Question

How many moles are in 2.98x10^23 particles?

Answer 1

`\boxed {\boxed {\sf 0.495 \ mol}}`

Step-by-step 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.