Respuesta :
Let the atomic mass of M metal be X.
The formula mass of metal hydroxide, [tex]M(OH)_2[/tex] = [tex]X+2\times 1+2\times 16 = (X+34) g/mol[/tex]
Mass percentage of oxygen in metal hydroxide, [tex]M(OH)_2[/tex] = 32.8%
Mass percentage is given as:
[tex]\frac{mass of element}{total mass of compound}\times 100[/tex]
Substituting the values:
[tex]\frac{2\times 16}{Y+34} = 32.8[/tex]%
[tex]\frac{2\times 16}{Y+34} = 0.328[/tex]
[tex]{32} = 0.328\times ({Y+34})[/tex]
[tex]32 = 0.328Y+11.152[/tex]
[tex]0.328Y = 20.848[/tex]
[tex]Y = \frac{20.848}{0.328} = 63.56[/tex]
The element having atomic mass [tex]63.56 u[/tex] is copper, [tex]Cu[/tex].
Hence, In metal hydroxide, [tex]M(OH_2)[/tex] the metal M is copper, [tex]Cu[/tex]. Formula of oxide is [tex]Cu(OH)_2[/tex].
The metal in the metal hydroxide is Copper, Cu.
Further Explanation
Mass percent is the ratio of an element's mass to the mass of the compound. It is mathematically expressed as:
[tex]mass \% \ of \ A = \frac{mass \ of \ element \ A}{mass \ of \ compound}[/tex]
In the problem, the mass percent of oxygen is given as 32.8%. This can be used to determine the mass of the compound:
[tex]mass \% \ of\ O \ = \frac{2 \times 16u}{mass \ of \ compound} \times 100\\32.8 \% \ O \ = \frac{2 \times 16u}{mass \ of \ compound} \times 100\\ 0.328 = \frac{2 \times 16u}{mass \ of \ compound}\\\\ mass \ of \ compound = \frac{32u}{0.328}\\\boxed {mass \ of \ compound \ = 97.561u}[/tex]
Now that the mass of the compound is known, the mass percent of hydrogen and of the metal, and the mass of the metal may be determined:
- Mass % of Hydrogen
[tex]mass \% \ of\ H \ = \frac{2 \times 1}{97.561u} \times 100\\\boxed {mass \% \ of \ H = 2.05\%}[/tex]
- Mass % of Metal, M & Mass of the Metal
[tex]mass \% \ of \ M = \frac{mass \ of \ M}{97.561 u} \times 100\\\\\[100 - (32.8+2.05)] = \frac{mass \ of \ M}{97.561u} \times 100\\65.15 = \frac{mass \ of \ M}{97.561 u} \times 100\\0.6515 = \frac{mass \ of \ M}{97.561 u} \\mass \ of \ M \ = (0.6516)(97.561)\\\boxed {\boxed {mass \ of \ M \ = 63.56 u}}[/tex]
From the mass of the metal, its identity may be known.
Using the periodic table, search for the metal that forms a +2 cation and has a mass of 63.56 u.
The metal that fits the criteria is Copper.
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Keywords: mass percent
