Question

Question #a3a16

Answer 1

The unknown metal is iron, or `Fe`.

So, you know that you get 2.327 g of your unknown metal for every 1.00 g of elemental oxygen. You can use these values to determine the percent composition of your oxide

`m_"oxide" = m_"metal" + m_"oxygen"`

`m_"oxide" = 2.327 + 1.00 = "3.327 g"`

This means that you get

`(2.327cancel("g"))/(3.327cancel("g")) * 100 = "69.94%"` `->` metal

`(1.0cancel("g"))/(3.327cancel("g")) * 100 = "30.06%"` `->` oxygen

To make the calculations easier, assume that you're dealing with a 100.0-g sample of `M_color(red)(2)O_color(blue)(3)`. You can determine how many moles of oxygen you'd get in this much oxide by using oxygen's molar mass.

Since oxygen has a percent composition of 30.06%, your sample will contain 30.06 g of oxygen. This means that you have

`30.06cancel("g") * "1 mole oxygen"/(16.00cancel("g")) = "1.879 moles"` `O`

Now use the known mole ratio that exists between the metal on oxygen to determine how many moles of metal the sample would have

`1.879cancel("moles O") * (color(red)(2)"moles metal")/(color(blue)(3)cancel("moles O")) = "1.253 moles M"`

Since the metal's percent composition in the oxide is equal to 69.94%, your sample will contain 69.94 g of metal. This means that its molar mass will be

`M_M = m/n = "69.94 g"/"1.253 moles" = color(green)("55.8 g/mol")`

Your unknown metal is iron, `Fe`, which has a molar mass of `"55.845 g/mol"`.