To calculate the number of moles in a given mass of a substance, we use the formula:
[tex]\[
\text{number of moles} = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
First, we need the molar mass of carbon dioxide (CO2). The molar mass is the sum of the molar masses of each element in the compound, multiplied by the number of atoms of each element in one molecule of the compound.
Carbon dioxide (CO2) consists of one carbon atom and two oxygen atoms. The approximate molar masses of carbon (C) and oxygen (O) are:
- Carbon (C): 12.01 grams per mole
- Oxygen (O): 16.00 grams per mole
Now, we calculate the molar mass of CO2:
[tex]\[
\text{Molar mass of CO2} = (1 \times \text{Molar mass of } C) + (2 \times \text{Molar mass of } O)
\][/tex]
[tex]\[
\text{Molar mass of CO2} = (1 \times 12.01 \text{ g/mol}) + (2 \times 16.00 \text{ g/mol})
\][/tex]
[tex]\[
\text{Molar mass of CO2} = 12.01 \text{ g/mol} + 32.00 \text{ g/mol}
\][/tex]
[tex]\[
\text{Molar mass of CO2} = 44.01 \text{ g/mol}
\][/tex]
Now that we have the molar mass of CO2, we can calculate the number of moles in 28 grams of CO2:
[tex]\[
\text{number of moles} = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
[tex]\[
\text{number of moles} = \frac{28 \text{ g}}{44.01 \text{ g/mol}}
\][/tex]
We use a calculator to find this value:
[tex]\[
\text{number of moles} \approx 0.636 \text{ moles (to three decimal places)}
\][/tex]
So, there are approximately 0.636 moles in 28 grams of CO2.
