To determine the number of moles found in an 83.6 gram sample of sodium acetate ([tex]$NaC_2H_3O_2$[/tex]), we need to follow these steps:
1. Determine the molar mass of sodium acetate ([tex]$NaC_2H_3O_2$[/tex]):
- Sodium ([tex]$Na$[/tex]) has an atomic mass of approximately 22.99 grams per mole.
- Carbon ([tex]$C$[/tex]) has an atomic mass of approximately 12.01 grams per mole. Since there are 2 carbon atoms in the formula, the total mass contributed by carbon is [tex]\( 12.01 \times 2 = 24.02 \)[/tex] grams per mole.
- Hydrogen ([tex]$H$[/tex]) has an atomic mass of approximately 1.01 grams per mole. Since there are 3 hydrogen atoms in the formula, the total mass contributed by hydrogen is [tex]\( 1.01 \times 3 = 3.03 \)[/tex] grams per mole.
- Oxygen ([tex]$O$[/tex]) has an atomic mass of approximately 16.00 grams per mole. Since there are 2 oxygen atoms in the formula, the total mass contributed by oxygen is [tex]\( 16.00 \times 2 = 32.00 \)[/tex] grams per mole.
Adding all these contributions together:
[tex]\[
\text{Molar mass of } NaC_2H_3O_2 = 22.99 + 24.02 + 3.03 + 32.00 = 81.99 \text{ grams per mole}
\][/tex]
2. Calculate the number of moles:
- We use the formula for the number of moles, which is:
[tex]\[
\text{Number of moles} = \frac{\text{mass of the sample}}{\text{molar mass}}
\][/tex]
- Given the mass of the sample is 83.6 grams, and the molar mass of sodium acetate is 81.99 grams per mole, we can substitute these values into the formula:
[tex]\[
\text{Number of moles} = \frac{83.6 \text{ grams}}{81.99 \text{ grams per mole}} = 1.0196365410415904 \text{ moles}
\][/tex]
Therefore, in an 83.6 gram sample of sodium acetate ([tex]$NaC_2H_3O_2$[/tex]), there are approximately 1.02 moles of the compound.
