Question

How many grams are they in 2.3 X 10^24 atoms of Ag?

Answer 1

`\boxed {\boxed {\sf 411.9833942 \ grams \ of \ silver}}`

Step-by-step explanation:

1. Convert Atoms to Moles

To convert atoms to moles, we use Avogadro's Number: 6.022*10²³. This tells us the amount of particles in 1 mole of a substance. In this case, it is atoms of silver.

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

Multiply by the given number of atoms.

`2.3 *10^(24) \ atoms \ Ag*\frac {6.022*10^(23) \ atoms \ Ag}{ 1 \ mol \ Ag}`

Flip the fractions so the atoms of silver cancel.

`2.3 *10^(24) \ atoms \ Ag*\frac {1 \ mol \ Ag}{ 6.022*10^(23) \ atoms \ Ag}`

`2.3 *10^(24) *\frac {1 \ mol \ Ag}{ 6.022*10^(23)}`

`\frac {2.3 *10^(24) \ mol \ Ag}{ 6.022*10^(23)} = 3.819329127 \ mol \ Ag`

2. Convert Moles to Grams

To convert from moles to grams, we use the molar mass. This can be found on the Periodic Table.

• Silver (Ag): 107.868 g/mol

Use this as a fraction.

`\frac { 107.868 \ g \ Ag}{ 1 \ mol \ Ag}`

Multiply by the number of moles we calculated. The moles of silver will cancel.

`3.819329127 \ mol \ Ag * \frac { 107.868 \ g \ Ag}{ 1 \ mol \ Ag}`

`3.819329127 \ * \frac { 107.868 \ g \ Ag}{ 1 }`

`411.9833942 \ g \ Ag`