Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To solve this problem, we will systematically explore the properties of each flask to determine which statement is true:
### Data Given:
- Flask Volume (both flasks): 2.0 L
- Temperature (both flasks): 298 K
- Mass of O2 in Flask A: 16.00 grams
- Mass of N2 in Flask B: 28.0 grams
### Molecular Weights:
- Molar Mass of O2: 32.00 g/mol
- Molar Mass of N2: 28.02 g/mol
### Calculations:
1. Number of Moles:
For Flask A (O2):
[tex]\[ \text{Moles of O2} = \frac{\text{mass}}{\text{molar mass}} = \frac{16.00 \text{ g}}{32.00 \text{ g/mol}} = 0.5 \text{ mol} \][/tex]
For Flask B (N2):
[tex]\[ \text{Moles of N2} = \frac{\text{mass}}{\text{molar mass}} = \frac{28.0 \text{ g}}{28.02 \text{ g/mol}} \approx 1.0 \text{ mol} \][/tex]
2. Using the Ideal Gas Law (PV = nRT):
Where R (gas constant) = 0.0821 L·atm/(mol·K)
For Flask A:
[tex]\[ P_A = \frac{n \cdot R \cdot T}{V} = \frac{0.5 \cdot 0.0821 \cdot 298}{2.0} \approx 6.12 \text{ atm} \][/tex]
For Flask B:
[tex]\[ P_B = \frac{n \cdot R \cdot T}{V} = \frac{1.0 \cdot 0.0821 \cdot 298}{2.0} \approx 12.22 \text{ atm} \][/tex]
3. Density:
Density is calculated as:
[tex]\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \][/tex]
For Flask A:
[tex]\[ \text{Density}_A = \frac{16.00 \text{ g}}{2.0 \text{ L}} = 8.0 \text{ g/L} \][/tex]
For Flask B:
[tex]\[ \text{Density}_B = \frac{28.0 \text{ g}}{2.0 \text{ L}} = 14.0 \text{ g/L} \][/tex]
4. Number of Molecules:
Using Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol):
For Flask A:
[tex]\[ \text{Number of molecules in Flask A} = 0.5 \text{ mol} \times 6.022 \times 10^{23} \approx 3.011 \times 10^{23} \text{ molecules} \][/tex]
For Flask B:
[tex]\[ \text{Number of molecules in Flask B} = 1.0 \text{ mol} \times 6.022 \times 10^{23} \approx 6.0177 \times 10^{23} \text{ molecules} \][/tex]
### Comparison of Statements:
- Statement a: Flask A contains molecules with higher average kinetic energy than Flask B.
- This is false because the average kinetic energy of gas molecules depends on temperature, which is the same for both flasks.
- Statement b: Flask A has a higher density than Flask B.
- This is false because the density of Flask A (8.0 g/L) is less than the density of Flask B (14.0 g/L).
- Statement c: Flask A contains fewer molecules than Flask B.
- This is true because Flask A contains approximately [tex]\(3.011 \times 10^{23}\)[/tex] molecules, which is less than the approximately [tex]\(6.0177 \times 10^{23}\)[/tex] molecules in Flask B.
- Statement d: Flask A has a higher pressure than Flask B.
- This is false because the pressure in Flask A (6.12 atm) is less than the pressure in Flask B (12.22 atm).
### Conclusion:
The correct statement is:
c. Flask A contains fewer molecules than Flask B.
### Data Given:
- Flask Volume (both flasks): 2.0 L
- Temperature (both flasks): 298 K
- Mass of O2 in Flask A: 16.00 grams
- Mass of N2 in Flask B: 28.0 grams
### Molecular Weights:
- Molar Mass of O2: 32.00 g/mol
- Molar Mass of N2: 28.02 g/mol
### Calculations:
1. Number of Moles:
For Flask A (O2):
[tex]\[ \text{Moles of O2} = \frac{\text{mass}}{\text{molar mass}} = \frac{16.00 \text{ g}}{32.00 \text{ g/mol}} = 0.5 \text{ mol} \][/tex]
For Flask B (N2):
[tex]\[ \text{Moles of N2} = \frac{\text{mass}}{\text{molar mass}} = \frac{28.0 \text{ g}}{28.02 \text{ g/mol}} \approx 1.0 \text{ mol} \][/tex]
2. Using the Ideal Gas Law (PV = nRT):
Where R (gas constant) = 0.0821 L·atm/(mol·K)
For Flask A:
[tex]\[ P_A = \frac{n \cdot R \cdot T}{V} = \frac{0.5 \cdot 0.0821 \cdot 298}{2.0} \approx 6.12 \text{ atm} \][/tex]
For Flask B:
[tex]\[ P_B = \frac{n \cdot R \cdot T}{V} = \frac{1.0 \cdot 0.0821 \cdot 298}{2.0} \approx 12.22 \text{ atm} \][/tex]
3. Density:
Density is calculated as:
[tex]\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \][/tex]
For Flask A:
[tex]\[ \text{Density}_A = \frac{16.00 \text{ g}}{2.0 \text{ L}} = 8.0 \text{ g/L} \][/tex]
For Flask B:
[tex]\[ \text{Density}_B = \frac{28.0 \text{ g}}{2.0 \text{ L}} = 14.0 \text{ g/L} \][/tex]
4. Number of Molecules:
Using Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol):
For Flask A:
[tex]\[ \text{Number of molecules in Flask A} = 0.5 \text{ mol} \times 6.022 \times 10^{23} \approx 3.011 \times 10^{23} \text{ molecules} \][/tex]
For Flask B:
[tex]\[ \text{Number of molecules in Flask B} = 1.0 \text{ mol} \times 6.022 \times 10^{23} \approx 6.0177 \times 10^{23} \text{ molecules} \][/tex]
### Comparison of Statements:
- Statement a: Flask A contains molecules with higher average kinetic energy than Flask B.
- This is false because the average kinetic energy of gas molecules depends on temperature, which is the same for both flasks.
- Statement b: Flask A has a higher density than Flask B.
- This is false because the density of Flask A (8.0 g/L) is less than the density of Flask B (14.0 g/L).
- Statement c: Flask A contains fewer molecules than Flask B.
- This is true because Flask A contains approximately [tex]\(3.011 \times 10^{23}\)[/tex] molecules, which is less than the approximately [tex]\(6.0177 \times 10^{23}\)[/tex] molecules in Flask B.
- Statement d: Flask A has a higher pressure than Flask B.
- This is false because the pressure in Flask A (6.12 atm) is less than the pressure in Flask B (12.22 atm).
### Conclusion:
The correct statement is:
c. Flask A contains fewer molecules than Flask B.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
