Two vessels $A$ and $B$ are of the same size and are at same temperature. A contains $1 \mathrm{~g}$ of hydrogen and $B$ contains $1 \mathrm{~g}$ of oxygen. $\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are the pressures of the gases in $\mathrm{A}$ and $\mathrm{B}$ respectively, then $\frac{P_A}{P_B}$ is: