To calculate the mass of each gas sample at Standard Temperature and Pressure (STP), follow these steps:
### Given Data
1. The volume of each gas at STP:
- Volume of CO[tex]\(_2\)[/tex] = 178 mL
- Volume of O[tex]\(_2\)[/tex] = 155 mL
- Volume of SF[tex]\(_6\)[/tex] = 1.25 L
2. Convert volumes for CO[tex]\(_2\)[/tex] and O[tex]\(_2\)[/tex] from mL to L:
- Volume of CO[tex]\(_2\)[/tex] in L = 178 mL / 1000 = 0.178 L
- Volume of O[tex]\(_2\)[/tex] in L = 155 mL / 1000 = 0.155 L
3. Molar masses of the gases (given in g/mol):
- CO[tex]\(_2\)[/tex] = 44.01 g/mol
- O[tex]\(_2\)[/tex] = 32.00 g/mol
- SF[tex]\(_6\)[/tex] = 146.06 g/mol
4. The molar volume of a gas at STP is 22.414 L/mol.
### Calculation Steps
#### (a) Mass of 178 mL (0.178 L) of CO[tex]\(_2\)[/tex]:
1. Determine the number of moles of CO[tex]\(_2\)[/tex]:
[tex]\[
\text{Moles of CO}_2 = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{0.178 \, \text{L}}{22.414 \, \text{L/mol}}
\][/tex]
2. Calculate the mass of CO[tex]\(_2\)[/tex]:
[tex]\[
\text{Mass of CO}_2 = \text{Moles of CO}_2 \times \text{Molar Mass of CO}_2 = \left(\frac{0.178}{22.414}\right) \times 44.01 \, \text{g}
\][/tex]
The result is approximately [tex]\(0.3495 \, \text{g}\)[/tex].
#### (b) Mass of 155 mL (0.155 L) of O[tex]\(_2\)[/tex]:
1. Determine the number of moles of O[tex]\(_2\)[/tex]:
[tex]\[
\text{Moles of O}_2 = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{0.155 \, \text{L}}{22.414 \, \text{L/mol}}
\][/tex]
2. Calculate the mass of O[tex]\(_2\)[/tex]:
[tex]\[
\text{Mass of O}_2 = \text{Moles of O}_2 \times \text{Molar Mass of O}_2 = \left(\frac{0.155}{22.414}\right) \times 32.00 \, \text{g}
\][/tex]
The result is approximately [tex]\(0.2213 \, \text{g}\)[/tex].
#### (c) Mass of 1.25 L of SF[tex]\(_6\)[/tex]:
1. Determine the number of moles of SF[tex]\(_6\)[/tex]:
[tex]\[
\text{Moles of SF}_6 = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{1.25 \, \text{L}}{22.414 \, \text{L/mol}}
\][/tex]
2. Calculate the mass of SF[tex]\(_6\)[/tex]:
[tex]\[
\text{Mass of SF}_6 = \text{Moles of SF}_6 \times \text{Molar Mass of SF}_6 = \left(\frac{1.25}{22.414}\right) \times 146.06 \, \text{g}
\][/tex]
The result is approximately [tex]\(8.1456 \, \text{g}\)[/tex].
### Summary
- The mass of 178 mL of CO[tex]\(_2\)[/tex] is approximately [tex]\(0.3495 \, \text{g}\)[/tex].
- The mass of 155 mL of O[tex]\(_2\)[/tex] is approximately [tex]\(0.2213 \, \text{g}\)[/tex].
- The mass of 1.25 L of SF[tex]\(_6\)[/tex] is approximately [tex]\(8.1456 \, \text{g}\)[/tex].
