(a) #"% P"#
Step 1. Calculate the mass of #"P"# in the precipitate
#"Mass of P" = 1.1682 color(red)(cancel(color(black)("g precipitate"))) × "30.97 g P"/(1876.5 color(red)(cancel(color(black)("g precipitate")))) = "0.019 280 g P"#
Step 2. Calculate the percent of #"P"# in the sample
#"% P" = "Mass of P"/"Mass of sample" × 100 % = ("0.019 280" color(red)(cancel(color(black)("g"))))/(0.2711 color(red)(cancel(color(black)("g")))) × 100 % = "7.112 %"#
(b) #"% P"_2"O"_5#
Step 3. Calculate the mass of #"P"_2"O"_5# equivalent to #"P"# in the precipitate
The skeleton chemical equation is
#M_text(r):color(white)(mmmm)1876.5color(white)(mmmmmmmmll)141.94#
#color(white)(mmm)2("NH"_4)_3"PO"_4"·12 MoO"_3 + … → "P"_2"O"_5 + …#
∴ #"Mass of P"_2"O"_5 = 1.1682 color(red)(cancel(color(black)("g precipitate"))) × ("141.94 g P"_2"O"_5)/(3753.0 color(red)(cancel(color(black)("g precipitate")))) = "0.044 182 g P"_2"O"_5#
Step 4. Calculate the #"% P"_2"O"_5#
#"% P"_2"O"_5 = ("Mass of P"_2"O"_5)/"Mass of sample" × 100 % = ("0.044 182" color(red)(cancel(color(black)("g"))))/(0.2711 color(red)(cancel(color(black)("g")))) × 100 % = "16.30 %"#
