Answer:
[tex]\boxed {\boxed {\sf 0.56 \ L \ CO_2}}[/tex]
Explanation:
We can convert particles to moles in 3 steps:
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.
[tex]\frac{6.022 *10^{23} \ particles \ CO_2}{1 \ mol \ CO_2}[/tex]
Since we are converting 1.5*10²² particles to moles, we multiply the ratio by that value.
[tex]1.5 *10^{22} \ particles\ CO_2*\frac{6.022 *10^{23} \ particles \ CO_2}{1 \ mol \ CO_2}[/tex]
Flip the ratio. It remains equivalent, but the units of particles of carbon dioxide can cancel.
[tex]1.5 *10^{22} \ particles\ CO_2*\frac{1 \ mol \ CO_2}{6.022 *10^{23} \ particles \ CO_2}[/tex]
[tex]1.5 *10^{22}*\frac{1 \ mol \ CO_2}{6.022 *10^{23} }[/tex]
[tex]\frac{1.5 *10^{22} }{6.022 *10^{23} }\ mol \ CO_2[/tex]
[tex]0.0249086682165 \ mol \ CO_2[/tex]
There are 22.4 liters in 1 mole of any gas. Let's set up another ratio.[tex]\frac{22.4 \ L \ CO_2}{1 \ mol \ CO_2}[/tex]
Multiply by the number of moles we calculated.
[tex]0.0249086682165\ mol \ CO_2*\frac{22.4 \ L \ CO_2}{1 \ mol \ CO_2}[/tex]
The units of moles of carbon dioxide cancel.
[tex]0.0249086682165*\frac{22.4 \ L \ CO_2}{1}[/tex]
[tex]0.0249086682165*{22.4 \ L \ CO_2[/tex]
[tex]0.55795416805\ L \ CO_2[/tex]
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.
[tex]0.56 \ L \ CO_2[/tex]
1.5*10²² particles of carbon dioxide is equal to 0.56 liters of carbon dioxide.
