(a) Vapour pressure of water
SATP is defined as 25 °C (298.15 K) and 1 bar.
At 25 °C, the vapor pressure of water is 3.17 kPa = 0.0317 bar,
(b) of hydrogen
Per Dalton's Law of Partial Pressures,
$P_"H₂" + P_"H₂O" = P_"atm"$
$P_"H₂" = P_"atm" - P_"H₂O" = "1 bar - 0.0317 bar" = "0.9683 bar"$
(c) Amount of hydrogen
$PV = nRT$
$n= (PV)/(RT) = (0.9683 color(red)(cancel(color(black)("bar"))) × 0.500 color(red)(cancel(color(black)("L"))))/("0.083 14" color(red)(cancel(color(black)("bar·L·K"^"-1")))"mol"^"-1" × 298.15 color(red)(cancel(color(black)("K")))) = "0.0199 mol"$