There's a little shortcut here where you don't need to use:
#PV=nRT#
Since pressure and temperature remain constant, and you know there are half as many moles of #N_2# as there are #H_2O#, then you can determine that the volume of #N_2# produced is half the volume of #H_2O# This only works with constant temperature and pressure with knowledge of the balanced chemical equation.
So you have 25 liters of #N_2#
If you actually want to calculate it:
One mole of gas at STP takes up about 22.4 L of space.
#(50L) / (22.4(L/(mol)))=2.23 mol (H_2O)#
#2.23 mol (H_2O)*(1mol(N_2))/(2mol(H_2O)) = 1.116 mol (N_2)#
STP means #T = 273.15 K# and #P = 1.0 atm#
#R# is the gas constant and for atm it is 0.08206
#V = (nRT)/P#
#V = ((1.12molN_2)(0.08206)(273.15K))/(1.0atm) = 25.0 L (N_2)#
