Question

How many atoms are there in 8.88 g Si?

Answer 1

`\boxed {\boxed {\sf 1.90 * 10^(23) \ atoms \ Si}}`

Step-by-step explanation:

We are asked to find how many atoms are in 8.88 grams of silicon.

1. Grams to Moles

First, we convert grams to moles. We use the molar mass or the mass of 1 mole of a substance. These values are found on the Periodic Table as they are equal to the atomic masses, but the units are grams per mole instead of atomic mass units.

Look up silicon's molar mass.

• Si: 28.085 g/mol

We will convert using dimensional analysis. Set up a conversion factor with the molar mass.

`\frac { 28.085 \ g \ Si}{1 \ mol \ Si}`

We are converting 8.88 grams of silicon to moles, so we multiply by this value.

`8.88 \ g \ Si *\frac { 28.085 \ g \ Si}{1 \ mol \ Si}`

Flip the fraction so the units of grams of silicon cancel.

`8.88 \ g \ Si *\frac{1 \ mol \ Si} { 28.085 \ g \ Si}`

`8.88 *\frac{1 \ mol \ Si} { 28.085 }`

`\frac {8.88} { 28.085 } \ mol \ Si`

`0.316183015845 \ mol \ Si`

2. Moles to Atoms

Next, we convert moles to atoms. We use Avogadro's Number or 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are atoms of silicon.

Set up another conversion factor.

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

Multiply by the number of moles we calculated.

`0.316183015845\ mol \ Si *\frac {6.022 * 10^(23) \ atoms \ Si}{1 \ mol \ Si}`

The units of moles of silicon cancel.

`0.316183015845 * \frac {6.022 * 10^(23) \ atoms \ Si}{1}`

`0.316183015845 * {{6.022 * 10^(23) \ atoms \ Si}`

`1.90405412 * 10^(23) \ atoms \ Si`

3. Significant Figures

The original measurement of 8.88 grams has 3 significant figures, so our answer must have the same.

For the number we calculated, that is the hundredth place. The 4 in the thousandth place tells us to leave the 0 in the hundredth place.

`1.90 * 10^(23) \ atoms \ Si`

8.88 grams of silicon contains 1.90 ×10²³ atoms of silicon.