Relative humidity is a ratio to a target that moves. The humidity ratio is not: it is a straight count of water, and heating the air does not change it by a gram.

$W = 0.62198\,\dfrac{p_v}{p - p_v}$ — read aloud W equals oh-point-six-two-one-nine-eight, p-v over p minus p-v. $W$ is the humidity ratio, kilograms of water vapour per kilogram of dry air; the trade quotes it in g/kg, and 9 g/kg is ordinary comfort air. $p_v$ is the water vapour's partial pressure in kilopascals, and $p$ is the total barometric pressure in the same units. Both pressures must wear the same unit; the ratio then cancels it.

Two things in that formula earn their keep. The 0.62198 is not a fudge factor — it is $M_{water}/M_{air} = 18.015/28.964$, the ratio of molar masses. Dalton's law counts MOLECULES and the humidity ratio counts KILOGRAMS, and that number is precisely the exchange rate between the two counts. And the denominator is $p - p_v$, not $p$: W is water per kilogram of DRY air, so what it is divided by is the dry air's own partial pressure. Use $p$ and you have quietly switched to a per-kilogram-of-mixture basis that nothing else in this chapter uses.

Here is why the trade reasons in W. Outdoor air at −10 °C and 80 % RH carries about 1.7 g/kg. Bring it inside, warm it to 21 °C, add nothing: it still carries 1.7 g/kg — and that is now about 11 % RH. Nothing was removed. The relative humidity fell because its denominator climbed. W never flinched, which is what makes it the honest one.

Units guide, they do not confess. Push them through every rearrangement: a pressure over a pressure leaves a bare ratio, which is what W and $\varphi$ both are. If the units refuse to cancel into the answer's units the rearrangement is WRONG, no appeal — but units that do work out never prove you right. The check runs one way only.