First, write the balanced chemical equation for the equilibrium and set up an ICE table.
#color(white)(XXXXXX)"N"_2 color(white)(X)+color(white)(X)"3H"_2 color(white)(l)⇌ color(white)(l)"2NH"_3#
#"I/atm": color(white)(Xll)1.05 color(white)(XXXl)2.02 color(white)(XXXll)0#
#"C/atm": color(white)(X)-x color(white)(XXX)-3x color(white)(XX)+2x#
#"E/atm": color(white)(l)1.05- x color(white)(X)2.02-3x color(white)(XX)2x#
#P_"tot" = P_"N₂" + P_"H₂" + P_"NH₃" = (1.05-x) " atm" + (2.02–3 x) " atm" + 2x " atm" = "2.02 atm"#
#1.05 – x + color(red)(cancel(color(black)(2.02))) – 3x + 2x = color(red)(cancel(color(black)(2.02)))0#
#P_"H₂" = (2.02 -3x) " atm" = (2.02 – 3×0.525)" atm" = (2.02 – 1.575) " atm" = "0.44 atm"#
The partial pressure of hydrogen is 0.44 atm.