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

Md Ariful Islam

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Md Ariful Islam

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

Notice that aluminium is said to have an 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 , the number of isg figs you gave for the mass of the sample.

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