Question

Question #77d3f

Answer 1

`"40 g mol"^(-1)`

Explanation:

The interesting thing about this problem is that you don't really need to know the compound's molecular formula, but you do need to know its empirical formula.

As you know, a compound's empirical formula tells you the smallest whole number ratio that exists between the elements that make up said compound.

In this case, if the molecular formula is said to `"M"_4"O"_8`, the empirical formula will be `"M"_1"O"_2`, since `1:2` is the smallest whole number ratio that exists between `4` and `8`.

So, your compound contains two moles of oxygen for every one mole of `"M"`.

Now, a `"18.00-g"` sample of this compound is said to contain a total of `"10 g"` of `"M"`. This of course implies that it contains

`m_"compound" = m_"M" + m_"O"`

`m_"O" = "18.00 g" - "10 g" = "8 g oxygen"`

At this point, all you really need to know if how many moles of oxygen you have in the sample. Use oxygen's molar mass to help you with that

`8 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16.0 color(red)(cancel(color(black)("g")))) = "0.5 moles O"`

This means that sample must contain

`0.5 color(red)(cancel(color(black)("moles O"))) * "1 mole M"/(2color(red)(cancel(color(black)("moles O")))) = "0.25 moles M"`

Finally, to get the molar mass of element `"M`", divide its mass by the number of moles it contains

`M_M = "10 g"/"0.25 moles" = color(green)("40 g mol"^(-1))`