The chemical formula for ammonium carbonate is #("NH"_4)_2"CO"_3"#. The formula indicates that in one mole of ammonium carbonate, there are two moles of ammonium ions, #"NH"_4"^+#.
To calculate moles of ammonium ions, requires two steps.
First determine moles #("NH"_4")"_2"CO"_3# in #"26.9 g (NH"_4")"_2"CO"_3# by multiplying by the inverse of its molar mass, #"96.086 g/mol"#.
#26.9color(red)cancel(color(black)("g (NH"_4")"_2"CO"_3))xx(1"mol (NH"_4")"_2"CO"_3)/(96.086color(red)cancel(color(black)("g (NH"_4")"_2"CO"_3)))="0.280 mol (NH"_4")"_2"CO"_3"#
Next determine the mol #"NH"_4"^+# in the sample, by multiplying mol #("NH"_4")"_2"CO"_3# by the mole ratio of #"NH"_4"^+# and #("NH"_4")"_2"CO"_3#.
#0.280color(red)cancel(color(black)("mol (NH"_4")"_2"CO"_3))xx(2"mol NH"_4^+)/(1color(red)cancel(color(black)("mol (NH"_4")"_2"CO"_3)))="0.560 NH"_4"^+#
rounded to three sig figs
