Answer
$0.000589\text{ g/mL}$
Work Step by Step
$PV = nRT$
Here since $n$ =mass(m)/molar mass(M) can solve the above equation to,
$P = \frac{dRT}{M}$ where $d$ is density
$d = \frac{PM}{RT} = \frac{1.00\times 10^{5}Pa \times 18.02\times 10^{-3} \text{ kg mol}^{-1} }{8.314JK^{-1}mol^{-1}\times 373K} \approx 0.000589\text{ g/mL}$
As $0.958>0.000589$, the gas is much less dense than liquid water.
