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Sagot :
Let's solve the given problem step by step to find the masses of various gas samples at Standard Temperature and Pressure (STP).
### Given Data:
- The volumes for each gas are provided.
- Standard Molar Volume (STP) is [tex]\( 22.4 \)[/tex] L per mole for any gas.
### Step-by-Step Solution:
#### (a) [tex]\( 178 \)[/tex] mL of [tex]\( CO_2 \)[/tex]
1. Convert the volume of [tex]\( CO_2 \)[/tex] to liters:
[tex]\[ \text{Volume of } CO_2 = 178 \text{ mL} = 0.178 \text{ L} \][/tex]
2. Calculate the moles of [tex]\( CO_2 \)[/tex]:
[tex]\[ \text{Moles of } CO_2 = \frac{\text{Volume of } CO_2}{\text{Molar Volume}} = \frac{0.178 \text{ L}}{22.4 \text{ L/mol}} \approx 0.007946 \][/tex]
3. Calculate the mass of [tex]\( CO_2 \)[/tex]:
Given molar mass of [tex]\( CO_2 \)[/tex] is [tex]\( 44.01 \)[/tex] g/mol,
[tex]\[ \text{Mass of } CO_2 = \text{Moles of } CO_2 \times \text{Molar Mass of } CO_2 = 0.007946 \text{ mol} \times 44.01 \text{ g/mol} \approx 0.3497 \text{ g} \][/tex]
#### (b) [tex]\( 155 \)[/tex] mL of [tex]\( O_2 \)[/tex]
1. Convert the volume of [tex]\( O_2 \)[/tex] to liters:
[tex]\[ \text{Volume of } O_2 = 155 \text{ mL} = 0.155 \text{ L} \][/tex]
2. Calculate the moles of [tex]\( O_2 \)[/tex]:
[tex]\[ \text{Moles of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar Volume}} = \frac{0.155 \text{ L}}{22.4 \text{ L/mol}} \approx 0.006920 \text{ mol} \][/tex]
3. Calculate the mass of [tex]\( O_2 \)[/tex]:
Given molar mass of [tex]\( O_2 \)[/tex] is [tex]\( 32.00 \)[/tex] g/mol,
[tex]\[ \text{Mass of } O_2 = \text{Moles of } O_2 \times \text{Molar Mass of } O_2 = 0.006920 \text{ mol} \times 32.00 \text{ g/mol} \approx 0.2214 \text{ g} \][/tex]
#### (c) [tex]\( 1.25 \)[/tex] L of [tex]\( SF_6 \)[/tex]
1. Volume is already in liters:
[tex]\[ \text{Volume of } SF_6 = 1.25 \text{ L} \][/tex]
2. Calculate the moles of [tex]\( SF_6 \)[/tex]:
[tex]\[ \text{Moles of } SF_6 = \frac{\text{Volume of } SF_6}{\text{Molar Volume}} = \frac{1.25 \text{ L}}{22.4 \text{ L/mol}} \approx 0.055804 \text{ mol} \][/tex]
3. Calculate the mass of [tex]\( SF_6 \)[/tex]:
Given molar mass of [tex]\( SF_6 \)[/tex] is [tex]\( 146.06 \)[/tex] g/mol,
[tex]\[ \text{Mass of } SF_6 = \text{Moles of } SF_6 \times \text{Molar Mass of } SF_6 = 0.055804 \text{ mol} \times 146.06 \text{ g/mol} \approx 8.1507 \text{ g} \][/tex]
### Summary:
- Mass of [tex]\( 178 \)[/tex] mL [tex]\( CO_2 \)[/tex] is approximately 0.3497 g.
- Mass of [tex]\( 155 \)[/tex] mL [tex]\( O_2 \)[/tex] is approximately 0.2214 g.
- Mass of [tex]\( 1.25 \)[/tex] L [tex]\( SF_6 \)[/tex] is approximately 8.1507 g.
