At a given temperature and a constant partial pressure, the mole...

According to Henry's law, the partial pressure of a gas over a solution is given by $p = K_H x$, where $K_H$ is Henry's law constant and $x$ is the mole fraction of the gas in the solution.

At a constant partial pressure, $K_H$ is inversely proportional to the mole fraction $x$, i.e., $K_H \propto \dfrac{1}{x}$.

The given mole fractions are:
$x_P = 2 \times 10^{-3}$
$x_Q = 5 \times 10^{-4} = 0.5 \times 10^{-3}$
$x_R = 1 \times 10^{-2} = 10 \times 10^{-3}$
$x_S = 8 \times 10^{-5} = 0.08 \times 10^{-3}$

The increasing order of mole fractions is $x_S < x_Q < x_P < x_R$.

Therefore, the increasing order of Henry's law constants is the reverse of the mole fraction order:
$\mathrm{R} < \mathrm{P} < \mathrm{Q} < \mathrm{S}$

Answer: $\mathrm{R} < \mathrm{P} < \mathrm{Q} < \mathrm{S}$