To calculate the number of formula units of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex] present in [tex]\( 0.248 \)[/tex] grams of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex]:
1. Determine the molar mass of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex]:
The molar mass of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex] can be found by summing the molar masses of its constituent atoms:
- Sodium (Na): [tex]\( 2 \times 22.99 \, \text{g/mol} = 45.98 \, \text{g/mol} \)[/tex]
- Sulfur (S): [tex]\( 32.06 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 4 \times 16.00 \, \text{g/mol} = 64.00 \, \text{g/mol} \)[/tex]
Thus, the molar mass of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex] is:
[tex]\[
45.98 + 32.06 + 64.00 = 142.04 \, \text{g/mol}
\][/tex]
2. Calculate the number of moles of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex] in [tex]\( 0.248 \)[/tex] grams:
The number of moles ([tex]\( n \)[/tex]) can be calculated using the formula:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
[tex]\[
n = \frac{0.248 \, \text{g}}{142.04 \, \text{g/mol}} = 0.0017459870459025628 \, \text{moles}
\][/tex]
3. Calculate the number of formula units of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex]:
The number of formula units (or molecules) can be determined by multiplying the number of moles by Avogadro's number ([tex]\( 6.022 \times 10^{23} \, \text{molecules/mol} \)[/tex]):
[tex]\[
\text{Number of formula units} = 0.0017459870459025628 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\][/tex]
[tex]\[
= 1.0514333990425234 \times 10^{21} \, \text{formula units}
\][/tex]
Therefore, there are approximately [tex]\( 1.051 \times 10^{21} \)[/tex] formula units of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex] present in [tex]\( 0.248 \)[/tex] grams of [tex]\( \text{Na}_2 \text{SO}_4 \)[/tex].
