Question

Calculate the number of atoms in 2.5 moles of Si.

Answer 1

`\boxed {\boxed {\sf About \ 1.5 * 10^(24) \ atoms \ Si}}`

Step-by-step explanation:

When converting from moles to atoms, we must use Avogadro's number. This number tells us there are 6.022 * 10²³ atoms in 1 mole. We can multiply this number by the number of moles.

First, we must set up Avogadro's number as a ratio.

`\frac {6.022 \ * 10^(23) \ atoms \ Si }{1 \ mol \ Si}}`

Next, multiply the number of moles by the ratio.

`2.5 \ mol \ Si *\frac {6.022 \ * 10^(23) \ atoms \ Si }{1 \ mol \ Si}}`

When we multiply, the moles of silicon will cancel.

`2.5 * \frac {6.022 \ * 10^(23) \ atoms \ Si }{1}}`

Since the denominator of the fraction is 1, we can cancel it out too.

`2.5 * {6.022 \ * 10^(23) \ atoms \ Si }`

`1.5055 * 10^(24) \ atoms \ Si`

The original measurement (2.5 moles) has 2 significant figures (2 and 5). Therefore we must round to 2 sig figs. For this question, 2 sig figs is the tenth place.

The 0 in the hundredth place tells us to leave the 5 in the tenth place.

`1.5 * 10^(24) \ atoms \ Si`

There are about 1.5 * 10²⁴ atoms of silicon.