The mass ratio of two elements in a compound is the mass of one element in a given amount of the compound divided by the mass of the other element.
Let's calculate the mass of #"Zn"# in 1 mol #"ZnI"_2#.
#"Mass of Zn" = 1 color(red)(cancel(color(black)("mol ZnI"_2))) × (1 color(red)(cancel(color(black)("mol Zn"))))/(1 color(red)(cancel(color(black)("mol ZnI"_2)))) × (65.38 "g Zn")/(1 color(red)(cancel(color(black)("mol Zn")))) = "65.38 g Zn"#
Also, the mass of #"I"# in 1 mol of #"ZnI"_2# is
#"Mass of I" = 1 color(red)(cancel(color(black)("mol ZnI"_2))) × (2 color(red)(cancel(color(black)("mol I"))))/(1 color(red)(cancel(color(black)("mol ZnI"_2)))) × (126.9 "g I")/(1 color(red)(cancel(color(black)("mol I")))) = "253.8 g I"#
∴#"Mass of Zn"/"Mass of I" = "65.38 g"/"253.8 g"#
To get the ratio in its smallest terms, we divide the numerator and the denominator by the smaller number (#"65.38 g")#.
Then
#"Mass of Zn"/"Mass of I" = 1/3.882#
