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

Aug 10, 2017

0.00005% $\text{w/w}$ ${\text{SO}}_{2}$ in $\text{air}$

This is basically a unit conversion. One way of defining a part-per-million, or $\text{ppm}$, is:

$\text{ppm" = "mg"/"kg}$

since there are $\text{1000 mg}$ in a $\text{g}$ and $\text{1000 g}$ in a $\text{kg}$. In this case, you have:

$\left(\text{0.5 mg SO"_2)/("kg air}\right)$

The percent by weight, or weight percent, or $\text{wt%}$, or $\text{%w/w}$, is defined as:

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

where $m$ is the mass in a given unit, such as $\text{g}$ or $\text{mg}$, 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, $\text{1 kg}$ is $1000000$ times as large (physically) as $\text{1 mg}$. So, in a sense, a $\text{ppm}$ is like a "percent", but $10000$ times smaller (physically).

In other words, a $\text{ppm}$ ("parts per million") is numerically $10000$ times the weight percent, or a "parts per hundred", or there are $\text{10000 ppm}$ 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")