fact in its own right, independent of whether that particular metal happens to be within or outside its limit; and a sample is only genuinely potable if EVERY measured contaminant is within its own limit — a single contaminant exceeding its limit, even while others are comfortably within range, makes the whole sample non-potable. Reading this kind of question means doing the full unit conversion for every species given, not just the one the question seems to be hinting at.
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- ✓For dilute aqueous solutions: 1 mg/dm₃ = 1 mg/L = 1 ppm
- ✓1 g/m₃ = 1 mg/dm₃; 1 microgram/mL = 1 mg/dm₃; 1 ppb = 0.001 ppm
- ✓A concentration exactly at the prescribed limit is not in excess of it — excess means strictly greater
- ✓A sample is potable only if EVERY measured contaminant is within its own limit, not just most of them
- ✓Convert every species to the same unit basis before making any comparison or potability judgement
Do not compare a raw measured value directly against a prescribed limit without first converting both to the same unit. A value given in g/m₃, micrograms/mL, ppm and ppb can only be compared meaningfully once every one of them is converted to a single common basis, like mg/dm₃.
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