# 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?

May 22, 2017

%Mg = $\frac{24.3}{58.3} \times 100 = 41.7$ %
%O = $\frac{2 \times 16}{58.3} \times 100 = 54.9$ %
%H = $\frac{2 \times 1}{58.3} \times 100 = 3.4$ %

The mass of magnesium in $97.4$ $g$ of $M g {\left(O H\right)}_{2}$ is $41.7$ % pf $97.4 = 40.6$ $g$.

#### Explanation:

The molar mass of $M g {\left(O H\right)}_{2}$ is $58.3$ $g m o {l}^{-} 1$. The formula mass contains one mole of $M g$ (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 = $\frac{24.3}{58.3} \times 100 = 41.7$ %
%O = $\frac{2 \times 16}{58.3} \times 100 = 54.9$ %
%H = $\frac{2 \times 1}{58.3} \times 100 = 3.4$ %

The mass of magnesium in $97.4$ $g$ of $M g {\left(O H\right)}_{2}$ is $41.7$ % pf $97.4 = 40.6$ $g$.

May 22, 2017

The composition of ${\text{Mg(OH)}}_{2}$ is $\text{41.67 % Mg, 54.87 % O, 3.457 % H}$.

#### 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)%)
$\textcolor{w h i t e}{m} \text{Mg} \textcolor{w h i t e}{m m l} 1 \textcolor{w h i t e}{m m l} 24.30 \textcolor{w h i t e}{m l} 24.30 \textcolor{w h i t e}{m} 41.67$
$\textcolor{w h i t e}{m} \text{O} \textcolor{w h i t e}{m m m} 2 \textcolor{w h i t e}{m l m} 16.00 \textcolor{w h i t e}{m l} 32.00 \textcolor{w h i t e}{m} 54.87$
$\textcolor{w h i t e}{m} \text{H} \textcolor{w h i t e}{m m m} 2 \textcolor{w h i t e}{m m m} 1.008 \textcolor{w h i t e}{m l} 2.016 \textcolor{w h i t e}{m} 3.457$
$\textcolor{w h i t e}{m m m m m} \text{Total } {M}_{\textrm{r}} = 58.32$

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

$\text{Mass of Mg" = 97.4 color(red)(cancel(color(black)("g Mg(OH)"_2))) × "41.67 g Mg"/(100 color(red)(cancel(color(black)("g Mg(OH)"_2)))) = "40.6 g Mg}$