Question

How many atoms are in 3.8 mol of calcium? Round your answer to 2 decimal places.

Answer 1

`\boxed {\boxed {\sf 2.29 *10^(24) \ atoms \ Ca}}`

Step-by-step explanation:

To convert from moles to atoms, we must use Avogadro's Number.

`6.022*10^(23)`

This number tells us the number of particles (atoms, molecules, ions, etc.) in 1 mole. In this case, the particles are atoms of calcium (Ca).

`6.022*10^(23) \ atoms \ Ca / 1 \ mol \ Ca`

1. Convert from moles to atoms.

Write Avogadro's number as a fraction.

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

Multiply the given number of moles of calcium (3.8) by the fraction created.

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

The moles of calcium will cancel.

`3.8 *\frac {6.022 *10^(23) \ atoms \ Ca} {1 }`

The denominator of 1 is insignifcant and we can turn this into a simple multiplication problem.

`3.8 * {6.022 *10^(23) \ atoms \ Ca}`

`2.28836*10^(24) \ atoms \ Ca`

2. Round

The problem tells us to round to 2 decimal places or the hundredth place.

`2.28836*10^(24) \ atoms \ Ca`

The 8 in the thousandth place tells us to round the 8 to a 9.

`2.29 *10^(24) \ atoms \ Ca`

There are about 2.29*10²⁴ atoms of calcium in 3.8 moles.