Discover a world of knowledge and community-driven answers at IDNLearn.com today. Our community provides timely and precise responses to help you understand and solve any issue you face.
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.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.
