Question

How many moles are in 2.98x10^23 particles?

Answer 1

Answer:

$\boxed {\boxed {\sf 0.495 \ mol}}$

Explanation:

We are given a number of particles and asked to convert to moles.

1. Convert Particles to Moles

1 mole of any substance contains the same number of particles (atoms, molecules, formula units) : 6.022 *10²³ or Avogadro's Number. For this question, the particles are not specified.

So, we know that 1 mole of this substance contains 6.022 *10²³ particles. Let's set up a ratio.

$\frac { 1 \ mol }{6.022*10^{23 } \ particles}}$

We are converting 2.98*10²³ particles to moles, so we multiply the ratio by that value.

$2.98*10^{23} \ particles *\frac { 1 \ mol }{6.022*10^{23 } \ particles}}$

The units of particles cancel.

$2.98*10^{23} *\frac { 1 \ mol }{6.022*10^{23 } }}$

$\frac { 2.98*10^{23}}{6.022*10^{23 } }} \ mol$

$0.4948522086 \ mol$

2. Round

The original measurement of particles (2.98*10²³) has 3 significant figures, so our answer must have the same.

For the number we found, 3 sig figs is the thousandth place.

The 8 in the ten-thousandth place (0.4948522086) tells us to round the 4 up to a 5 in the thousandth place.

$0.495 \ mol$

2.98*10²³ particles are equal to approximately 0.495 moles.