Question

How many moles are there in 3.01x10^24 atoms of argon?

Answer 1

Answer:

$\boxed {\boxed {\sf 5.00 \ mol \ Ar }}$

Explanation:

To convert from mole to atoms, we must use Avogadro's Number: 6.022*10²³. This number tells us the particles (atoms, ions, molecules, etc.) in 1 mole of a substance. In this case, the particles are atoms of argon.

Let's create a ratio.

$\frac {6.022*10^{23} \ atoms \ Ar}{1 \ mol \ Ar}$

Multiply by the given number of atoms.

$3.01*10^{24} \ atoms \ Ar *\frac {6.022*10^{23} \ atoms \ Ar}{1 \ mol \ Ar}$

Flip the fraction so the atoms of argon will cancel.

$3.01*10^{24} \ atoms \ Ar *\frac {1 \ mol \ Ar}{6.022*10^{23} \ atoms \ Ar}$

$3.01*10^{24} *\frac {1 \ mol \ Ar}{6.022*10^{23}}$

$\frac {3.01*10^{24} \ mol \ Ar}{6.022*10^{23}}$

$4.998339422 \ mol \ Ar$

The original measurement of atoms has 3 significant figures, so our answer must have the same. For the number we calculated, that is the hundredth place. The 8 in the thousandth place tells us to round the 9 to a 0, which also rounds the 9 in the tenths place to a 0, then the 4 to a 5.

$5.00 \ mol \ Ar$

There are 5.00 moles of argon.