Question

How many atoms are in 1g of Hg

Answer 1

7.5275 x 10^21

Step-by-step explanation:

Answer 2

`\boxed {\boxed {\sf 3 * 10^(21) \ atoms \ Hg}}`

Step-by-step explanation:

We are asked to find how many atoms are in 1 gram of mercury.

1. Convert 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 equivalent to the atomic masses on the Periodic Table, but the units are grams per mole instead of atomic mass units.

Look up mercury's molar mass.

• Hg: 200.59 g/mol

We convert using dimensional analysis, so we create a ratio using the molar mass.

`\frac { 200.59 \ g \ Hg}{ 1 \ mol \ Hg}`

We are converting 1 gram of mercury to moles, so we multiply the ratio by this value.

`1 \ g \ Hg *\frac { 200.59 \ g \ Hg}{ 1 \ mol \ Hg}`

Flip the ratio so the units of grams of mercury cancel out.

`1 \ g \ Hg *\frac{ 1 \ mol \ Hg} { 200.59 \ g \ Hg}`

`1 *\frac{ 1 \ mol \ Hg} { 200.59}`

`\frac{ 1} { 200.59} \ mol \ Hg`

`0.004985293385 \ mol \ Hg`

2. Convert 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) in 1 mole of a substance. In this case, the particles are atoms of mercury.

We will use dimensional analysis and set up another ratio.

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

Multiply by the number of moles we calculated.

`0.004985293385 \ mol \ Hg * \frac {6.022 * 10^(23) \ atoms \ Hg}{ 1 \ mol \ Hg}`

The units of moles of mercury cancel.

`0.004985293385 * \frac {6.022 * 10^(23) \ atoms \ Hg}{ 1 }`

`3.00214368 * 10^(21) \ atoms \ Hg`

3. Round

The original measurement of grams has 1 significant figures, so our answer must have the same. For the number we calculated, that is the ones place. The 0 in the tenths place tells us to leave the 3 in the ones place.

`3 * 10^(21) \ atoms \ Hg`

There are approximately 3×10²¹ atoms of mercury in 1 gram of mercury.