Question

How many liters of CO2 are present in a sample with 1.5 x 1022 particles?

Answer 1

`\boxed {\boxed {\sf 0.56 \ L \ CO_2}}`

Step-by-step explanation:

We can convert particles to moles in 3 steps:

1. Convert Particles to Moles

First, we must convert particles to moles. 1 mole of any substance contains the same number of particles: 6.022*10²³ or Avogadro's Number. For this problem, we have particles of carbon dioxide or CO₂. We can make a ratio.

`(6.022 *10^(23) \ particles \ CO_2)/(1 \ mol \ CO_2)`

Since we are converting 1.5*10²² particles to moles, we multiply the ratio by that value.

`1.5 *10^(22) \ particles\ CO_2*(6.022 *10^(23) \ particles \ CO_2)/(1 \ mol \ CO_2)`

Flip the ratio. It remains equivalent, but the units of particles of carbon dioxide can cancel.

`1.5 *10^(22) \ particles\ CO_2*(1 \ mol \ CO_2)/(6.022 *10^(23) \ particles \ CO_2)`

`1.5 *10^(22)*(1 \ mol \ CO_2)/(6.022 *10^(23) )`

`(1.5 *10^(22) )/(6.022 *10^(23) )\ mol \ CO_2`

`0.0249086682165 \ mol \ CO_2`

2. Convert Moles to Liters

There are 22.4 liters in 1 mole of any gas. Let's set up another ratio.
`(22.4 \ L \ CO_2)/(1 \ mol \ CO_2)`

Multiply by the number of moles we calculated.

`0.0249086682165\ mol \ CO_2*(22.4 \ L \ CO_2)/(1 \ mol \ CO_2)`

The units of moles of carbon dioxide cancel.

`0.0249086682165*(22.4 \ L \ CO_2)/(1)`

`0.0249086682165*{22.4 \ L \ CO_2`

`0.55795416805\ L \ CO_2`

3. Round

The original measurement of particles (1.5*10²²) has 2 significant figures (1 and 5). Our answer must have the same number. For the number we calculated, that is the hundredth place.

The 7 in the thousandth place (0.55795416805) tells us to round the 5 in the hundredth place up to a 6.

`0.56 \ L \ CO_2`

1.5*10²² particles of carbon dioxide is equal to 0.56 liters of carbon dioxide.