Question

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`?

Answer 1

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

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

Explanation:

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`.

Answer 2

The composition of `"Mg(OH)"_2` is `"41.67 % Mg, 54.87 % O, 3.457 % H"`.

Explanation:

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"`