The empirical formula is the simplest whole-number ratio of atoms in a compound.
The ratio of atoms is the same as the ratio of moles. So our job is to calculate the molar ratio of #"Ag"# to #"O"#.
#"Mass of Ag = 7.96 g"#
#"Mass of silver oxide = mass of Ag + mass of O"#
#"8.55 g = 7.96 g + mass of O"#
#"Mass of O = (8.55 – 7.96) g = 0.59 g"#
#"Moles of Ag" = 7.96 color(red)(cancel(color(black)("g Ag"))) × "1 mol Ag"/(107.9color(red)(cancel(color(black)( "g Ag")))) = "0.073 77 mol Ag"#
#"Moles of O "= 0.59 color(red)(cancel(color(black)("g O"))) × "1 mol O"/(16.00 color(red)(cancel(color(black)("g O")))) = "0.0369 mol O"#
To get this into an integer ratio, we divide both numbers by the smaller value.
From this point on, I like to summarize the calculations in a table.
#"Element"color(white)(Ag) "Mass/g"color(white)(X) "Moles"color(white)(Xll) "Ratio"color(white)(mll)"Integers"#
#stackrel(—————————————————-———)(color(white)(m)"Ag" color(white)(XXXm)7.96 color(white)(Xm)0.073 77
color(white)(Xll)2.00color(white)(mmm)2)#
#color(white)(ml)"O" color(white)(XXXXl)0.59 color(white)(mm)"0.0369 color(white)(Xml)1 color(white)(mmmml)1#
There are 2 mol of #"Ag"# for 1 mol of #"O"#.
The empirical formula of silver oxide is #"Ag"_2"O"#.
Here is a video that illustrates how to determine an empirical formula.