Each value is a rounded result from the calculations, providing the mass of the gas samples at Standard Temperature and Pressure.
### Given Data:
- The volumes for each gas are provided.
- Standard Molar Volume (STP) is [tex]\( 22.4 \)[/tex] L per mole for any gas.
### Step-by-Step Solution:
#### (a) [tex]\( 178 \)[/tex] mL of [tex]\( CO_2 \)[/tex]
1. Convert the volume of [tex]\( CO_2 \)[/tex] to liters:
[tex]\[ \text{Volume of } CO_2 = 178 \text{ mL} = 0.178 \text{ L} \][/tex]
2. Calculate the moles of [tex]\( CO_2 \)[/tex]:
[tex]\[ \text{Moles of } CO_2 = \frac{\text{Volume of } CO_2}{\text{Molar Volume}} = \frac{0.178 \text{ L}}{22.4 \text{ L/mol}} \approx 0.007946 \][/tex]
3. Calculate the mass of [tex]\( CO_2 \)[/tex]:
Given molar mass of [tex]\( CO_2 \)[/tex] is [tex]\( 44.01 \)[/tex] g/mol,
[tex]\[ \text{Mass of } CO_2 = \text{Moles of } CO_2 \times \text{Molar Mass of } CO_2 = 0.007946 \text{ mol} \times 44.01 \text{ g/mol} \approx 0.3497 \text{ g} \][/tex]
#### (b) [tex]\( 155 \)[/tex] mL of [tex]\( O_2 \)[/tex]
1. Convert the volume of [tex]\( O_2 \)[/tex] to liters:
[tex]\[ \text{Volume of } O_2 = 155 \text{ mL} = 0.155 \text{ L} \][/tex]
2. Calculate the moles of [tex]\( O_2 \)[/tex]:
[tex]\[ \text{Moles of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar Volume}} = \frac{0.155 \text{ L}}{22.4 \text{ L/mol}} \approx 0.006920 \text{ mol} \][/tex]
3. Calculate the mass of [tex]\( O_2 \)[/tex]:
Given molar mass of [tex]\( O_2 \)[/tex] is [tex]\( 32.00 \)[/tex] g/mol,
[tex]\[ \text{Mass of } O_2 = \text{Moles of } O_2 \times \text{Molar Mass of } O_2 = 0.006920 \text{ mol} \times 32.00 \text{ g/mol} \approx 0.2214 \text{ g} \][/tex]
#### (c) [tex]\( 1.25 \)[/tex] L of [tex]\( SF_6 \)[/tex]
1. Volume is already in liters:
[tex]\[ \text{Volume of } SF_6 = 1.25 \text{ L} \][/tex]
2. Calculate the moles of [tex]\( SF_6 \)[/tex]:
[tex]\[ \text{Moles of } SF_6 = \frac{\text{Volume of } SF_6}{\text{Molar Volume}} = \frac{1.25 \text{ L}}{22.4 \text{ L/mol}} \approx 0.055804 \text{ mol} \][/tex]
3. Calculate the mass of [tex]\( SF_6 \)[/tex]:
Given molar mass of [tex]\( SF_6 \)[/tex] is [tex]\( 146.06 \)[/tex] g/mol,
[tex]\[ \text{Mass of } SF_6 = \text{Moles of } SF_6 \times \text{Molar Mass of } SF_6 = 0.055804 \text{ mol} \times 146.06 \text{ g/mol} \approx 8.1507 \text{ g} \][/tex]
### Summary:
- Mass of [tex]\( 178 \)[/tex] mL [tex]\( CO_2 \)[/tex] is approximately 0.3497 g.
- Mass of [tex]\( 155 \)[/tex] mL [tex]\( O_2 \)[/tex] is approximately 0.2214 g.
- Mass of [tex]\( 1.25 \)[/tex] L [tex]\( SF_6 \)[/tex] is approximately 8.1507 g.
Each value is a rounded result from the calculations, providing the mass of the gas samples at Standard Temperature and Pressure.
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