Question

How many atoms can be found in a sample of 75g of silicon

Answer 1

7.505x1022 maybe? I forget.

Answer 2

Answer:

$\boxed {\boxed {\sf 1.6 \times 10^{24} \ atoms \ Si}}$

Explanation:

We are asked to find how many atoms are in a sample of 75 grams of silicon.

1. Convert Grams to Moles

First, we must convert grams to moles using the molar mass. This is the mass of 1 mole of a substance. The molar mass is found on the Periodic Table because it is equal to the atomic mass, but the units are grams per mole instead of atomic mass units.

Look up the molar mass of silicon.

• Si: 28.085 g/mol

We convert using dimensional analysis, so we must set up a conversion factor.

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

We are converting 75 grams of silicon to moles, so we multiply by this value.

$75 \ g \ Si*\frac {28.085 \ g \ Si}{1 \ mol \ Si}$

Flip the conversion factor so the units of grams of silicon cancel.

$75 \ g \ Si*\frac {1 \ mol \ Si}{28.085 \ g \ Si}$

$75 *\frac {1 \ mol \ Si}{28.085 }$

$\frac {75}{28.085} \ mol \ Si$

$2.670464661 \ mol \ Si$

2. Convert Moles to Atoms

Next, we convert moles to atoms using 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 problem, the particles are atoms of silicon.

Set up another conversion factor, this time with Avogadro's Number.

$\frac {6.022 \times 10^{23} \ atoms \ Si}{1 \ mol \ Si}$

Multiply by the number of moles we found.

$2.670464661 \ mol \ Si*\frac {6.022 \times 10^{23} \ atoms \ Si}{1 \ mol \ Si}$

The units of moles of silicon cancel.

$2.670464661 *\frac {6.022 \times 10^{23} \ atoms \ Si}{1 }$

$2.670464661 * {6.022 \times 10^{23} \ atoms \ Si}$

$1.60815382 \times 10^{24} \ atoms \ Si$

The original value of grams (75) has 2 significant figures, so our answer must have the same. For the number we found, that is the tenths place. The 0 in the hundredths place tells us to leave the 6 in the tenths place.

$1.6 \times 10^{24} \ atoms \ Si$