Calculate the percentages by mass of magnesium, oxygen and hydrogen in magnesium hydroxide, #Mg(OH)_2#. What is the mass of magnesium in #97.4# #g# of #Mg(OH)_2#?

The molar mass of #Mg(OH)_2# is #58.3# #gmol^-1#. The formula mass contains one mole of #Mg# #(24.3# #gmol^-1)# and two moles each of #O# #(16# #gmol^-1)# and hydrogen #H# #(1# #gmol^-1)#.

That means the percentages of each element are:

%Mg = #24.3/58.3xx100 = 41.7# %
%O = #(2xx16)/58.3xx100=54.9# %
%H = #(2xx1)/58.3xx100=3.4# %

These percentages add to 100%.

The mass of magnesium in #97.4# #g# of #Mg(OH)_2# is #41.7# % pf #97.4 = 40.6# #g#.

Calculate the mass percentages

#bb("Atom"color(white)(m)"No." color(white)(mm)A_text(r)color(white)(mm)M_text(r)color(white)(mll)%)#
#color(white)(m)"Mg"color(white)(mml)1color(white)(mml)24.30color(white)(ml)24.30color(white)(m)41.67#
#color(white)(m)"O"color(white)(mmm)2color(white)(mlm)16.00color(white)(ml)32.00color(white)(m)54.87#
#color(white)(m) "H"color(white)(mmm)2color(white)(mmm)1.008 color(white)(ml)2.016color(white)(m)3.457#
#color(white)(mmmmm)"Total "M_text(r) = 58.32#

The formula for mass percent is

#color(blue)(bar(ul(|color(white)(a/a)"Mass %" = "mass of component"/"total mass" × 100 %color(white)(a/a)|)))" "#

#"% Mg" = 24.30/58.32 × 100 % = 41.67 %#

#"% O" = 32.00/58.32 × 100 % = 54.87 %#

#"% H" = 2.016/58.32 × 100 % = 3.457 %#

Calculate the mass of magnesium

#"Mass of Mg" = 97.4 color(red)(cancel(color(black)("g Mg(OH)"_2))) × "41.67 g Mg"/(100 color(red)(cancel(color(black)("g Mg(OH)"_2)))) = "40.6 g Mg"#