Question

The atomic weight of aluminum is 26.982 u, how many aluminum atoms are there in a 4.55g sample of aluminum?

Answer 1

`1.02 * 10^(23)"atoms of Al"`

Explanation:

The key to this problem is the correct interpretation of what atomic weight means.

Notice that aluminium is said to have an atomic mass of `"26.982 u"`. The unit used here is the unified atomic mass unit, `u`.

The unified atomic mass unit is defined as `1/12"th"` of the mass of a neutral carbon-12 atom and is approximately equal to the mass of one nucleon, as in the mass of one proton or one neutron. Also, you should know that you have

`"1 u" color(white)(x) = color(white)(x)"1 g/mol"`

This means that the mass of one mole of aluminium atoms will be `"26.982 g"`.

As you know, one mole of any element contains exactly `6.022 * 10^(23)` atoms of that element.

This means that if you know how many moles of aluminium you have in `"4.55 g"`, you can use Avogadro's number to find the number of atoms.

`4.55 color(red)(cancel(color(black)("g"))) * "1 mole Al"/(26.982color(red)(cancel(color(black)("g")))) = "0.168631 moles Al"`

Therefore, you will have

`0.168631color(red)(cancel(color(black)("moles of Al"))) * (6.022 * 10^(23)"atoms of Al")/(1color(red)(cancel(color(black)("mole Al")))) = color(green)(1.02 * 10^(23)"atoms of Al")`

The answer is rounded to three sig figs, the number of isg figs you gave for the mass of the sample.