How to calculate the gas constant of saturated moist air at 16 degree Celsius and 1.013 bar?
I'm not sure where to go with this. I just know that the saturated vapor pressure from steam tables, at 16 degree Celsius is 0.018173 bar. Is this data even useful for calculating the gas constant?
$$R=\frac{N_A \, k_B}{M}$$ with specific gas constant $R$, Avogadro number $N_A$, Boltzmann constant $k_B$ and molar mass $M$.
For a mixture of ideal gases (remembering $pV = N k_B T$): $$x_i = \frac{N_i}{N} = \frac{p_i}{p}$$ with pressure $p$, volume $V$, number of molecules $N$, temperature $T$ and mole fraction $x$. Indices refer to individual species, non-indexed values are for the mixture: $p_{\mathrm{Water}}$ = water partial gas pressure, $p$ = total pressure. Remember that $V_i=V$ and $T_i=T$ for mixtures.
Finally (see Wikipedia), $$M =\sum_j \, x_j \, M_j$$
You have $p_{\mathrm{Water}}$ and $p$, which allows you to calculate $p_{\mathrm{Air}}$ (the difference), all $x_i$, then $M$ and finally $R$.
