Question

If the concentration of `"SO"_2` in air is `"0.5 ppm"`, what is the percent by mass?

Answer 1

`0.00005%` `"w/w"` `"SO"_2` in `"air"`

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This is basically a unit conversion. One way of defining a part-per-million, or `"ppm"`, is:

`"ppm" = "mg"/"kg"`

since there are `"1000 mg"` in a `"g"` and `"1000 g"` in a `"kg"`. In this case, you have:

`("0.5 mg SO"_2)/("kg air")`

The percent by weight, or weight percent, or `"wt%"`, or `"%w/w"`, is defined as:

`"%w/w" = (m_("component"))/(m_"total") xx 100%`,

where `m` is the mass in a given unit, such as `"g"` or `"mg"`, as long as both masses have the same units.

We just need to convert one of the units to the other. As the name suggests, `"1 kg"` is `1000000` times as large (physically) as `"1 mg"`. So, in a sense, a `"ppm"` is like a "percent", but `10000` times smaller (physically).

In other words, a `"ppm"` ("parts per million") is numerically `10000` times the weight percent, or a "parts per hundred", or there are `"10000 ppm"` for every `%`.

`"0.5 parts per million" xx ("1 part per hundred")/("10000 parts per million")`

`= color(blue)(0.00005% "w/w SO"_2 " in air")`