Question

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

Answer 1

Answer:

$\boxed {\boxed {\sf 2.29 *10^{24} \ atoms \ Ca}}$

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.