Answer:
[tex]\boxed {\boxed {\sf 38.11 \ L}}[/tex]
Explanation:
To find the volume, we need to convert grams to moles, then moles to liters.
We convert grams to moles using the molar mass. This is the mass of 1 mole of a substance. It is the same as the atomic mass found on the Periodic Table, but the units are grams per mole (not atomic mass units).
We have the compound carbon dioxide or CO₂. Look up the molar masses of the individual elements.
Notice that oxygen has a subscript of 2, so there are 2 atoms in each molecule. We have to multiply oxygen's molar mass by 2 before adding carbon's.
Use this value as a ratio.
[tex]\frac {44.009 \ g\ CO_2}{1 \ mol \ CO_2}[/tex]
Multiply by the given number of grams: 74.87
[tex]74.87 \ g\ CO_2*\frac {44.009 \ g\ CO_2}{1 \ mol \ CO_2}[/tex]
Flip the ratio so the units of grams cancel.
[tex]74.87 \ g\ CO_2*\frac {1 \ mol \ CO_2}{44.009 \ g\ CO_2}[/tex]
[tex]74.87 *\frac {1 \ mol \ CO_2}{44.009 }[/tex]
[tex]{74.87 \ mol \ CO_2}{44.009 } = 1.701242928 \ mol \ CO_2[/tex]
Any gas at standard temperature and pressure (STP) has a volume of 22.4 liters per mole.
[tex]\frac {22.4 \ L}{1 \ mol \ CO_2}[/tex]
Multiply by the number of moles we calculated.
[tex]1.701242928 \ mol \ CO_2*\frac {22.4 \ L}{1 \ mol \ CO_2}[/tex]
The units of moles cancel.
[tex]1.701242928 *\frac {22.4 \ L}{1 }[/tex]
[tex]1.701242928 *{22.4 \ L}= 38.10784158 \ L[/tex]
The original measurement has 4 significant figures, so our answer must have the same. For the number we calculated, that is the hundredth place.
The 7 tells us to round the 0 10 a 1.
[tex]38.11 \ L[/tex]
