Moles and mass are both measures of the quantity of a substance, in this case `CO_2.`
We can convert between two representations of the same quantity in different units if we can find a relationship between the units. When converting between grams (mass) and moles, we use the molar mass.
The molar mass of a molecular formula such as that of `CO_2` is found by adding the molar masses of all of the atoms in the formula. A molecule of carbon dioxide contains one atom of carbon and two atoms of oxygen, so we have
molar mass of `CO_2` = molar mass of C + 2 * (molar mass of O)
Using the Periodic Table to find that the molar mass of carbon is 12.01 g and that of oxygen is 16.00 g, we get
molar mass of `CO_2` = 12.01 g + 2 * (16.00 g)
= 44.01 g.
We can write that 1 mole `CO_2` = 44.01 g `CO_2`
Any time we have an equality, if we divide both sides by the same quantity, the results are still equal, so we can divide both sides by 44.01 g `CO_2` and get
`("1 mole")/(44.01 g) = 1`
We can always multiply anything by 1 without changing the quantity. This is called a conversion factor, because it converts a quantity from being expressed in one unit to another without changing the value of the quantity.
In the problem we are given 11 g of `CO_2` .
The best way to set up a unit conversion problem is to write the given first, then multiply by the conversion factor. We get
`11 g CO_2 * ("1 mole")/(44.01 g) = 0.2499 "mole" * (g)/(g) CO_2`
Anything divided by itself is equal to 1, so the g/g term disappears. We say "the grams cancel" since they appear in both numerator and denominator. Our answer is in moles.
One step remains. The given value has two significant figures. Since all we did was multiply, our answer should have two significant figures. Thus we get
11 g `CO_2` = 0.25 mole `CO_2` . ` `